# bibtab

bibtype: article
filename: elefunt.bib
label: Iacono:2021:BEF
author: Roberto Iacono
title: Bounding the Error Function
journal: j-COMPUT-SCI-ENG
volume: 23
number: 4
pages: 65--68
year: 2021
CODEN: CSENFA
DOI: https://doi.org/10.1109/MCSE.2021.3083778
ISSN: 1521-9615 (print), 1558-366X (electronic) OR 15219615 (print), 1558366X (electronic)
ISSNL: 1521-9615 OR 15219615
bibdate: Thu Jul 29 07:00:57 2021
bibtimestamp: 2021.07.29 07:00:57 ???
fjournal: Computing in Science and Engineering
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992
rawauthor: Roberto Iacono
rawtitle: Bounding the Error Function
bibsource:
https://www.math.utah.edu/pub/tex/bib/computscieng.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
Prompted by previous work published in this magazine, in this article we focus on the derivation of global analytical bounds for the error function of a real argument. Using an integral representation of this function, we obtain two simple and accurate lower bounds, which complement a well-known upper bound given long ago by Polya.

rawabstract:
Prompted by previous work published in this magazine, in this article we focus on the derivation of global analytical bounds for the error function of a real argument. Using an integral representation of this function, we obtain two simple and accurate lower bounds, which complement a well-known upper bound given long ago by P{\'o}lya.

entry:
@Article{Iacono:2021:BEF,
  author =       "Roberto Iacono",
  title =        "Bounding the Error Function",
  journal =      j-COMPUT-SCI-ENG,
  volume =       "23",
  number =       "4",
  pages =        "65--68",
  year =         "2021",
  CODEN =        "CSENFA",
  DOI =          "https://doi.org/10.1109/MCSE.2021.3083778",
  ISSN =         "1521-9615 (print), 1558-366X (electronic)",
  ISSN-L =       "1521-9615",
  bibdate =      "Thu Jul 29 07:00:57 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computscieng.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Prompted by previous work published in this magazine,
                 in this article we focus on the derivation of global
                 analytical bounds for the error function of a real
                 argument. Using an integral representation of this
                 function, we obtain two simple and accurate lower
                 bounds, which complement a well-known upper bound given
                 long ago by P{\'o}lya.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing in Science and Engineering",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
}


bibtype: article
filename: elefunt.bib
label: Johansson:2021:APC
author: Fredrik Johansson
title: Arbitrary-Precision Computation of the Gamma Function
journal: arXiv.org
pages: 1--51
day: 17
month: sep
monthnumber: 9
year: 2021
DOI: https://doi.org/10.48550/arXiv.2109.0839
bibdate: Sun Dec 04 11:01:23 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2022.12.04 11:01:23 ???
URL: https://arxiv.org/abs/2109.08392
acknowledgement: ack-nhfb
rawauthor: Fredrik Johansson
rawtitle: Arbitrary-Precision Computation of the Gamma Function
abstract:
We discuss the best methods available for computing the gamma function $ Gamma (z) $ in arbitrary-precision arithmetic with rigorous error bounds. We address different cases: rational, algebraic, real or complex arguments; large or small arguments; low or high precision; with or without precomputation. The methods also cover the log-gamma function $ log Gamma (z) $, the digamma function $ psi (z) $, and derivatives $ Gamma ^(n)(z) $ and $ psi ^(n)(z) $. Besides attempting to summarize the existing state of the art, we present some new formulas, estimates, bounds and algorithmic improvements and discuss implementation results.

rawabstract:
We discuss the best methods available for computing the gamma function $ \Gamma (z) $ in arbitrary-precision arithmetic with rigorous error bounds. We address different cases: rational, algebraic, real or complex arguments; large or small arguments; low or high precision; with or without precomputation. The methods also cover the log-gamma function $ \log \Gamma (z) $, the digamma function $ \psi (z) $, and derivatives $ \Gamma^{(n)}(z) $ and $ \psi^{(n)}(z) $. Besides attempting to summarize the existing state of the art, we present some new formulas, estimates, bounds and algorithmic improvements and discuss implementation results.

entry:
@Article{Johansson:2021:APC,
  author =       "Fredrik Johansson",
  title =        "Arbitrary-Precision Computation of the Gamma
                 Function",
  journal =      "arXiv.org",
  pages =        "1--51",
  day =          "17",
  month =        sep,
  year =         "2021",
  DOI =          "https://doi.org/10.48550/arXiv.2109.0839",
  bibdate =      "Sun Dec 04 11:01:23 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://arxiv.org/abs/2109.08392",
  abstract =     "We discuss the best methods available for computing
                 the gamma function $ \Gamma (z) $ in
                 arbitrary-precision arithmetic with rigorous error
                 bounds. We address different cases: rational,
                 algebraic, real or complex arguments; large or small
                 arguments; low or high precision; with or without
                 precomputation. The methods also cover the log-gamma
                 function $ \log \Gamma (z) $, the digamma function $
                 \psi (z) $, and derivatives $ \Gamma^{(n)}(z) $ and $
                 \psi^{(n)}(z) $. Besides attempting to summarize the
                 existing state of the art, we present some new
                 formulas, estimates, bounds and algorithmic
                 improvements and discuss implementation results.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Kang:2021:NEE
author: Hongchao Kang and Hong Wang
journal: j-APPL-NUM-MATH
volume: 160
pages: 23--41
month: feb
monthnumber: 2
year: 2021
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
bibdate: Tue Dec 29 07:52:55 MST 2020
bibtimestamp: 2020.12.29 07:52:55 MST
URL: http://www.sciencedirect.com/science/article/pii/S0168927420302932
fjournal: Applied Numerical Mathematics: Transactions of IMACS
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274
rawauthor: Hongchao Kang and Hong Wang
title:
Numerical evaluation and error analysis of many different oscillatory Bessel transforms via confluent hypergeometric function

rawtitle:
Numerical evaluation and error analysis of many different oscillatory {Bessel} transforms via confluent hypergeometric function

entry:
@Article{Kang:2021:NEE,
  author =       "Hongchao Kang and Hong Wang",
  title =        "Numerical evaluation and error analysis of many
                 different oscillatory {Bessel} transforms via confluent
                 hypergeometric function",
  journal =      j-APPL-NUM-MATH,
  volume =       "160",
  number =       "??",
  pages =        "23--41",
  month =        feb,
  year =         "2021",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Tue Dec 29 07:52:55 MST 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0168927420302932",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274",
}


bibtype: article
filename: elefunt.bib
label: Langdon:2021:GID
author: William B. Langdon and Oliver Krauss
title: Genetic Improvement of Data for Maths Functions
journal: j-TELO
volume: 1
number: 2
pages: 7:1--7:30
month: jun
monthnumber: 6
year: 2021
DOI: https://doi.org/10.1145/3461016
ISSN: 2688-299X (print), 2688-3007 (electronic) OR 2688299X (print), 26883007 (electronic)
ISSNL: 2688-299X OR 2688299X
bibdate: Sat Aug 21 15:11:10 MDT 2021
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/telo.bib
bibtimestamp: 2021.08.21 15:11:10 MDT
URL: https://dl.acm.org/doi/10.1145/3461016
fjournal: ACM Transactions on Evolutionary Learning and Optimization
acknowledgement: ack-nhfb
articleno: 7
journalURL: https://dl.acm.org/loi/telo
rawauthor: William B. Langdon and Oliver Krauss
rawtitle: Genetic Improvement of Data for Maths Functions
abstract:
We use continuous optimisation and manual code changes to evolve up to 1024 Newton--Raphson numerical values embedded in an open source GNU C library glibc square root sqrt to implement a double precision cube root routine cbrt, binary logarithm log2 and reciprocal square root function for C in seconds. The GI inverted square root $ x-1 / 2 $ is far more accurate than Quake's InvSqrt, Quare root. GI shows potential for automatically creating mobile or low resource mote smart dust bespoke custom mathematical libraries with new functionality.

rawabstract:
We use continuous optimisation and manual code changes to evolve up to 1024 Newton--Raphson numerical values embedded in an open source GNU C library glibc square root sqrt to implement a double precision cube root routine cbrt, binary logarithm log2 and reciprocal square root function for C in seconds. The GI inverted square root $ x{-1 / 2} $ is far more accurate than Quake's InvSqrt, Quare root. GI shows potential for automatically creating mobile or low resource mote smart dust bespoke custom mathematical libraries with new functionality.

entry:
@Article{Langdon:2021:GID,
  author =       "William B. Langdon and Oliver Krauss",
  title =        "Genetic Improvement of Data for Maths Functions",
  journal =      j-TELO,
  volume =       "1",
  number =       "2",
  pages =        "7:1--7:30",
  month =        jun,
  year =         "2021",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3461016",
  ISSN =         "2688-299X (print), 2688-3007 (electronic)",
  ISSN-L =       "2688-299X",
  bibdate =      "Sat Aug 21 15:11:10 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/telo.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3461016",
  abstract =     "We use continuous optimisation and manual code changes
                 to evolve up to 1024 Newton--Raphson numerical values
                 embedded in an open source GNU C library glibc square
                 root sqrt to implement a double precision cube root
                 routine cbrt, binary logarithm log2 and reciprocal
                 square root function for C in seconds. The GI inverted
                 square root $ x{-1 / 2} $ is far more accurate than
                 Quake's InvSqrt, Quare root. GI shows potential for
                 automatically creating mobile or low resource mote
                 smart dust bespoke custom mathematical libraries with
                 new functionality.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Evolutionary Learning and
                 Optimization",
  journal-URL =  "https://dl.acm.org/loi/telo",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lim:2021:HPC
author: Jay P. Lim and Santosh Nagarakatte
title: High performance correctly rounded math libraries for 32-bit floating point representations
publisher: pub-ACM
address: pub-ACM:adr
pages: 7:1--7:30
month: jun
monthnumber: 6
year: 2021
DOI: https://doi.org/10.1145/3453483.3454049
bibdate: Tue Sep 24 15:06:44 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.09.24 15:06:44 ???
URL: https://github.com/rutgers-apl/rlibm-32
keywords: binary32; correctly rounded functions; posit32
acknowledgement: ack-nhfb
rawauthor: Jay P. Lim and Santosh Nagarakatte
rawtitle: High performance correctly rounded math libraries for 32-bit floating point representations
booktitle:
Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation

abstract:
This paper proposes a set of techniques to develop correctly rounded math libraries for 32-bit float and posit types. It enhances our RLIBM approach that frames the problem of generating correctly rounded libraries as a linear programming problem in the context of 16-bit types to scale to 32-bit types. Specifically, this paper proposes new algorithms to (1) generate polynomials that produce correctly rounded outputs for all inputs using counterexample guided polynomial generation, (2) generate efficient piecewise polynomials with bit-pattern based domain splitting, and (3) deduce the amount of freedom available to produce correct results when range reduction involves multiple elementary functions. The resultant math library for the 32-bit float type is faster than state-of-the-art math libraries while producing the correct output for all inputs. We have also developed a set of correctly rounded elementary functions for 32-bit posits.

rawabstract:
This paper proposes a set of techniques to develop correctly rounded math libraries for 32-bit float and posit types. It enhances our RLIBM approach that frames the problem of generating correctly rounded libraries as a linear programming problem in the context of 16-bit types to scale to 32-bit types. Specifically, this paper proposes new algorithms to (1) generate polynomials that produce correctly rounded outputs for all inputs using counterexample guided polynomial generation, (2) generate efficient piecewise polynomials with bit-pattern based domain splitting, and (3) deduce the amount of freedom available to produce correct results when range reduction involves multiple elementary functions. The resultant math library for the 32-bit float type is faster than state-of-the-art math libraries while producing the correct output for all inputs. We have also developed a set of correctly rounded elementary functions for 32-bit posits.

rawbooktitle:
Proceedings of the {42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation}

entry:
@InProceedings{Lim:2021:HPC,
  author =       "Jay P. Lim and Santosh Nagarakatte",
  booktitle =    "Proceedings of the {42nd ACM SIGPLAN International
                 Conference on Programming Language Design and
                 Implementation}",
  title =        "High performance correctly rounded math libraries for
                 32-bit floating point representations",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  month =        jun,
  year =         "2021",
  DOI =          "https://doi.org/10.1145/3453483.3454049",
  bibdate =      "Tue Sep 24 15:06:44 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://github.com/rutgers-apl/rlibm-32",
  abstract =     "This paper proposes a set of techniques to develop
                 correctly rounded math libraries for 32-bit float and
                 posit types. It enhances our RLIBM approach that frames
                 the problem of generating correctly rounded libraries
                 as a linear programming problem in the context of
                 16-bit types to scale to 32-bit types. Specifically,
                 this paper proposes new algorithms to (1) generate
                 polynomials that produce correctly rounded outputs for
                 all inputs using counterexample guided polynomial
                 generation, (2) generate efficient piecewise
                 polynomials with bit-pattern based domain splitting,
                 and (3) deduce the amount of freedom available to
                 produce correct results when range reduction involves
                 multiple elementary functions. The resultant math
                 library for the 32-bit float type is faster than
                 state-of-the-art math libraries while producing the
                 correct output for all inputs. We have also developed a
                 set of correctly rounded elementary functions for
                 32-bit posits.",
  acknowledgement = ack-nhfb,
  description =  "RLIBM-32 is both a math library that provides
                 correctly rounded result for all inputs and tools used
                 to generate the correct polynomials. The techniques
                 behind the tools will be appearing at PLDI 2021.
                 Currently, RLIBM-32 supports a number of elementary
                 functions for float and posit32
                 representations.\par

                 List of float functions supported by
                 RLIBM-32:\par

                 log(x), log2(x), log10(x) \\
                 exp(x), exp2(x), exp10(x) \\
                 sinh(x), cosh(x) \\
                 sinpi(x), cospi(x)\par

                 List of posit32 functions supported by
                 RLIBM-32:\par

                 log(x), log2(x), log10(x) \\
                 exp(x), exp2(x), exp10(x) \\
                 sinh(x), cosh(x)",
  keywords =     "binary32; correctly rounded functions; posit32",
  remark-1 =     "From page 360: ``Our RLibm approach [31, 32] generates
                 polynomials that approximate the correctly rounded
                 result rather than the real value of the elementary
                 function. \ldots{} Using the RLibm approach, we have
                 been successful in generating correctly rounded
                 libraries with 16-bit types such as bfloat16 and
                 posit16.''",
  remark-2 =     "From page 360: ``A naive use of the RLibm approach
                 with 32-bit types will generate more than a billion
                 constraints, which is beyond the capabilities of
                 current LP solvers.''",
  remark-3 =     "From page 361: ``Our elementary functions for floats
                 are faster than existing libraries: Intel's libm,
                 Glibc's libm, CR-LIBM [13], and Metalibm [25]. Unlike
                 existing libraries, our functions produce correctly
                 rounded results for all inputs. We have developed the
                 first correctly rounded implementations of functions
                 for 32-bit posits.''",
  remark-4 =     "From page 363: ``All internal computation such as
                 range reduction, polynomial evaluation, and output
                 compensation is performed in representation H where H
                 has higher precision than T. To attain good
                 performance, H is a representation that is supported in
                 hardware (e.g., double).''",
  remark-5 =     "From page 368: ``CR-LIBM has correctly rounded
                 functions for double precision. However, CR-LIBM does
                 not produce correctly rounded results for 32-bit floats
                 due to double rounding. There are no math libraries
                 available for posit32. All posit32 values can be
                 exactly represented in double.''",
  remark-6 =     "From page 370: ``All three re-purposed math libraries
                 produce wrong results for some inputs. RLibm-32
                 provides the first correctly rounded functions for the
                 posit32 type.''",
  remark-7 =     "From page 372: ``This paper extends our prior work on
                 RLibm [31, 32] and John Gustafson's Minefield method
                 [20], which advocate approximating the correctly
                 rounded value rather than real value of an elementary
                 function.''",
  remark-8 =     "From page 372: ``We have used RLibm to create
                 correctly rounded functions for 16-bit types: bfloat16
                 and posit16.''",
}


bibtype: article
filename: elefunt.bib
label: Lipovetsky:2021:BRI
author: Stan Lipovetsky
journal: j-TECHNOMETRICS
volume: 62
number: 4
pages: 560--560
year: 2021
CODEN: TCMTA2
DOI: https://doi.org/10.1080/00401706.2020.1825632
ISSN: 0040-1706 (print), 1537-2723 (electronic) OR 00401706 (print), 15372723 (electronic)
ISSNL: 0040-1706 OR 00401706
bibdate: Fri Feb 5 17:42:52 MST 2021
bibtimestamp: 2021.02.05 17:42:52 MST
fjournal: Technometrics
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/utch20
onlinedate: 23 Oct 2020
rawauthor: Stan Lipovetsky
title:
Book Review: booktitle Integrals Related to the Error Function, by Nikolai E. Korotkov and Alexander N. Korotkov. Boca Raton, FL: Chapman and Hall / CRC Press, Taylor & Francis Group, 2020, 228 pp., $140.00 (hardback), $46.36 (eBook), ISBN: 978-0-367-40820-6 (hardback)

bibsource:
http://www.tandf.co.uk/journals/titles/00401706.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/technometrics2020.bib

rawtitle:
Book Review: {{\booktitle{Integrals Related to the Error Function}}, by Nikolai E. Korotkov and Alexander N. Korotkov. Boca Raton, FL: Chapman and Hall\slash CRC Press, Taylor \& Francis Group, 2020, 228 pp., \$140.00 (hardback), \$46.36 (eBook), ISBN: 978-0-367-40820-6 (hardback)}

entry:
@Article{Lipovetsky:2021:BRI,
  author =       "Stan Lipovetsky",
  title =        "Book Review: {{\booktitle{Integrals Related to the
                 Error Function}}, by Nikolai E. Korotkov and Alexander
                 N. Korotkov. Boca Raton, FL: Chapman and Hall\slash CRC
                 Press, Taylor \& Francis Group, 2020, 228 pp., \$140.00
                 (hardback), \$46.36 (eBook), ISBN: 978-0-367-40820-6
                 (hardback)}",
  journal =      j-TECHNOMETRICS,
  volume =       "62",
  number =       "4",
  pages =        "560--560",
  year =         "2021",
  CODEN =        "TCMTA2",
  DOI =          "https://doi.org/10.1080/00401706.2020.1825632",
  ISSN =         "0040-1706 (print), 1537-2723 (electronic)",
  ISSN-L =       "0040-1706",
  bibdate =      "Fri Feb 5 17:42:52 MST 2021",
  bibsource =    "http://www.tandf.co.uk/journals/titles/00401706.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/technometrics2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Technometrics",
  journal-URL =  "http://www.tandfonline.com/loi/utch20",
  onlinedate =   "23 Oct 2020",
}


bibtype: techreport
filename: elefunt.bib
label: MPFR:2021:MLA
author: The MPFR Team
title: The MPFR Library: Algorithms and Proofs
type: Report
pages: 69
day: 5
month: nov
monthnumber: 11
year: 2021
bibdate: Tue Mar 14 13:13:13 2023
bibtimestamp: 2023.03.14 13:13:13 ???
URL: https://www.mpfr.org/algorithms.pdf
acknowledgement: ack-nhfb
rawauthor: {The MPFR Team}
rawtitle: The {MPFR} Library: Algorithms and Proofs
entry:
@TechReport{MPFR:2021:MLA,
  author =       "{The MPFR Team}",
  title =        "The {MPFR} Library: Algorithms and Proofs",
  type =         "Report",
  institution =  "????",
  address =      "????",
  pages =        "69",
  day =          "5",
  month =        nov,
  year =         "2021",
  bibdate =      "Tue Mar 14 13:13:13 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.mpfr.org/algorithms.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Patankar:2021:RBC
author: Udayan S. Patankar and Ants Koel
title: Review of Basic Classes of Dividers Based on Division Algorithm
journal: j-IEEE-ACCESS
volume: 9
pages: 23035--23069
year: 2021
DOI: https://doi.org/10.1109/access.2021.3055735
ISSN: 2169-3536 OR 21693536
ISSNL: 2169-3536 OR 21693536
bibdate: Thu Apr 10 15:08:12 2025
bibtimestamp: 2025.04.10 15:08:12 ???
fjournal: IEEE Access
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639
rawauthor: Udayan S. Patankar and Ants Koel
rawtitle: Review of Basic Classes of Dividers Based on Division Algorithm
entry:
@Article{Patankar:2021:RBC,
  author =       "Udayan S. Patankar and Ants Koel",
  title =        "Review of Basic Classes of Dividers Based on Division
                 Algorithm",
  journal =      j-IEEE-ACCESS,
  volume =       "9",
  pages =        "23035--23069",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/access.2021.3055735",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Thu Apr 10 15:08:12 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
}


bibtype: article
filename: elefunt.bib
label: Snyder:2021:CRA
author: W. Van Snyder
title: Corrigendum: Remark on Algorithm 723: Fresnel Integrals
journal: j-TOMS
volume: 47
number: 4
pages: 37:1--37:1
month: dec
monthnumber: 12
year: 2021
CODEN: ACMSCU
DOI: https://doi.org/10.1145/3452336
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Sep 29 06:58:41 MDT 2021
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 2021.09.29 06:58:41 MDT
note: See cite Snyder:1993:AFI.
URL: https://dl.acm.org/doi/10.1145/3452336
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
articleno: 37
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. Van Snyder
rawnote: See \cite{Snyder:1993:AFI}.
rawtitle: Corrigendum: {Remark on Algorithm 723: Fresnel Integrals}
abstract:
There are mistakes and typographical errors in Remark on Algorithm 723: Fresnel Integrals, which appeared in ACM Transactions on Mathematical Software 22, 4 (December 1996). This remark corrects those errors. The software provided to Collected Algorithms of the ACM was correct.

rawabstract:
There are mistakes and typographical errors in Remark on Algorithm 723: Fresnel Integrals, which appeared in ACM Transactions on Mathematical Software 22, 4 (December 1996). This remark corrects those errors. The software provided to Collected Algorithms of the ACM was correct.

entry:
@Article{Snyder:2021:CRA,
  author =       "W. Van Snyder",
  title =        "Corrigendum: {Remark on Algorithm 723: Fresnel
                 Integrals}",
  journal =      j-TOMS,
  volume =       "47",
  number =       "4",
  pages =        "37:1--37:1",
  month =        dec,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3452336",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 29 06:58:41 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Snyder:1993:AFI}.",
  URL =          "https://dl.acm.org/doi/10.1145/3452336",
  abstract =     "There are mistakes and typographical errors in Remark
                 on Algorithm 723: Fresnel Integrals, which appeared in
                 ACM Transactions on Mathematical Software 22, 4
                 (December 1996). This remark corrects those errors. The
                 software provided to Collected Algorithms of the ACM
                 was correct.",
  acknowledgement = ack-nhfb,
  articleno =    "37",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Walczyk:2021:IAF
author: Cezary J. Walczyk and Leonid V. Moroz and Jan L. Cieslinski
title: Improving the Accuracy of the Fast Inverse Square Root by Modifying Newton--Raphson Corrections
journal: j-ENTROPY
volume: 23
number: 1
pages: 86:1--86:20
month: jan
monthnumber: 1
year: 2021
CODEN: ENTRFG
DOI: https://doi.org/10.3390/e23010086
ISSN: 1099-4300 OR 10994300
ISSNL: 1099-4300 OR 10994300
bibdate: Wed Dec 20 07:52:39 2023
bibtimestamp: 2023.12.20 07:52:39 ???
fjournal: Entropy
acknowledgement: ack-nhfb
journalURL: https://www.mdpi.com/journal/entropy/
rawauthor: Cezary J. Walczyk and Leonid V. Moroz and Jan L. Cie{\'s}li{\'n}ski
rawtitle: Improving the Accuracy of the Fast Inverse Square Root by Modifying {Newton--Raphson} Corrections
entry:
@Article{Walczyk:2021:IAF,
  author =       "Cezary J. Walczyk and Leonid V. Moroz and Jan L.
                 Cie{\'s}li{\'n}ski",
  title =        "Improving the Accuracy of the Fast Inverse Square Root
                 by Modifying {Newton--Raphson} Corrections",
  journal =      j-ENTROPY,
  volume =       "23",
  number =       "1",
  pages =        "86:1--86:20",
  month =        jan,
  year =         "2021",
  CODEN =        "ENTRFG",
  DOI =          "https://doi.org/10.3390/e23010086",
  ISSN =         "1099-4300",
  ISSN-L =       "1099-4300",
  bibdate =      "Wed Dec 20 07:52:39 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Entropy",
  journal-URL =  "https://www.mdpi.com/journal/entropy/",
}


bibtype: misc
filename: elefunt.bib
label: Anonymous:2022:DLM
author: Anonymous
title: Digital Library of Mathematical Functions: Date: 2010
pages: 86:1--86:20
day: 14
month: mar
monthnumber: 3
year: 2022
bibdate: Wed Oct 25 18:20:12 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.25 18:20:12 ???
acknowledgement: ack-nhfb
howpublished: NIST Web site
rawauthor: Anonymous
rawtitle: Digital Library of Mathematical Functions: Date: 2010
URL:
https://dlmf.nist.gov/; https://www.nist.gov/mathematics-statistics/digital-library-mathematical-functions

abstract:
In 2010, NIST released the Digital Library of Mathematical Functions (DLMF), an online successor to the classic Abramowitz and Stegun booktitle Handbook of Mathematical Functions. [cite Abramowitz:1964:HMF]

remark:
From the site: ``By the late 1990s it [the 1964 Handbook] was still the most widely distributed and cited publication of all time, regularly seeing more than 2000 citations per year.''

rawabstract:
In 2010, NIST released the Digital Library of Mathematical Functions (DLMF), an online successor to the classic Abramowitz and Stegun \booktitle{Handbook of Mathematical Functions}. [\cite{Abramowitz:1964:HMF}]

entry:
@Misc{Anonymous:2022:DLM,
  author =       "Anonymous",
  title =        "Digital Library of Mathematical Functions: Date:
                 2010",
  howpublished = "NIST Web site",
  day =          "14",
  month =        mar,
  year =         "2022",
  bibdate =      "Wed Oct 25 18:20:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://dlmf.nist.gov/;
                 https://www.nist.gov/mathematics-statistics/digital-library-mathematical-functions",
  abstract =     "In 2010, NIST released the Digital Library of
                 Mathematical Functions (DLMF), an online successor to
                 the classic Abramowitz and Stegun \booktitle{Handbook
                 of Mathematical Functions}.
                 [\cite{Abramowitz:1964:HMF}]",
  acknowledgement = ack-nhfb,
  remark =       "From the site: ``By the late 1990s it [the 1964
                 Handbook] was still the most widely distributed and
                 cited publication of all time, regularly seeing more
                 than 2000 citations per year.''",
}


bibtype: inproceedings
filename: elefunt.bib
label: Borges:2022:HLA
author: Carlos F. Borges and Claude-Pierre Jeannerod and Jean-Michel Muller
title: High-level algorithms for correctly-rounded reciprocal square roots
crossref: IEEE:2022:ISC
pages: 18--25
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00013
bibdate: Thu Sep 21 10:14:25 2023
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Carlos F. Borges and Claude-Pierre Jeannerod and Jean-Michel Muller
rawtitle: High-level algorithms for correctly-rounded reciprocal square roots
entry:
@InProceedings{Borges:2022:HLA,
  author =       "Carlos F. Borges and Claude-Pierre Jeannerod and
                 Jean-Michel Muller",
  title =        "High-level algorithms for correctly-rounded reciprocal
                 square roots",
  crossref =     "IEEE:2022:ISC",
  pages =        "18--25",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00013",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: inproceedings
filename: elefunt.bib
label: Bruguera:2022:LLH
author: Javier D. Bruguera
title: Low-Latency and High-Bandwidth Pipelined Radix-64 Division and Square Root Unit
crossref: IEEE:2022:ISC
pages: 10--17
year: 2022
DOI: https://doi.org/10.1109/ARITH54963.2022.00012
bibdate: Thu Sep 21 10:14:25 2023
bibtimestamp: 2023.09.21 10:14:25 ???
keywords: ARITH-29
acknowledgement: ack-nhfb
rawauthor: Javier D. Bruguera
rawtitle: Low-Latency and High-Bandwidth Pipelined Radix-64 Division and Square Root Unit
entry:
@InProceedings{Bruguera:2022:LLH,
  author =       "Javier D. Bruguera",
  title =        "Low-Latency and High-Bandwidth Pipelined Radix-64
                 Division and Square Root Unit",
  crossref =     "IEEE:2022:ISC",
  pages =        "10--17",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00012",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}


bibtype: article
filename: elefunt.bib
label: Causley:2022:GFI
author: Matthew F. Causley
title: The gamma function via interpolation
journal: j-NUMER-ALGORITHMS
volume: 90
number: 2
pages: 687--707
month: jun
monthnumber: 6
year: 2022
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-021-01204-8
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Sun May 8 06:36:19 MDT 2022
bibtimestamp: 2022.05.08 06:36:19 MDT
URL: https://link.springer.com/article/10.1007/s11075-021-01204-8
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
ajournal: Numer. Algorithms
journalURL: http://link.springer.com/journal/11075
rawauthor: Matthew F. Causley
rawtitle: The gamma function via interpolation
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib

entry:
@Article{Causley:2022:GFI,
  author =       "Matthew F. Causley",
  title =        "The gamma function via interpolation",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "90",
  number =       "2",
  pages =        "687--707",
  month =        jun,
  year =         "2022",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-021-01204-8",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Sun May 8 06:36:19 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "https://link.springer.com/article/10.1007/s11075-021-01204-8",
  acknowledgement = ack-nhfb,
  ajournal =     "Numer. Algorithms",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}


bibtype: article
filename: elefunt.bib
label: Cojean:2022:GML
author: Terry Cojean and Yu-Hsiang Mike Tsai and Hartwig Anzt
title: Ginkgo --- a math library designed for platform portability
journal: j-PARALLEL-COMPUTING
volume: 111
pages: ??--??
month: jul
monthnumber: 7
year: 2022
CODEN: PACOEJ
DOI: https://doi.org/10.1016/j.parco.2022.102902
ISSN: 0167-8191 (print), 1872-7336 (electronic) OR 01678191 (print), 18727336 (electronic)
ISSNL: 0167-8191 OR 01678191
bibdate: Mon May 9 07:06:37 MDT 2022
bibtimestamp: 2022.05.09 07:06:37 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0167819122000096
fjournal: Parallel Computing
acknowledgement: ack-nhfb
articleno: 102902
journalURL: http://www.sciencedirect.com/science/journal/01678191
rawauthor: Terry Cojean and Yu-Hsiang Mike Tsai and Hartwig Anzt
rawtitle: {Ginkgo} --- a math library designed for platform portability
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib

abstract:
In an era of increasing computer system diversity, the portability of software from one system to another plays a central role. Software portability is important for the software developers as many software projects have a lifetime longer than a specific system, e.g., a supercomputer, and it is important for the domain scientists that realize their scientific application in a software framework and want to be able to run on one or another system. On a high level, there exist two approaches for realizing platform portability: (1) implementing software using a portability layer leveraging any technique which always generates specific kernels from another language or through an interface for running on different architectures; and (2) providing backends for different hardware architectures, with the backends typically differing in how and in which programming language functionality is realized due to using the language of choice for each hardware (e.g., CUDA kernels for NVIDIA GPUs, SYCL (DPC++) kernels to targeting Intel GPUs and other supported hardware, ldots ). In practice, these two approaches can be combined in applications to leverage their respective strengths. In this paper, we present how we realize portability across different hardware architectures for the Ginkgo library by following the second strategy and the goal to not only port to new hardware architectures but also achieve good performance. We present the Ginkgo library design, separating algorithms from hardware-specific kernels forming the distinct hardware executors, and report our experience when adding execution backends for NVIDIA, AMD, and Intel GPUs. We also present the performance we achieve with this approach for distinct hardware backends.

rawabstract:
In an era of increasing computer system diversity, the portability of software from one system to another plays a central role. Software portability is important for the software developers as many software projects have a lifetime longer than a specific system, e.g., a supercomputer, and it is important for the domain scientists that realize their scientific application in a software framework and want to be able to run on one or another system. On a high level, there exist two approaches for realizing platform portability: (1) implementing software using a portability layer leveraging any technique which always generates specific kernels from another language or through an interface for running on different architectures; and (2) providing backends for different hardware architectures, with the backends typically differing in how and in which programming language functionality is realized due to using the language of choice for each hardware (e.g., CUDA kernels for NVIDIA GPUs, SYCL (DPC++) kernels to targeting Intel GPUs and other supported hardware, \ldots). In practice, these two approaches can be combined in applications to leverage their respective strengths. In this paper, we present how we realize portability across different hardware architectures for the Ginkgo library by following the second strategy and the goal to not only port to new hardware architectures but also achieve good performance. We present the Ginkgo library design, separating algorithms from hardware-specific kernels forming the distinct hardware executors, and report our experience when adding execution backends for NVIDIA, AMD, and Intel GPUs. We also present the performance we achieve with this approach for distinct hardware backends.

entry:
@Article{Cojean:2022:GML,
  author =       "Terry Cojean and Yu-Hsiang Mike Tsai and Hartwig
                 Anzt",
  title =        "{Ginkgo} --- a math library designed for platform
                 portability",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "111",
  number =       "??",
  pages =        "??--??",
  month =        jul,
  year =         "2022",
  CODEN =        "PACOEJ",
  DOI =          "https://doi.org/10.1016/j.parco.2022.102902",
  ISSN =         "0167-8191 (print), 1872-7336 (electronic)",
  ISSN-L =       "0167-8191",
  bibdate =      "Mon May 9 07:06:37 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167819122000096",
  abstract =     "In an era of increasing computer system diversity, the
                 portability of software from one system to another
                 plays a central role. Software portability is important
                 for the software developers as many software projects
                 have a lifetime longer than a specific system, e.g., a
                 supercomputer, and it is important for the domain
                 scientists that realize their scientific application in
                 a software framework and want to be able to run on one
                 or another system. On a high level, there exist two
                 approaches for realizing platform portability: (1)
                 implementing software using a portability layer
                 leveraging any technique which always generates
                 specific kernels from another language or through an
                 interface for running on different architectures; and
                 (2) providing backends for different hardware
                 architectures, with the backends typically differing in
                 how and in which programming language functionality is
                 realized due to using the language of choice for each
                 hardware (e.g., CUDA kernels for NVIDIA GPUs, SYCL
                 (DPC++) kernels to targeting Intel GPUs and other
                 supported hardware, \ldots). In practice, these two
                 approaches can be combined in applications to leverage
                 their respective strengths. In this paper, we present
                 how we realize portability across different hardware
                 architectures for the Ginkgo library by following the
                 second strategy and the goal to not only port to new
                 hardware architectures but also achieve good
                 performance. We present the Ginkgo library design,
                 separating algorithms from hardware-specific kernels
                 forming the distinct hardware executors, and report our
                 experience when adding execution backends for NVIDIA,
                 AMD, and Intel GPUs. We also present the performance we
                 achieve with this approach for distinct hardware
                 backends.",
  acknowledgement = ack-nhfb,
  articleno =    "102902",
  fjournal =     "Parallel Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01678191",
}


bibtype: inproceedings
filename: elefunt.bib
label: Gao:2022:TFI
author: Zhanyuan Gao and Laiping Zhao and Haonan Chen
editor: IEEE
booktitle: 2022 IEEE / ACIS 22nd International Conference on Computer and Information Science (ICIS)
title: A Trigonometric Function Instruction Set Extension Method Based on RISC-V
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 119--126
year: 2022
DOI: https://doi.org/10.1109/ICIS54925.2022.9882453
bibdate: Sat Dec 16 15:51:40 2023
bibtimestamp: 2023.12.16 15:51:40 ???
acknowledgement: ack-nhfb
rawauthor: Zhanyuan Gao and Laiping Zhao and Haonan Chen
rawbooktitle: {2022 IEEE\slash ACIS 22nd International Conference on Computer and Information Science (ICIS)}
raweditor: {IEEE}
rawtitle: A Trigonometric Function Instruction Set Extension Method Based on {RISC-V}
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib

entry:
@InProceedings{Gao:2022:TFI,
  author =       "Zhanyuan Gao and Laiping Zhao and Haonan Chen",
  editor =       "{IEEE}",
  booktitle =    "{2022 IEEE\slash ACIS 22nd International Conference on
                 Computer and Information Science (ICIS)}",
  title =        "A Trigonometric Function Instruction Set Extension
                 Method Based on {RISC-V}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "119--126",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ICIS54925.2022.9882453",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Hao:2022:DVP
author: Jiangwei Hao and Jinchen Xu and YuanYuan Xia
title: Design of variable precision transcendental function automatic generator
journal: j-J-SUPERCOMPUTING
volume: 78
number: 2
pages: 2196--2218
month: feb
monthnumber: 2
year: 2022
CODEN: JOSUED
DOI: https://doi.org/10.1007/s11227-021-03937-8
ISSN: 0920-8542 (print), 1573-0484 (electronic) OR 09208542 (print), 15730484 (electronic)
ISSNL: 0920-8542 OR 09208542
bibdate: Mon Feb 28 16:44:34 MST 2022
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jsuper.bib
bibtimestamp: 2022.02.28 16:44:34 MST
URL: https://link.springer.com/article/10.1007/s11227-021-03937-8
fjournal: The Journal of Supercomputing
acknowledgement: ack-nhfb
ajournal: J. Supercomputing
journalURL: http://link.springer.com/journal/11227
rawauthor: Jiangwei Hao and Jinchen Xu and YuanYuan Xia
rawtitle: Design of variable precision transcendental function automatic generator
entry:
@Article{Hao:2022:DVP,
  author =       "Jiangwei Hao and Jinchen Xu and YuanYuan Xia",
  title =        "Design of variable precision transcendental function
                 automatic generator",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "78",
  number =       "2",
  pages =        "2196--2218",
  month =        feb,
  year =         "2022",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-021-03937-8",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Mon Feb 28 16:44:34 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
  URL =          "https://link.springer.com/article/10.1007/s11227-021-03937-8",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Supercomputing",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}


bibtype: article
filename: elefunt.bib
label: Howard:2022:AAA
author: Roy M. Howard
title: Arbitrarily Accurate Analytical Approximations for the Error Function
journal: j-MATH-COMPUT-APPL
volume: 27
number: 1
pages: 14:1--14:44
month: feb
monthnumber: 2
year: 2022
DOI: https://doi.org/10.3390/mca27010014
ISSN: 2297-8747 OR 22978747
ISSNL: 2297-8747 OR 22978747
bibdate: Sun Feb 18 06:28:42 MST 2024
bibtimestamp: 2024.02.18 06:28:42 MST
URL: https://www.mdpi.com/2297-8747/27/1/14
fjournal: Mathematical and Computational Applications
acknowledgement: ack-nhfb
ajournal: Math. Comput. Appl.
articleno: 14
journalURL: https://www.mdpi.com/journal/mca
rawauthor: Roy M. Howard
rawtitle: Arbitrarily Accurate Analytical Approximations for the Error Function
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/math-comput-appl.bib

entry:
@Article{Howard:2022:AAA,
  author =       "Roy M. Howard",
  title =        "Arbitrarily Accurate Analytical Approximations for the
                 Error Function",
  journal =      j-MATH-COMPUT-APPL,
  volume =       "27",
  number =       "1",
  pages =        "14:1--14:44",
  month =        feb,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.3390/mca27010014",
  ISSN =         "2297-8747",
  ISSN-L =       "2297-8747",
  bibdate =      "Sun Feb 18 06:28:42 MST 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/math-comput-appl.bib",
  URL =          "https://www.mdpi.com/2297-8747/27/1/14",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Appl.",
  articleno =    "14",
  fjournal =     "Mathematical and Computational Applications",
  journal-URL =  "https://www.mdpi.com/journal/mca",
}


bibtype: article
filename: elefunt.bib
label: Lim:2022:OPA
author: Jay P. Lim and Santosh Nagarakatte
journal: j-PACMPL
volume: 6
number: POPL
pages: 3:1--3:28
month: jan
monthnumber: 1
year: 2022
DOI: https://doi.org/10.1145/3498664
ISSN: 2475-1421 (electronic) OR 24751421 (electronic)
ISSNL: 2475-1421 OR 24751421
bibdate: Thu May 26 06:32:48 MDT 2022
bibtimestamp: 2022.05.26 06:32:48 MDT
URL: https://dl.acm.org/doi/10.1145/3498664
fjournal: Proceedings of the ACM on Programming Languages (PACMPL)
keywords: correct rounding; elementary functions
acknowledgement: ack-nhfb
articleno: 3
journalURL: https://dl.acm.org/loi/pacmpl
rawauthor: Jay P. Lim and Santosh Nagarakatte
title:
One polynomial approximation to produce correctly rounded results of an elementary function for multiple representations and rounding modes

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/pacmpl.bib

abstract:
Mainstream math libraries for floating point (FP) do not produce correctly rounded results for all inputs. In contrast, CR-LIBM and RLIBM provide correctly rounded implementations for a specific FP representation with one rounding mode. Using such libraries for a representation with a new rounding mode or with different precision will result in wrong results due to double rounding. This paper proposes a novel method to generate a single polynomial approximation that produces correctly rounded results for all inputs for multiple rounding modes and multiple precision configurations. To generate a correctly rounded library for n-bits, our key idea is to generate a polynomial approximation for a representation with n+2-bits using the round-to-odd mode. We prove that the resulting polynomial approximation will produce correctly rounded results for all five rounding modes in the standard and for multiple representations with k-bits such that $ |E| + 1 < k leq n $, where $ |E| $ is the number of exponent bits in the representation. Similar to our prior work in the RLIBM project, we approximate the correctly rounded result when we generate the library with n+2-bits using the round-to-odd mode. We also generate polynomial approximations by structuring it as a linear programming problem but propose enhancements to polynomial generation to handle the round-to-odd mode. Our prototype is the first 32-bit float library that produces correctly rounded results with all rounding modes in the IEEE standard for all inputs with a single polynomial approximation. It also produces correctly rounded results for any FP configuration ranging from 10-bits to 32-bits while also being faster than mainstream libraries.

rawabstract:
Mainstream math libraries for floating point (FP) do not produce correctly rounded results for all inputs. In contrast, CR-LIBM and RLIBM provide correctly rounded implementations for a specific FP representation with one rounding mode. Using such libraries for a representation with a new rounding mode or with different precision will result in wrong results due to double rounding. This paper proposes a novel method to generate a single polynomial approximation that produces correctly rounded results for all inputs for multiple rounding modes and multiple precision configurations. To generate a correctly rounded library for n-bits, our key idea is to generate a polynomial approximation for a representation with n+2-bits using the round-to-odd mode. We prove that the resulting polynomial approximation will produce correctly rounded results for all five rounding modes in the standard and for multiple representations with k-bits such that $ |E| + 1 < k \leq n $, where $ |E| $ is the number of exponent bits in the representation. Similar to our prior work in the RLIBM project, we approximate the correctly rounded result when we generate the library with n+2-bits using the round-to-odd mode. We also generate polynomial approximations by structuring it as a linear programming problem but propose enhancements to polynomial generation to handle the round-to-odd mode. Our prototype is the first 32-bit float library that produces correctly rounded results with all rounding modes in the IEEE standard for all inputs with a single polynomial approximation. It also produces correctly rounded results for any FP configuration ranging from 10-bits to 32-bits while also being faster than mainstream libraries.

rawtitle:
One polynomial approximation to produce correctly rounded results of an elementary function for multiple representations and rounding modes

entry:
@Article{Lim:2022:OPA,
  author =       "Jay P. Lim and Santosh Nagarakatte",
  title =        "One polynomial approximation to produce correctly
                 rounded results of an elementary function for multiple
                 representations and rounding modes",
  journal =      j-PACMPL,
  volume =       "6",
  number =       "POPL",
  pages =        "3:1--3:28",
  month =        jan,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3498664",
  ISSN =         "2475-1421 (electronic)",
  ISSN-L =       "2475-1421",
  bibdate =      "Thu May 26 06:32:48 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3498664",
  abstract =     "Mainstream math libraries for floating point (FP) do
                 not produce correctly rounded results for all inputs.
                 In contrast, CR-LIBM and RLIBM provide correctly
                 rounded implementations for a specific FP
                 representation with one rounding mode. Using such
                 libraries for a representation with a new rounding mode
                 or with different precision will result in wrong
                 results due to double rounding. This paper proposes a
                 novel method to generate a single polynomial
                 approximation that produces correctly rounded results
                 for all inputs for multiple rounding modes and multiple
                 precision configurations. To generate a correctly
                 rounded library for n-bits, our key idea is to generate
                 a polynomial approximation for a representation with
                 n+2-bits using the round-to-odd mode. We prove that the
                 resulting polynomial approximation will produce
                 correctly rounded results for all five rounding modes
                 in the standard and for multiple representations with
                 k-bits such that $ |E| + 1 < k \leq n $, where $ |E| $
                 is the number of exponent bits in the representation.
                 Similar to our prior work in the RLIBM project, we
                 approximate the correctly rounded result when we
                 generate the library with n+2-bits using the
                 round-to-odd mode. We also generate polynomial
                 approximations by structuring it as a linear
                 programming problem but propose enhancements to
                 polynomial generation to handle the round-to-odd mode.
                 Our prototype is the first 32-bit float library that
                 produces correctly rounded results with all rounding
                 modes in the IEEE standard for all inputs with a single
                 polynomial approximation. It also produces correctly
                 rounded results for any FP configuration ranging from
                 10-bits to 32-bits while also being faster than
                 mainstream libraries.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "Proceedings of the ACM on Programming Languages
                 (PACMPL)",
  journal-URL =  "https://dl.acm.org/loi/pacmpl",
  keywords =     "correct rounding; elementary functions",
}


bibtype: inproceedings
filename: elefunt.bib
label: Oh:2022:EPA
author: Hyun Woo Oh and Won Sik Jeong and Seung Eun Lee
editor: IEEE
booktitle: 2022 19th International SoC Design Conference (ISOCC)
title: Evaluation of Posit Arithmetic on Machine Learning based on Approximate Exponential Functions
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 358--359
year: 2022
DOI: https://doi.org/10.1109/ISOCC56007.2022.10031524
bibdate: Fri Dec 15 09:21:55 2023
bibtimestamp: 2023.12.15 09:21:55 ???
acknowledgement: ack-nhfb
rawauthor: Hyun Woo Oh and Won Sik Jeong and Seung Eun Lee
rawbooktitle: {2022 19th International SoC Design Conference (ISOCC)}
raweditor: {IEEE}
rawtitle: Evaluation of Posit Arithmetic on Machine Learning based on Approximate Exponential Functions
entry:
@InProceedings{Oh:2022:EPA,
  author =       "Hyun Woo Oh and Won Sik Jeong and Seung Eun Lee",
  editor =       "{IEEE}",
  booktitle =    "{2022 19th International SoC Design Conference
                 (ISOCC)}",
  title =        "Evaluation of Posit Arithmetic on Machine Learning
                 based on Approximate Exponential Functions",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "358--359",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ISOCC56007.2022.10031524",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Patel:2022:LPG
author: Pragnesh Patel and Aman Arora and Earl Swartzlander and Lizy John
booktitle: 2022 23rd International Symposium on Quality Electronic Design (ISQED)
title: LogGen: a Parameterized Generator for Designing Floating-Point Logarithm Units for Deep Learning
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1--7
year: 2022
DOI: https://doi.org/10.1109/ISQED54688.2022.9806139
bibdate: Wed Oct 1 06:40:18 2025
bibtimestamp: 2025.10.01 06:40:18 ???
acknowledgement: ack-nhfb
rawauthor: Pragnesh Patel and Aman Arora and Earl Swartzlander and Lizy John
rawbooktitle: {2022 23rd International Symposium on Quality Electronic Design (ISQED)}
rawtitle: {LogGen}: a Parameterized Generator for Designing Floating-Point Logarithm Units for Deep Learning
keywords:
ASIC; Deep learning; Deep Learning Hardware; Delays; Digital signal processing; Floating-point Arithmetic; FPGA; Generator; Generators; Logarithm; Measurement; Memory management; Pipelines; Tools

entry:
@InProceedings{Patel:2022:LPG,
  author =       "Pragnesh Patel and Aman Arora and Earl Swartzlander
                 and Lizy John",
  booktitle =    "{2022 23rd International Symposium on Quality
                 Electronic Design (ISQED)}",
  title =        "{LogGen}: a Parameterized Generator for Designing
                 Floating-Point Logarithm Units for Deep Learning",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--7",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ISQED54688.2022.9806139",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ASIC; Deep learning; Deep Learning Hardware; Delays;
                 Digital signal processing; Floating-point Arithmetic;
                 FPGA; Generator; Generators; Logarithm; Measurement;
                 Memory management; Pipelines; Tools",
}


bibtype: article
filename: elefunt.bib
label: Takekawa:2022:FPC
author: Takashi Takekawa
title: Fast parallel calculation of modified Bessel function of the second kind and its derivatives
journal: j-SOFTWAREX
volume: 17
pages: ??--??
month: jan
monthnumber: 1
year: 2022
DOI: https://doi.org/10.1016/j.softx.2021.100923
ISSN: 2352-7110 OR 23527110
ISSNL: 2352-7110 OR 23527110
bibdate: Mon Feb 28 10:41:25 MST 2022
bibtimestamp: 2022.02.28 10:41:25 MST
URL: http://www.sciencedirect.com/science/article/pii/S2352711021001655
fjournal: SoftwareX
acknowledgement: ack-nhfb
articleno: 100923
journalURL: https://www.sciencedirect.com/journal/softwarex/issues
rawauthor: Takashi Takekawa
rawtitle: Fast parallel calculation of modified {Bessel} function of the second kind and its derivatives
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/softwarex.bib

entry:
@Article{Takekawa:2022:FPC,
  author =       "Takashi Takekawa",
  title =        "Fast parallel calculation of modified {Bessel}
                 function of the second kind and its derivatives",
  journal =      j-SOFTWAREX,
  volume =       "17",
  number =       "??",
  pages =        "??--??",
  month =        jan,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.softx.2021.100923",
  ISSN =         "2352-7110",
  ISSN-L =       "2352-7110",
  bibdate =      "Mon Feb 28 10:41:25 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/softwarex.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S2352711021001655",
  acknowledgement = ack-nhfb,
  articleno =    "100923",
  fjournal =     "SoftwareX",
  journal-URL =  "https://www.sciencedirect.com/journal/softwarex/issues",
}


bibtype: article
filename: elefunt.bib
label: Akdemir:2023:ABC
author: S. Akdemir and S. Ozay and E. Oztekin
title: Asymptotic behavior of Clebsch--Gordan coefficients
journal: j-J-MATH-CHEM
volume: 62
number: 10
pages: 2761--2775
month: nov
monthnumber: 11
year: 2023
CODEN: JMCHEG
DOI: https://doi.org/10.1007/s10910-023-01544-x
ISSN: 0259-9791 (print), 1572-8897 (electronic) OR 02599791 (print), 15728897 (electronic)
ISSNL: 0259-9791 OR 02599791
bibdate: Tue Aug 5 06:18:24 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.08.05 06:18:24 ???
fjournal: Journal of Mathematical Chemistry
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10910
rawauthor: S. Akdemir and S. {\"O}zay and E. {\"O}ztekin
rawtitle: Asymptotic behavior of {Clebsch--Gordan} coefficients
entry:
@Article{Akdemir:2023:ABC,
  author =       "S. Akdemir and S. {\"O}zay and E. {\"O}ztekin",
  title =        "Asymptotic behavior of {Clebsch--Gordan} coefficients",
  journal =      j-J-MATH-CHEM,
  volume =       "62",
  number =       "10",
  pages =        "2761--2775",
  month =        nov,
  year =         "2023",
  CODEN =        "JMCHEG",
  DOI =          "https://doi.org/10.1007/s10910-023-01544-x",
  ISSN =         "0259-9791 (print), 1572-8897 (electronic)",
  ISSN-L =       "0259-9791",
  bibdate =      "Tue Aug  5 06:18:24 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Chemistry",
  journal-URL =  "http://link.springer.com/journal/10910",
}


bibtype: article
filename: elefunt.bib
label: Ananthanarayan:2023:EAD
author: B. Ananthanarayan and Souvik Bera and S. Friot and O. Marichev and Tanay Pathak
title: On the evaluation of the Appell $ F_2 $ double hypergeometric function
journal: j-COMP-PHYS-COMM
volume: 284
pages: Article 108589
month: mar
monthnumber: 3
year: 2023
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2022.108589
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Sat Feb 25 06:01:54 MST 2023
bibtimestamp: 2023.02.25 06:01:54 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465522003083
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: B. Ananthanarayan and Souvik Bera and S. Friot and O. Marichev and Tanay Pathak
rawtitle: On the evaluation of the {Appell} {$ F_2 $} double hypergeometric function
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Ananthanarayan:2023:EAD,
  author =       "B. Ananthanarayan and Souvik Bera and S. Friot and O.
                 Marichev and Tanay Pathak",
  title =        "On the evaluation of the {Appell} {$ F_2 $} double
                 hypergeometric function",
  journal =      j-COMP-PHYS-COMM,
  volume =       "284",
  number =       "??",
  pages =        "Article 108589",
  month =        mar,
  year =         "2023",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2022.108589",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 06:01:54 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465522003083",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: inproceedings
filename: elefunt.bib
label: Bavier:2023:VNF
author: Eric Bavier and Nicholas Knight and Hugues de Lassus Saint-Genies and Eric Love
title: Vectorized Nonlinear Functions with the RISC-V Vector Extension
crossref: IEEE:2023:PIS
pages: 127--130
year: 2023
DOI: https://doi.org/10.1109/ARITH58626.2023.00032
bibdate: Wed May 8 09:17:31 2024
bibtimestamp: 2024.05.08 09:17:31 ???
acknowledgement: ack-nhfb
rawauthor: Eric Bavier and Nicholas Knight and Hugues de Lassus Saint-Geni{\`e}s and Eric Love
rawtitle: Vectorized Nonlinear Functions with the {RISC-V} Vector Extension
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib

keywords:
ARITH-30; floating point; Instruction sets; Libraries; Pipelines; RISC-V vectors; scalable vectors; Software; Software algorithms; vector mathematical functions; Vectors; Writing

entry:
@InProceedings{Bavier:2023:VNF,
  author =       "Eric Bavier and Nicholas Knight and Hugues de Lassus
                 Saint-Geni{\`e}s and Eric Love",
  title =        "Vectorized Nonlinear Functions with the {RISC-V}
                 Vector Extension",
  crossref =     "IEEE:2023:PIS",
  pages =        "127--130",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00032",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-30; floating point; Instruction sets; Libraries;
                 Pipelines; RISC-V vectors; scalable vectors; Software;
                 Software algorithms; vector mathematical functions;
                 Vectors; Writing",
}


bibtype: article
filename: elefunt.bib
label: Blanchard:2023:NMD
author: Jeffrey D. Blanchard and Marc Chamberland
title: Newton's Method Without Division
journal: j-AMER-MATH-MONTHLY
volume: 130
number: 7
pages: 606--617
year: 2023
CODEN: AMMYAE
DOI: https://doi.org/10.1080/00029890.2022.2093573
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Fri Aug 25 08:24:37 MDT 2023
bibtimestamp: 2023.08.25 08:24:37 MDT
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00029890.html; https://www.tandfonline.com/loi/uamm20
onlinedate: 04 Aug 2023
rawauthor: Jeffrey D. Blanchard and Marc Chamberland
rawtitle: {Newton}'s Method Without Division
bibsource:
https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Blanchard:2023:NMD,
  author =       "Jeffrey D. Blanchard and Marc Chamberland",
  title =        "{Newton}'s Method Without Division",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "130",
  number =       "7",
  pages =        "606--617",
  year =         "2023",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2022.2093573",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Fri Aug 25 08:24:37 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "04 Aug 2023",
}


bibtype: inproceedings
filename: elefunt.bib
label: Brisebarre:2023:TME
author: Nicolas Brisebarre and Silviu-Ioan Filip
title: Towards Machine-Efficient Rational $ L^infty $-Approximations of Mathematical Functions
crossref: IEEE:2023:PIS
pages: 119--126
year: 2023
DOI: https://doi.org/10.1109/ARITH58626.2023.00029
bibdate: Wed May 8 09:17:31 2024
bibtimestamp: 2024.05.08 09:17:31 ???
keywords: Approximation algorithms; ARITH-30; Behavioral sciences; Digital arithmetic; Software
acknowledgement: ack-nhfb
rawauthor: Nicolas Brisebarre and Silviu-Ioan Filip
rawtitle: Towards Machine-Efficient Rational {$ L^\infty $}-Approximations of Mathematical Functions
entry:
@InProceedings{Brisebarre:2023:TME,
  author =       "Nicolas Brisebarre and Silviu-Ioan Filip",
  title =        "Towards Machine-Efficient Rational {$ L^\infty
                 $}-Approximations of Mathematical Functions",
  crossref =     "IEEE:2023:PIS",
  pages =        "119--126",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00029",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Approximation algorithms; ARITH-30; Behavioral
                 sciences; Digital arithmetic; Software",
}


bibtype: inproceedings
filename: elefunt.bib
label: deLamarliere:2023:SFP
author: Paul Geneau de Lamarliere and Guillaume Melquiond and Florian Faissole
title: Slimmer Formal Proofs for Mathematical Libraries
crossref: IEEE:2023:PIS
pages: 32--35
year: 2023
DOI: https://doi.org/10.1109/ARITH58626.2023.00026
bibdate: Wed May 8 09:17:31 2024
bibtimestamp: 2024.05.08 09:17:31 ???
acknowledgement: ack-nhfb
rawauthor: Paul Geneau de Lamarli{\`e}re and Guillaume Melquiond and Florian Faissole
rawtitle: Slimmer Formal Proofs for Mathematical Libraries
keywords:
ARITH-30; Behavioral sciences; Codes; Coq proof assistant; Costs; Digital arithmetic; Floating-point arithmetic; Formal methods; Libraries; Mathematical libraries; Writing

entry:
@InProceedings{deLamarliere:2023:SFP,
  author =       "Paul Geneau de Lamarli{\`e}re and Guillaume Melquiond
                 and Florian Faissole",
  title =        "Slimmer Formal Proofs for Mathematical Libraries",
  crossref =     "IEEE:2023:PIS",
  pages =        "32--35",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00026",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-30; Behavioral sciences; Codes; Coq proof
                 assistant; Costs; Digital arithmetic; Floating-point
                 arithmetic; Formal methods; Libraries; Mathematical
                 libraries; Writing",
}


bibtype: article
filename: elefunt.bib
label: Gil:2023:EGF
author: Amparo Gil and Andrzej Odrzywolek and Javier Segura and Nico M. Temme
journal: j-COMP-PHYS-COMM
volume: 283
pages: Article 108563
month: feb
monthnumber: 2
year: 2023
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2022.108563
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Dec 5 09:16:39 MST 2022
bibtimestamp: 2022.12.05 09:16:39 MST
URL: http://www.sciencedirect.com/science/article/pii/S001046552200282X
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Amparo Gil and Andrzej Odrzywo{\l}ek and Javier Segura and Nico M. Temme
title:
Evaluation of the generalized Fermi--Dirac integral and its derivatives for moderate / large values of the parameters

bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
Evaluation of the generalized {Fermi--Dirac} integral and its derivatives for moderate\slash large values of the parameters

entry:
@Article{Gil:2023:EGF,
  author =       "Amparo Gil and Andrzej Odrzywo{\l}ek and Javier Segura
                 and Nico M. Temme",
  title =        "Evaluation of the generalized {Fermi--Dirac} integral
                 and its derivatives for moderate\slash large values of
                 the parameters",
  journal =      j-COMP-PHYS-COMM,
  volume =       "283",
  number =       "??",
  pages =        "Article 108563",
  month =        feb,
  year =         "2023",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2022.108563",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Dec 5 09:16:39 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S001046552200282X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: inproceedings
filename: elefunt.bib
label: Graillat:2023:PCH
author: Stef Graillat and Youness Ibrahimy and Clothilde Jeangoudoux and Christoph Lauter
title: A parallel compensated Horner scheme for SIMD architecture
crossref: IEEE:2023:PIS
pages: 131--138
year: 2023
DOI: https://doi.org/10.1109/ARITH58626.2023.00010
bibdate: Wed May 8 09:17:31 2024
bibtimestamp: 2024.05.08 09:17:31 ???
acknowledgement: ack-nhfb
rawauthor: Stef Graillat and Youness Ibrahimy and Clothilde Jeangoudoux and Christoph Lauter
rawtitle: A parallel compensated {Horner} scheme for {SIMD} architecture
keywords:
ARITH-30; AVX; compensated algorithms; Computer architecture; Computers; Costs; Digital arithmetic; error-free transformations; Horner scheme; Limiting; parallel algorithms; polynomial evaluation; Registers; rounding errors; Scalability; SIMD

entry:
@InProceedings{Graillat:2023:PCH,
  author =       "Stef Graillat and Youness Ibrahimy and Clothilde
                 Jeangoudoux and Christoph Lauter",
  title =        "A parallel compensated {Horner} scheme for {SIMD}
                 architecture",
  crossref =     "IEEE:2023:PIS",
  pages =        "131--138",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00010",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-30; AVX; compensated algorithms; Computer
                 architecture; Computers; Costs; Digital arithmetic;
                 error-free transformations; Horner scheme; Limiting;
                 parallel algorithms; polynomial evaluation; Registers;
                 rounding errors; Scalability; SIMD",
}


bibtype: techreport
filename: elefunt.bib
label: Hubrecht:2023:TCRa
author: Tom Hubrecht and Claude-Pierre Jeannerod and Paul Zimmermann
title: Towards a correctly-rounded and fast power function in binary64 arithmetic
type: Report
institution: DI-ENS --- Departement d'informatique --- ENS Paris
address: Paris, France
pages: 131--138
day: 12
month: jul
monthnumber: 7
year: 2023
bibdate: Mon May 13 12:00:21 2024
bibtimestamp: 2024.05.13 12:00:21 ???
URL: https://inria.hal.science/hal-04159652v1/
remark: This is a longer version of cite Hubrecht:2023:TCRb with proofs.
acknowledgement: ack-nhfb
rawauthor: Tom Hubrecht and Claude-Pierre Jeannerod and Paul Zimmermann
rawtitle: Towards a correctly-rounded and fast power function in binary64 arithmetic
abstract:
We design algorithms for the correct rounding of the power function $ x^y $ in the binary64 IEEE 754 format, for all rounding modes, modulo the knowledge of hardest-to-round cases. Our implementation of these algorithms largely outperforms previous correctly-rounded implementations and is not far from the efficiency of current mathematical libraries, which are not correctly-rounded. Still, we expect our algorithms can be further improved for speed. The proofs of correctness are fully detailed in an extended version of this paper, with the goal to enable a formal proof of these algorithms. We hope this work will motivate the next IEEE 754 revision committee to require correct rounding for mathematical functions.

rawabstract:
We design algorithms for the correct rounding of the power function $ x^y $ in the binary64 IEEE 754 format, for all rounding modes, modulo the knowledge of hardest-to-round cases. Our implementation of these algorithms largely outperforms previous correctly-rounded implementations and is not far from the efficiency of current mathematical libraries, which are not correctly-rounded. Still, we expect our algorithms can be further improved for speed. The proofs of correctness are fully detailed in an extended version of this paper, with the goal to enable a formal proof of these algorithms. We hope this work will motivate the next IEEE 754 revision committee to require correct rounding for mathematical functions.

entry:
@TechReport{Hubrecht:2023:TCRa,
  author =       "Tom Hubrecht and Claude-Pierre Jeannerod and Paul
                 Zimmermann",
  title =        "Towards a correctly-rounded and fast power function in
                 binary64 arithmetic",
  type =         "Report",
  institution =  "DI-ENS --- D{\'e}partement d'informatique --- ENS
                 Paris",
  address =      "Paris, France",
  day =          "12",
  month =        jul,
  year =         "2023",
  bibdate =      "Mon May 13 12:00:21 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://inria.hal.science/hal-04159652v1/",
  abstract =     "We design algorithms for the correct rounding of the
                 power function $ x^y $ in the binary64 IEEE 754 format,
                 for all rounding modes, modulo the knowledge of
                 hardest-to-round cases. Our implementation of these
                 algorithms largely outperforms previous
                 correctly-rounded implementations and is not far from
                 the efficiency of current mathematical libraries, which
                 are not correctly-rounded. Still, we expect our
                 algorithms can be further improved for speed. The
                 proofs of correctness are fully detailed in an extended
                 version of this paper, with the goal to enable a formal
                 proof of these algorithms. We hope this work will
                 motivate the next IEEE 754 revision committee to
                 require correct rounding for mathematical functions.",
  acknowledgement = ack-nhfb,
  remark =       "This is a longer version of \cite{Hubrecht:2023:TCRb}
                 with proofs.",
}


bibtype: inproceedings
filename: elefunt.bib
label: Hubrecht:2023:TCRb
author: Tom Hubrecht and Claude-Pierre Jeannerod and Paul Zimmermann
title: Towards a correctly-rounded and fast power function in binary64 arithmetic
crossref: IEEE:2023:PIS
pages: 111--118
year: 2023
DOI: https://doi.org/10.1109/ARITH58626.2023.00028
bibdate: Fri Dec 08 15:03:08 2023
bibtimestamp: 2023.12.08 15:03:08 ???
remark: See also longer versions cite Hubrecht:2023:TCRa,Hubrecht:2024:TCR.
acknowledgement: ack-nhfb
rawauthor: Tom Hubrecht and Claude-Pierre Jeannerod and Paul Zimmermann
rawtitle: Towards a correctly-rounded and fast power function in binary64 arithmetic
URL:
https://arith2023.arithsymposium.org/slides/S6_PaulZimmermannS6P1.pdf; https://inria.hal.science/hal-04159652v1/file/pow.pdf; https://inria.hal.science/hal-04326201

abstract:
We design algorithms for the correct rounding of the power function $ x^y $ in the binary64 IEEE 754 format, for all rounding modes, modulo the knowledge of hardest-to-round cases. Our implementation of these algorithms largely outperforms previous correctly-rounded implementations and is not far from the efficiency of current mathematical libraries, which are not correctly-rounded. Still, we expect our algorithms can be further improved for speed. The proofs of correctness are fully detailed, with the goal to enable a formal proof of these algorithms. We hope this work will motivate the next IEEE 754 revision committee to require correct rounding for mathematical functions.

keywords:
ARITH-30; binary64 format; correct rounding; Digital arithmetic; double precision; efficiency; Error analysis; IEEE 754; Libraries; power function; Prediction algorithms; Software; Software algorithms; Switches

rawabstract:
We design algorithms for the correct rounding of the power function $ x^y $ in the binary64 IEEE 754 format, for all rounding modes, modulo the knowledge of hardest-to-round cases. Our implementation of these algorithms largely outperforms previous correctly-rounded implementations and is not far from the efficiency of current mathematical libraries, which are not correctly-rounded. Still, we expect our algorithms can be further improved for speed. The proofs of correctness are fully detailed, with the goal to enable a formal proof of these algorithms. We hope this work will motivate the next IEEE 754 revision committee to require correct rounding for mathematical functions.

entry:
@InProceedings{Hubrecht:2023:TCRb,
  author =       "Tom Hubrecht and Claude-Pierre Jeannerod and Paul
                 Zimmermann",
  title =        "Towards a correctly-rounded and fast power function in
                 binary64 arithmetic",
  crossref =     "IEEE:2023:PIS",
  pages =        "111--118",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00028",
  bibdate =      "Fri Dec 08 15:03:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arith2023.arithsymposium.org/slides/S6_PaulZimmermannS6P1.pdf;
                 https://inria.hal.science/hal-04159652v1/file/pow.pdf;
                 https://inria.hal.science/hal-04326201",
  abstract =     "We design algorithms for the correct rounding of the
                 power function $ x^y $ in the binary64 IEEE 754 format,
                 for all rounding modes, modulo the knowledge of
                 hardest-to-round cases. Our implementation of these
                 algorithms largely outperforms previous
                 correctly-rounded implementations and is not far from
                 the efficiency of current mathematical libraries, which
                 are not correctly-rounded. Still, we expect our
                 algorithms can be further improved for speed. The
                 proofs of correctness are fully detailed, with the goal
                 to enable a formal proof of these algorithms. We hope
                 this work will motivate the next IEEE 754 revision
                 committee to require correct rounding for mathematical
                 functions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-30; binary64 format; correct rounding; Digital
                 arithmetic; double precision; efficiency; Error
                 analysis; IEEE 754; Libraries; power function;
                 Prediction algorithms; Software; Software algorithms;
                 Switches",
  remark =       "See also longer versions
                 \cite{Hubrecht:2023:TCRa,Hubrecht:2024:TCR}.",
}


bibtype: article
filename: elefunt.bib
label: Mansfield:2023:MSR
author: Daniel F. Mansfield
title: Mesopotamian square root approximation by a sequence of rectangles
journal: j-BRITISH-J-HIST-MATH
volume: 38
number: 3
pages: 175--188
year: 2023
DOI: https://doi.org/10.1080/26375451.2023.2215652
ISSN: 1749-8430 (print), 1749-8341 (electronic) OR 17498430 (print), 17498341 (electronic)
ISSNL: 1749-8341 OR 17498341
bibdate: Thu Apr 25 11:06:30 MDT 2024
bibtimestamp: 2024.04.25 11:06:30 MDT
URL: http://www.tandfonline.com/doi/full/10.1080/26375451.2023.2215652
fjournal: BSHM Bulletin: Journal of the British Society for the History of Mathematics
acknowledgement: ack-nhfb
ajournal: BSHM Bull.
journalURL: http://www.tandfonline.com/loi/tbsh20
onlinedate: 09 Jun 2023
rawauthor: Daniel F. Mansfield
rawtitle: {Mesopotamian} square root approximation by a sequence of rectangles
bibsource:
https://www.math.utah.edu/pub/tex/bib/bshm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Mansfield:2023:MSR,
  author =       "Daniel F. Mansfield",
  title =        "{Mesopotamian} square root approximation by a sequence
                 of rectangles",
  journal =      j-BRITISH-J-HIST-MATH,
  volume =       "38",
  number =       "3",
  pages =        "175--188",
  year =         "2023",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/26375451.2023.2215652",
  ISSN =         "1749-8430 (print), 1749-8341 (electronic)",
  ISSN-L =       "1749-8341",
  bibdate =      "Thu Apr 25 11:06:30 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/bshm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.tandfonline.com/doi/full/10.1080/26375451.2023.2215652",
  acknowledgement = ack-nhfb,
  ajournal =     "BSHM Bull.",
  fjournal =     "BSHM Bulletin: Journal of the British Society for the
                 History of Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/tbsh20",
  onlinedate =   "09 Jun 2023",
}


bibtype: article
filename: elefunt.bib
label: Pradhan:2023:ETB
author: Chetana Pradhan and Martin Letras and Jurgen Teich
journal: j-TECS
volume: 22
number: 4
pages: 73:1--73:??
month: jul
monthnumber: 7
year: 2023
DOI: https://doi.org/10.1145/3580737
ISSN: 1539-9087 (print), 1558-3465 (electronic) OR 15399087 (print), 15583465 (electronic)
ISSNL: 1539-9087 OR 15399087
bibdate: Thu Aug 10 07:21:24 MDT 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/tecs.bib
bibtimestamp: 2023.08.10 07:21:24 MDT
URL: https://dl.acm.org/doi/10.1145/3580737
fjournal: ACM Transactions on Embedded Computing Systems
acknowledgement: ack-nhfb
ajournal: ACM Trans. Embed. Comput. Syst.
articleno: 73
journalURL: https://dl.acm.org/loi/tecs
rawauthor: Chetana Pradhan and Martin Letras and J{\"u}rgen Teich
title:
Efficient Table-based Function Approximation on FPGAs Using Interval Splitting and BRAM Instantiation

abstract:
This article proposes a novel approach for the generation of memory-efficient table-based function approximation circuits for edge devices in general and FPGAs in particular. Given a function $ f(x) $ to be approximated in a given interval $ [x_0, x_0 + a) $ and a maximum approximation error $ E_a $, the goal is to determine a function table implementation with a minimized memory footprint, i.e., number of entries that need to be stored. Rather than state-of-the-art work performing an equidistant sampling of the given interval by so-called breakpoints and using linear interpolation between two adjacent breakpoints to determine $ f(x) $ at the maximum error bound, we propose and compare three algorithms for splitting the given interval into sub-intervals to reduce the required memory footprint drastically based on the observation that in sub-intervals of low gradient, a coarser sampling grid may be assumed while guaranteeing the maximum interpolation error bound $ E_a $. Experiments on elementary mathematical functions show that a large fraction in memory footprint may be saved. Second, a hardware architecture implementing the sub-interval selection, breakpoint lookup, and interpolation at a latency of just 9 clock cycles is introduced. Third, for each generated circuit design, BRAMs are automatically instantiated rather than synthesizing the reduced footprint function table using LUT primitives, providing an additional degree of resource efficiency. The approach presented here for FPGAs can equally be applied to other circuit technologies for fast and, at the same time, memory-optimized function approximation at the edge.

rawabstract:
This article proposes a novel approach for the generation of memory-efficient table-based function approximation circuits for edge devices in general and FPGAs in particular. Given a function $ f(x) $ to be approximated in a given interval $ [x_0, x_0 + a) $ and a maximum approximation error $ E_a $, the goal is to determine a function table implementation with a minimized memory footprint, i.e., number of entries that need to be stored. Rather than state-of-the-art work performing an equidistant sampling of the given interval by so-called breakpoints and using linear interpolation between two adjacent breakpoints to determine $ f(x) $ at the maximum error bound, we propose and compare three algorithms for splitting the given interval into sub-intervals to reduce the required memory footprint drastically based on the observation that in sub-intervals of low gradient, a coarser sampling grid may be assumed while guaranteeing the maximum interpolation error bound $ E_a $. Experiments on elementary mathematical functions show that a large fraction in memory footprint may be saved. Second, a hardware architecture implementing the sub-interval selection, breakpoint lookup, and interpolation at a latency of just 9 clock cycles is introduced. Third, for each generated circuit design, BRAMs are automatically instantiated rather than synthesizing the reduced footprint function table using LUT primitives, providing an additional degree of resource efficiency. The approach presented here for FPGAs can equally be applied to other circuit technologies for fast and, at the same time, memory-optimized function approximation at the edge.

rawtitle:
Efficient Table-based Function Approximation on {FPGAs} Using Interval Splitting and {BRAM} Instantiation

entry:
@Article{Pradhan:2023:ETB,
  author =       "Chetana Pradhan and Martin Letras and J{\"u}rgen
                 Teich",
  title =        "Efficient Table-based Function Approximation on
                 {FPGAs} Using Interval Splitting and {BRAM}
                 Instantiation",
  journal =      j-TECS,
  volume =       "22",
  number =       "4",
  pages =        "73:1--73:??",
  month =        jul,
  year =         "2023",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3580737",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Thu Aug 10 07:21:24 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/tecs.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3580737",
  abstract =     "This article proposes a novel approach for the
                 generation of memory-efficient table-based function
                 approximation circuits for edge devices in general and
                 FPGAs in particular. Given a function $ f(x) $ to be
                 approximated in a given interval $ [x_0, x_0 + a) $ and
                 a maximum approximation error $ E_a $, the goal is to
                 determine a function table implementation with a
                 minimized memory footprint, i.e., number of entries
                 that need to be stored. Rather than state-of-the-art
                 work performing an equidistant sampling of the given
                 interval by so-called breakpoints and using linear
                 interpolation between two adjacent breakpoints to
                 determine $ f(x) $ at the maximum error bound, we
                 propose and compare three algorithms for splitting the
                 given interval into sub-intervals to reduce the
                 required memory footprint drastically based on the
                 observation that in sub-intervals of low gradient, a
                 coarser sampling grid may be assumed while guaranteeing
                 the maximum interpolation error bound $ E_a $.
                 Experiments on elementary mathematical functions show
                 that a large fraction in memory footprint may be saved.
                 Second, a hardware architecture implementing the
                 sub-interval selection, breakpoint lookup, and
                 interpolation at a latency of just 9 clock cycles is
                 introduced. Third, for each generated circuit design,
                 BRAMs are automatically instantiated rather than
                 synthesizing the reduced footprint function table using
                 LUT primitives, providing an additional degree of
                 resource efficiency. The approach presented here for
                 FPGAs can equally be applied to other circuit
                 technologies for fast and, at the same time,
                 memory-optimized function approximation at the edge.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Embed. Comput. Syst.",
  articleno =    "73",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "https://dl.acm.org/loi/tecs",
}


bibtype: article
filename: elefunt.bib
label: Slevinsky:2023:RAE
author: Richard M. Slevinsky and Hassan Safouhi
title: A recursive algorithm for an efficient and accurate computation of incomplete Bessel functions
journal: j-NUMER-ALGORITHMS
volume: 92
number: 1
pages: 973--983
month: jan
monthnumber: 1
year: 2023
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-022-01438-0
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Mon Jan 30 12:22:09 MST 2023
bibtimestamp: 2023.01.30 12:22:09 MST
URL: https://link.springer.com/article/10.1007/s11075-022-01438-0
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
ajournal: Numer. Algorithms
journalURL: http://link.springer.com/journal/11075
rawauthor: Richard M. Slevinsky and Hassan Safouhi
rawtitle: A recursive algorithm for an efficient and accurate computation of incomplete {Bessel} functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib

entry:
@Article{Slevinsky:2023:RAE,
  author =       "Richard M. Slevinsky and Hassan Safouhi",
  title =        "A recursive algorithm for an efficient and accurate
                 computation of incomplete {Bessel} functions",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "92",
  number =       "1",
  pages =        "973--983",
  month =        jan,
  year =         "2023",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-022-01438-0",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Jan 30 12:22:09 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "https://link.springer.com/article/10.1007/s11075-022-01438-0",
  acknowledgement = ack-nhfb,
  ajournal =     "Numer. Algorithms",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}


bibtype: article
filename: elefunt.bib
label: Ananthanarayan:2024:OWR
author: B. Ananthanarayan and Souvik Bera and S. Friot and Tanay Pathak
journal: j-COMP-PHYS-COMM
volume: 300
pages: ??--??
month: jul
monthnumber: 7
year: 2024
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2024.109162
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon May 6 07:51:16 MDT 2024
bibtimestamp: 2024.05.06 07:51:16 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0010465524000857
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
articleno: 109162
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: B. Ananthanarayan and Souvik Bera and S. Friot and Tanay Pathak
title:
pkg Olsson.wl and pkg ROC2.wl: Mathematica packages for transformations of multivariable hypergeometric functions and regions of convergence for their series representations in the two variables case

bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathematica.bib

rawtitle:
\pkg{Olsson.wl} and \pkg{ROC2.wl}: {Mathematica} packages for transformations of multivariable hypergeometric functions and regions of convergence for their series representations in the two variables case

entry:
@Article{Ananthanarayan:2024:OWR,
  author =       "B. Ananthanarayan and Souvik Bera and S. Friot and
                 Tanay Pathak",
  title =        "\pkg{Olsson.wl} and \pkg{ROC2.wl}: {Mathematica}
                 packages for transformations of multivariable
                 hypergeometric functions and regions of convergence for
                 their series representations in the two variables
                 case",
  journal =      j-COMP-PHYS-COMM,
  volume =       "300",
  number =       "??",
  pages =        "??--??",
  month =        jul,
  year =         "2024",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2024.109162",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon May 6 07:51:16 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465524000857",
  acknowledgement = ack-nhfb,
  articleno =    "109162",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Briggs:2024:ISM
author: Ian Briggs and Yash Lad and Pavel Panchekha
title: Implementation and Synthesis of Math Library Functions
journal: j-PACMPL
volume: 8
number: POPL
pages: 32:1--32:??
month: jan
monthnumber: 1
year: 2024
DOI: https://doi.org/10.1145/3632874
ISSN: 2475-1421 (electronic) OR 24751421 (electronic)
ISSNL: 2475-1421 OR 24751421
bibdate: Fri May 10 10:23:39 MDT 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/pacmpl.bib
bibtimestamp: 2024.05.10 10:23:39 MDT
URL: https://dl.acm.org/doi/10.1145/3632874
fjournal: Proceedings of the ACM on Programming Languages (PACMPL)
acknowledgement: ack-nhfb
ajournal: Proc. ACM Program. Lang.
articleno: 32
journalURL: https://dl.acm.org/loi/pacmpl
rawauthor: Ian Briggs and Yash Lad and Pavel Panchekha
rawtitle: Implementation and Synthesis of Math Library Functions
abstract:
Achieving speed and accuracy for math library functions like exp, sin, and log is difficult. This is because low-level implementation languages like C do not help math library developers catch mathematical errors, build implementations incrementally, or separate high-level and low-level decision making. This ultimately puts development of such functions out of reach for all but the most experienced experts. To address this, we introduce MegaLibm, a domain-specific language for implementing, testing, and tuning math library implementations. MegaLibm is safe, modular, and tunable. Implementations in MegaLibm can automatically detect mathematical mistakes like sign flips via semantic wellformedness checks, and components like range reductions can be implemented in a modular, composable way, simplifying implementations. Once the high-level algorithm is done, tuning parameters like working precisions and evaluation schemes can be adjusted through orthogonal tuning parameters to achieve the desired speed and accuracy. MegaLibm also enables math library developers to work interactively, compiling, testing, and tuning their implementations and invoking tools like Sollya and type-directed synthesis to complete components and synthesize entire implementations. MegaLibm can express 8 state-of-the-art math library implementations with comparable speed and accuracy to the original C code, and can synthesize 5 variations and 3 from-scratch implementations with minimal guidance.

rawabstract:
Achieving speed and accuracy for math library functions like exp, sin, and log is difficult. This is because low-level implementation languages like C do not help math library developers catch mathematical errors, build implementations incrementally, or separate high-level and low-level decision making. This ultimately puts development of such functions out of reach for all but the most experienced experts. To address this, we introduce MegaLibm, a domain-specific language for implementing, testing, and tuning math library implementations. MegaLibm is safe, modular, and tunable. Implementations in MegaLibm can automatically detect mathematical mistakes like sign flips via semantic wellformedness checks, and components like range reductions can be implemented in a modular, composable way, simplifying implementations. Once the high-level algorithm is done, tuning parameters like working precisions and evaluation schemes can be adjusted through orthogonal tuning parameters to achieve the desired speed and accuracy. MegaLibm also enables math library developers to work interactively, compiling, testing, and tuning their implementations and invoking tools like Sollya and type-directed synthesis to complete components and synthesize entire implementations. MegaLibm can express 8 state-of-the-art math library implementations with comparable speed and accuracy to the original C code, and can synthesize 5 variations and 3 from-scratch implementations with minimal guidance.

entry:
@Article{Briggs:2024:ISM,
  author =       "Ian Briggs and Yash Lad and Pavel Panchekha",
  title =        "Implementation and Synthesis of Math Library
                 Functions",
  journal =      j-PACMPL,
  volume =       "8",
  number =       "POPL",
  pages =        "32:1--32:??",
  month =        jan,
  year =         "2024",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3632874",
  ISSN =         "2475-1421 (electronic)",
  ISSN-L =       "2475-1421",
  bibdate =      "Fri May 10 10:23:39 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3632874",
  abstract =     "Achieving speed and accuracy for math library
                 functions like exp, sin, and log is difficult. This is
                 because low-level implementation languages like C do
                 not help math library developers catch mathematical
                 errors, build implementations incrementally, or
                 separate high-level and low-level decision making. This
                 ultimately puts development of such functions out of
                 reach for all but the most experienced experts. To
                 address this, we introduce MegaLibm, a domain-specific
                 language for implementing, testing, and tuning math
                 library implementations. MegaLibm is safe, modular, and
                 tunable. Implementations in MegaLibm can automatically
                 detect mathematical mistakes like sign flips via
                 semantic wellformedness checks, and components like
                 range reductions can be implemented in a modular,
                 composable way, simplifying implementations. Once the
                 high-level algorithm is done, tuning parameters like
                 working precisions and evaluation schemes can be
                 adjusted through orthogonal tuning parameters to
                 achieve the desired speed and accuracy. MegaLibm also
                 enables math library developers to work interactively,
                 compiling, testing, and tuning their implementations
                 and invoking tools like Sollya and type-directed
                 synthesis to complete components and synthesize entire
                 implementations. MegaLibm can express 8
                 state-of-the-art math library implementations with
                 comparable speed and accuracy to the original C code,
                 and can synthesize 5 variations and 3 from-scratch
                 implementations with minimal guidance.",
  acknowledgement = ack-nhfb,
  ajournal =     "Proc. ACM Program. Lang.",
  articleno =    "32",
  fjournal =     "Proceedings of the ACM on Programming Languages
                 (PACMPL)",
  journal-URL =  "https://dl.acm.org/loi/pacmpl",
}


bibtype: techreport
filename: elefunt.bib
label: Brisebarre:2024:CRE
author: Nicolas Brisebarre and Guillaume Hanrot and Jean-Michel Muller and Paul Zimmermann
title: Correctly-rounded evaluation of a function: why, how, and at what cost?
type: Report
number: hal-04474530
institution: CNRS --- Centre National de la Recherche Scientifique and others
address: Paris, France
pages: 29
day: 23
month: feb
monthnumber: 2
year: 2024
bibdate: Fri Feb 23 16:11:08 2024
bibtimestamp: 2024.02.23 16:11:08 ???
URL: https://hal.science/hal-04474530
acknowledgement: ack-nhfb
rawauthor: Nicolas Brisebarre and Guillaume Hanrot and Jean-Michel Muller and Paul Zimmermann
rawtitle: Correctly-rounded evaluation of a function: why, how, and at what cost?
abstract:
The goal of this paper is to convince the reader that a future standard for floating-point arithmetic should require the availability of a correctly-rounded version of a well-chosen core set of elementary functions. We discuss the interest and feasibility of this requirement. We also give answers to common objections we have received over the last 10 years.

keywords:
algorithmic number theory; approximation theory; Computer arithmetic; elementary functions; floating-point arithmetic; lattice basis reduction; LLL algorithm; standardization

rawabstract:
The goal of this paper is to convince the reader that a future standard for floating-point arithmetic should require the availability of a correctly-rounded version of a well-chosen core set of elementary functions. We discuss the interest and feasibility of this requirement. We also give answers to common objections we have received over the last 10 years.

entry:
@TechReport{Brisebarre:2024:CRE,
  author =       "Nicolas Brisebarre and Guillaume Hanrot and
                 Jean-Michel Muller and Paul Zimmermann",
  title =        "Correctly-rounded evaluation of a function: why, how,
                 and at what cost?",
  type =         "Report",
  number =       "hal-04474530",
  institution =  "CNRS --- Centre National de la Recherche Scientifique
                 and others",
  address =      "Paris, France",
  pages =        "29",
  day =          "23",
  month =        feb,
  year =         "2024",
  bibdate =      "Fri Feb 23 16:11:08 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.science/hal-04474530",
  abstract =     "The goal of this paper is to convince the reader that
                 a future standard for floating-point arithmetic should
                 require the availability of a correctly-rounded version
                 of a well-chosen core set of elementary functions. We
                 discuss the interest and feasibility of this
                 requirement. We also give answers to common objections
                 we have received over the last 10 years.",
  acknowledgement = ack-nhfb,
  keywords =     "algorithmic number theory; approximation theory;
                 Computer arithmetic; elementary functions;
                 floating-point arithmetic; lattice basis reduction; LLL
                 algorithm; standardization",
}


bibtype: article
filename: elefunt.bib
label: Cameron:2024:AHM
author: Thomas R. Cameron and Stef Graillat
title: Accurate Horner methods in real and complex floating-point arithmetic
journal: j-BIT-NUM-MATH
volume: 64
number: 2
pages: ??--??
month: jun
monthnumber: 6
year: 2024
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/s10543-024-01017-w
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Tue May 28 15:02:24 MDT 2024
bibtimestamp: 2024.05.28 15:02:24 MDT
URL: https://link.springer.com/article/10.1007/s10543-024-01017-w
fjournal: BIT Numerical Mathematics
acknowledgement: ack-nhfb
ajournal: Bit Num. Math.
articleno: 17
journalURL: http://link.springer.com/journal/10543
rawauthor: Thomas R. Cameron and Stef Graillat
rawtitle: Accurate {Horner} methods in real and complex floating-point arithmetic
bibsource:
https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Cameron:2024:AHM,
  author =       "Thomas R. Cameron and Stef Graillat",
  title =        "Accurate {Horner} methods in real and complex
                 floating-point arithmetic",
  journal =      j-BIT-NUM-MATH,
  volume =       "64",
  number =       "2",
  pages =        "??--??",
  month =        jun,
  year =         "2024",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-024-01017-w",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Tue May 28 15:02:24 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://link.springer.com/article/10.1007/s10543-024-01017-w",
  acknowledgement = ack-nhfb,
  ajournal =     "Bit Num. Math.",
  articleno =    "17",
  fjournal =     "BIT Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: article
filename: elefunt.bib
label: Dempsey:2024:PBI
author: Kevin M. Dempsey
title: Principal Branches of Inverse Trigonometric and Inverse Hyperbolic Functions
journal: j-ACM-COMM-COMP-ALGEBRA
volume: 58
number: 3
pages: 45--56
month: sep
monthnumber: 9
year: 2024
DOI: https://doi.org/10.1145/3717582.3717583
ISSN: 1932-2232 (print), 1932-2240 (electronic) OR 19322232 (print), 19322240 (electronic)
ISSNL: 1932-2232 OR 19322232
bibdate: Sat Apr 19 05:48:11 MDT 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/sigsam.bib
bibtimestamp: 2025.04.19 05:48:11 MDT
fjournal: ACM Communications in Computer Algebra
acknowledgement: ack-nhfb
ajournal: ACM Commun. Computer Algebr.
journalURL: https://dl.acm.org/loi/sigsam-cca
rawauthor: Kevin M. Dempsey
rawtitle: Principal Branches of Inverse Trigonometric and Inverse Hyperbolic Functions
abstract:
We discuss principal branches for five square root functions and for the inverse trigonometric and inverse hyperbolic functions. We take the standard reference in this area to be the NIST Digital Library of Mathematical Functions (DLMF). We adopt the notation for and the definitions of the principal branches of the inverse functions in the DLMF. Similarly, the branch cuts for the inverse functions are defined as per the DLMF. Our goal is to use complex analysis to turn the definitions of the principal branches in the DLMF into concrete expressions that hold on the entirety of their respective cut planes. The square root principal branch expressions are new breakthrough discoveries that lead smoothly to four of the concrete expressions. We expand the number of concrete expressions in Sections 4.23 and 4.37 in the DLMF from two to eight. Three of these eight concrete expressions were in print in 1924. One of the latter is still awaiting inclusion in the DLMF. Taken altogether, we provide a computationally efficient resource for computer algebra in programming languages, specifically for the principal branches of the inverse trigonometric and inverse hyperbolic functions.

rawabstract:
We discuss principal branches for five square root functions and for the inverse trigonometric and inverse hyperbolic functions. We take the standard reference in this area to be the NIST Digital Library of Mathematical Functions (DLMF). We adopt the notation for and the definitions of the principal branches of the inverse functions in the DLMF. Similarly, the branch cuts for the inverse functions are defined as per the DLMF. Our goal is to use complex analysis to turn the definitions of the principal branches in the DLMF into concrete expressions that hold on the entirety of their respective cut planes. The square root principal branch expressions are new breakthrough discoveries that lead smoothly to four of the concrete expressions. We expand the number of concrete expressions in Sections 4.23 and 4.37 in the DLMF from two to eight. Three of these eight concrete expressions were in print in 1924. One of the latter is still awaiting inclusion in the DLMF. Taken altogether, we provide a computationally efficient resource for computer algebra in programming languages, specifically for the principal branches of the inverse trigonometric and inverse hyperbolic functions.

entry:
@Article{Dempsey:2024:PBI,
  author =       "Kevin M. Dempsey",
  title =        "Principal Branches of Inverse Trigonometric and
                 Inverse Hyperbolic Functions",
  journal =      j-ACM-COMM-COMP-ALGEBRA,
  volume =       "58",
  number =       "3",
  pages =        "45--56",
  month =        sep,
  year =         "2024",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3717582.3717583",
  ISSN =         "1932-2232 (print), 1932-2240 (electronic)",
  ISSN-L =       "1932-2232",
  bibdate =      "Sat Apr 19 05:48:11 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
  abstract =     "We discuss principal branches for five square root
                 functions and for the inverse trigonometric and inverse
                 hyperbolic functions. We take the standard reference in
                 this area to be the NIST Digital Library of
                 Mathematical Functions (DLMF). We adopt the notation
                 for and the definitions of the principal branches of
                 the inverse functions in the DLMF. Similarly, the
                 branch cuts for the inverse functions are defined as
                 per the DLMF. Our goal is to use complex analysis to
                 turn the definitions of the principal branches in the
                 DLMF into concrete expressions that hold on the
                 entirety of their respective cut planes. The square
                 root principal branch expressions are new breakthrough
                 discoveries that lead smoothly to four of the concrete
                 expressions. We expand the number of concrete
                 expressions in Sections 4.23 and 4.37 in the DLMF from
                 two to eight. Three of these eight concrete expressions
                 were in print in 1924. One of the latter is still
                 awaiting inclusion in the DLMF. Taken altogether, we
                 provide a computationally efficient resource for
                 computer algebra in programming languages, specifically
                 for the principal branches of the inverse trigonometric
                 and inverse hyperbolic functions.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Commun. Computer Algebr.",
  fjournal =     "ACM Communications in Computer Algebra",
  journal-URL =  "https://dl.acm.org/loi/sigsam-cca",
}


bibtype: article
filename: elefunt.bib
label: Harris:2024:UDS
title: Unified Digit Selection for Radix-4 Recurrence Division and Square Root
journal: j-IEEE-TRANS-COMPUT
volume: 73
number: 1
pages: 292--300
month: jan
monthnumber: 1
year: 2024
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2023.3305760
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Dec 27 15:37:27 2023
bibtimestamp: 2023.12.27 15:37:27 ???
fjournal: IEEE Transactions on Computers
keywords: division; minimally-redundant radix-4; RISC-V; square root; SRT
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawtitle: Unified Digit Selection for Radix-4 Recurrence Division and Square Root
author:
David Harris and James Stine and Milo Ercegovac and Alberto Nannarelli and Katherine Parry and Cedar Turek

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib; https://www.math.utah.edu/pub/tex/bib/risc-v.bib

rawauthor:
David Harris and James Stine and Milo Ercegovac and Alberto Nannarelli and Katherine Parry and Cedar Turek

entry:
@Article{Harris:2024:UDS,
  author =       "David Harris and James Stine and Milo Ercegovac and
                 Alberto Nannarelli and Katherine Parry and Cedar
                 Turek",
  title =        "Unified Digit Selection for Radix-4 Recurrence
                 Division and Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "73",
  number =       "1",
  pages =        "292--300",
  month =        jan,
  year =         "2024",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2023.3305760",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Dec 27 15:37:27 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "division; minimally-redundant radix-4; RISC-V; square
                 root; SRT",
}


bibtype: techreport
filename: elefunt.bib
label: Hubrecht:2024:TCR
author: Tom Hubrecht and Claude-Pierre Jeannerod and Paul Zimmermann and Laurence Rideau and Laurent Thery
title: Towards a correctly-rounded and fast power function in binary64 arithmetic
type: Report
institution: DI-ENS --- Departement d'informatique --- ENS Paris
address: Paris, France
pages: 292--300
day: 8
month: feb
monthnumber: 2
year: 2024
bibdate: Mon May 13 12:00:21 2024
bibtimestamp: 2024.05.13 12:00:21 ???
URL: https://inria.hal.science/hal-04159652v2/
acknowledgement: ack-nhfb
rawtitle: Towards a correctly-rounded and fast power function in binary64 arithmetic
abstract:
We design algorithms for the correct rounding of the power function $ x^y $ in the binary64 IEEE 754 format, for all rounding modes, modulo the knowledge of hardest-to-round cases. Our implementation of these algorithms largely outperforms previous correctly-rounded implementations and is not far from the efficiency of current mathematical libraries, which are not correctly-rounded. Still, we expect our algorithms can be further improved for speed. The proofs of correctness are fully detailed and have been formally verified. We hope this work will motivate the next IEEE 754 revision committee to require correct rounding for mathematical functions.

remark:
This is a longer version of cite Hubrecht:2023:TCRb with proofs and remarks by the final two authors on the formal verification.

rawabstract:
We design algorithms for the correct rounding of the power function $ x^y $ in the binary64 IEEE 754 format, for all rounding modes, modulo the knowledge of hardest-to-round cases. Our implementation of these algorithms largely outperforms previous correctly-rounded implementations and is not far from the efficiency of current mathematical libraries, which are not correctly-rounded. Still, we expect our algorithms can be further improved for speed. The proofs of correctness are fully detailed and have been formally verified. We hope this work will motivate the next IEEE 754 revision committee to require correct rounding for mathematical functions.

rawauthor:
Tom Hubrecht and Claude-Pierre Jeannerod and Paul Zimmermann and Laurence Rideau and Laurent Th{\'e}ry

entry:
@TechReport{Hubrecht:2024:TCR,
  author =       "Tom Hubrecht and Claude-Pierre Jeannerod and Paul
                 Zimmermann and Laurence Rideau and Laurent Th{\'e}ry",
  title =        "Towards a correctly-rounded and fast power function in
                 binary64 arithmetic",
  type =         "Report",
  institution =  "DI-ENS --- D{\'e}partement d'informatique --- ENS
                 Paris",
  address =      "Paris, France",
  day =          "8",
  month =        feb,
  year =         "2024",
  bibdate =      "Mon May 13 12:00:21 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://inria.hal.science/hal-04159652v2/",
  abstract =     "We design algorithms for the correct rounding of the
                 power function $ x^y $ in the binary64 IEEE 754 format,
                 for all rounding modes, modulo the knowledge of
                 hardest-to-round cases. Our implementation of these
                 algorithms largely outperforms previous
                 correctly-rounded implementations and is not far from
                 the efficiency of current mathematical libraries, which
                 are not correctly-rounded. Still, we expect our
                 algorithms can be further improved for speed. The
                 proofs of correctness are fully detailed and have been
                 formally verified. We hope this work will motivate the
                 next IEEE 754 revision committee to require correct
                 rounding for mathematical functions.",
  acknowledgement = ack-nhfb,
  remark =       "This is a longer version of \cite{Hubrecht:2023:TCRb}
                 with proofs and remarks by the final two authors on the
                 formal verification.",
}


bibtype: article
filename: elefunt.bib
label: Kowalenko:2024:AVT
author: Victor Kowalenko
title: Algorithms for Various Trigonometric Power Sums
journal: j-ALGORITHMS-BASEL
volume: 17
number: 8
pages: 292--300
year: 2024
CODEN: ALGOCH
DOI: https://doi.org/10.3390/a17080373
ISSN: 1999-4893 (electronic) OR 19994893 (electronic)
ISSNL: 1999-4893 OR 19994893
bibdate: Fri Aug 30 05:57:31 2024
bibtimestamp: 2024.08.30 05:57:31 ???
URL: https://www.mdpi.com/1999-4893/17/8/373
fjournal: Algorithms (Basel)
remark: See cite Rosenberg:1963:FTP,Dronyuk:2025:ACG.
acknowledgement: ack-nhfb
articleno: 373
journalURL: https://www.mdpi.com/journal/algorithms
rawauthor: Victor Kowalenko
rawtitle: Algorithms for Various Trigonometric Power Sums
bibsource:
https://www.math.utah.edu/pub/tex/bib/algorithms.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
In this paper, algorithms for different types of trigonometric power sums are developed and presented. Although interesting in their own right, these trigonometric power sums arise during the creation of an algorithm for the four types of twisted trigonometric power sums defined in the introduction. The primary aim in evaluating these sums is to obtain exact results in a rational form, as opposed to standard or direct evaluation, which often results in machine-dependent decimal values that can be affected by round-off errors. Moreover, since the variable, m, appearing in the denominators of the arguments of the trigonometric functions in these sums, can remain algebraic in the algorithms/codes, one can also obtain polynomial solutions in powers of m and the variable r that appears in the cosine factor accompanying the trigonometric power. The degrees of these polynomials are found to be dependent upon v, the value of the trigonometric power in the sum, which must always be specified.

rawabstract:
In this paper, algorithms for different types of trigonometric power sums are developed and presented. Although interesting in their own right, these trigonometric power sums arise during the creation of an algorithm for the four types of twisted trigonometric power sums defined in the introduction. The primary aim in evaluating these sums is to obtain exact results in a rational form, as opposed to standard or direct evaluation, which often results in machine-dependent decimal values that can be affected by round-off errors. Moreover, since the variable, m, appearing in the denominators of the arguments of the trigonometric functions in these sums, can remain algebraic in the algorithms/codes, one can also obtain polynomial solutions in powers of m and the variable r that appears in the cosine factor accompanying the trigonometric power. The degrees of these polynomials are found to be dependent upon v, the value of the trigonometric power in the sum, which must always be specified.

entry:
@Article{Kowalenko:2024:AVT,
  author =       "Victor Kowalenko",
  title =        "Algorithms for Various Trigonometric Power Sums",
  journal =      j-ALGORITHMS-BASEL,
  volume =       "17",
  number =       "8",
  year =         "2024",
  CODEN =        "ALGOCH",
  DOI =          "https://doi.org/10.3390/a17080373",
  ISSN =         "1999-4893 (electronic)",
  ISSN-L =       "1999-4893",
  bibdate =      "Fri Aug 30 05:57:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/algorithms.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.mdpi.com/1999-4893/17/8/373",
  abstract =     "In this paper, algorithms for different types of
                 trigonometric power sums are developed and presented.
                 Although interesting in their own right, these
                 trigonometric power sums arise during the creation of
                 an algorithm for the four types of twisted
                 trigonometric power sums defined in the introduction.
                 The primary aim in evaluating these sums is to obtain
                 exact results in a rational form, as opposed to
                 standard or direct evaluation, which often results in
                 machine-dependent decimal values that can be affected
                 by round-off errors. Moreover, since the variable, m,
                 appearing in the denominators of the arguments of the
                 trigonometric functions in these sums, can remain
                 algebraic in the algorithms/codes, one can also obtain
                 polynomial solutions in powers of m and the variable r
                 that appears in the cosine factor accompanying the
                 trigonometric power. The degrees of these polynomials
                 are found to be dependent upon v, the value of the
                 trigonometric power in the sum, which must always be
                 specified.",
  acknowledgement = ack-nhfb,
  articleno =    "373",
  fjournal =     "Algorithms (Basel)",
  journal-URL =  "https://www.mdpi.com/journal/algorithms",
  remark =       "See \cite{Rosenberg:1963:FTP,Dronyuk:2025:ACG}.",
}


bibtype: misc
filename: elefunt.bib
label: Muller:2024:SNC
author: Jean-Michel Muller
title: Some notes on correct rounding of functions
pages: 31
day: 18
month: sep
monthnumber: 9
year: 2024
bibdate: Thu Sep 19 15:27:07 2024
bibtimestamp: 2024.09.19 15:27:07 ???
acknowledgement: ack-nhfb
howpublished: Attachment to STDS-754 mailing list
rawauthor: Jean-Michel Muller
rawtitle: Some notes on correct rounding of functions
entry:
@Misc{Muller:2024:SNC,
  author =       "Jean-Michel Muller",
  title =        "Some notes on correct rounding of functions",
  howpublished = "Attachment to STDS-754 mailing list",
  pages =        "31",
  day =          "18",
  month =        sep,
  year =         "2024",
  bibdate =      "Thu Sep 19 15:27:07 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Yoshida:2024:CIB
author: Toshio Yoshida and Yoshinori Adachi
title: Computation of incomplete beta function ratios $ I_x(a, b) $ with Deuflhard's algorithm
journal: j-NUMER-ALGORITHMS
volume: 97
number: 1
pages: 373--390
month: sep
monthnumber: 9
year: 2024
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-023-01707-6
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Wed Aug 7 06:17:56 MDT 2024
bibtimestamp: 2024.08.07 06:17:56 MDT
URL: https://link.springer.com/article/10.1007/s11075-023-01707-6
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
ajournal: Numer. Algorithms
journalURL: http://link.springer.com/journal/11075
rawauthor: Toshio Yoshida and Yoshinori Adachi
rawtitle: Computation of incomplete beta function ratios {$ I_x(a, b) $} with {Deuflhard}'s algorithm
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib

entry:
@Article{Yoshida:2024:CIB,
  author =       "Toshio Yoshida and Yoshinori Adachi",
  title =        "Computation of incomplete beta function ratios {$
                 I_x(a, b) $} with {Deuflhard}'s algorithm",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "97",
  number =       "1",
  pages =        "373--390",
  month =        sep,
  year =         "2024",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-023-01707-6",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Aug 7 06:17:56 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "https://link.springer.com/article/10.1007/s11075-023-01707-6",
  acknowledgement = ack-nhfb,
  ajournal =     "Numer. Algorithms",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}


bibtype: article
filename: elefunt.bib
label: Zaghloul:2024:CFI
author: Mofreh R. Zaghloul and Leen Alrawas
title: Calculation of Fresnel integrals of real and complex arguments up to 28 significant digits
journal: j-NUMER-ALGORITHMS
volume: 96
number: 2
pages: 489--506
month: jun
monthnumber: 6
year: 2024
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-023-01654-2
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Tue May 21 07:35:40 MDT 2024
bibtimestamp: 2024.05.21 07:35:40 MDT
URL: https://link.springer.com/article/10.1007/s11075-023-01654-2
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
ajournal: Numer. Algorithms
journalURL: http://link.springer.com/journal/11075
rawauthor: Mofreh R. Zaghloul and Leen Alrawas
rawtitle: Calculation of {Fresnel} integrals of real and complex arguments up to 28 significant digits
keywords:
complex cosine integral C(z); complex sine integral S(z); Fresnel functions; real cosine integral C(x); real sine integral S(x)

entry:
@Article{Zaghloul:2024:CFI,
  author =       "Mofreh R. Zaghloul and Leen Alrawas",
  title =        "Calculation of {Fresnel} integrals of real and complex
                 arguments up to 28 significant digits",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "96",
  number =       "2",
  pages =        "489--506",
  month =        jun,
  year =         "2024",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-023-01654-2",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Tue May 21 07:35:40 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "https://link.springer.com/article/10.1007/s11075-023-01654-2",
  acknowledgement = ack-nhfb,
  ajournal =     "Numer. Algorithms",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "complex cosine integral C(z); complex sine integral
                 S(z); Fresnel functions; real cosine integral C(x);
                 real sine integral S(x)",
}


bibtype: article
filename: elefunt.bib
label: Zaghloul:2024:EMP
author: Mofreh R. Zaghloul
journal: j-NUMER-ALGORITHMS
volume: 95
number: 3
pages: 1291--1308
month: mar
monthnumber: 3
year: 2024
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-023-01608-8
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Wed Feb 14 08:54:32 MST 2024
bibtimestamp: 2024.02.14 08:54:32 MST
URL: https://link.springer.com/article/10.1007/s11075-023-01608-8
fjournal: Numerical Algorithms
keywords: Dawson(x); erf(x); erfc(x)
acknowledgement: ack-nhfb
ajournal: Numer. Algorithms
journalURL: http://link.springer.com/journal/11075
rawauthor: Mofreh R. Zaghloul
title:
Efficient multiple-precision computation of the scaled complementary error function and the Dawson integral

rawtitle:
Efficient multiple-precision computation of the scaled complementary error function and the {Dawson} integral

entry:
@Article{Zaghloul:2024:EMP,
  author =       "Mofreh R. Zaghloul",
  title =        "Efficient multiple-precision computation of the scaled
                 complementary error function and the {Dawson}
                 integral",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "95",
  number =       "3",
  pages =        "1291--1308",
  month =        mar,
  year =         "2024",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-023-01608-8",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Feb 14 08:54:32 MST 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "https://link.springer.com/article/10.1007/s11075-023-01608-8",
  acknowledgement = ack-nhfb,
  ajournal =     "Numer. Algorithms",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Dawson(x); erf(x); erfc(x)",
}


bibtype: article
filename: elefunt.bib
label: Zaghloul:2024:ENA
author: Mofreh R. Zaghloul
journal: j-NUMER-ALGORITHMS
volume: 95
pages: 1--19
year: 2024
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-023-01727-2
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Tue Feb 20 15:50:26 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.02.20 15:50:26 ???
fjournal: Numerical Algorithms
keywords: Dawson(x); erf(x); erfc(x)
remark: [20-Feb-2024] Available at journal Web site, but not yet assigned to a journal volume.
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Mofreh R. Zaghloul
title:
Efficient numerical algorithms for multi-precision and multi-accuracy calculation of the error functions and Dawson integral with complex arguments

rawtitle:
Efficient numerical algorithms for multi-precision and multi-accuracy calculation of the error functions and {Dawson} integral with complex arguments

entry:
@Article{Zaghloul:2024:ENA,
  author =       "Mofreh R. Zaghloul",
  title =        "Efficient numerical algorithms for multi-precision and
                 multi-accuracy calculation of the error functions and
                 {Dawson} integral with complex arguments",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "95",
  number =       "??",
  pages =        "1--19",
  month =        "????",
  year =         "2024",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-023-01727-2",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Tue Feb 20 15:50:26 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Dawson(x); erf(x); erfc(x)",
  remark =       "[20-Feb-2024] Available at journal Web site, but not
                 yet assigned to a journal volume.",
}


bibtype: article
filename: elefunt.bib
label: Anonymous:2025:Cd
author: Anonymous
title: Correction
journal: j-J-STAT-COMPUT-SIMUL
volume: 95
number: 15
pages: 3397--3399
year: 2025
CODEN: JSCSAJ
DOI: https://doi.org/10.1080/00949655.2025.2525617
ISSNL: 0094-9655 OR 00949655
bibdate: Thu Oct 2 07:55:18 MDT 2025
bibtimestamp: 2025.10.02 07:55:18 MDT
note: See cite Das:2025:NMC.
fjournal: Journal of Statistical Computation and Simulation
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/gscs20
onlinedate: 16 Jul 2025
rawauthor: Anonymous
rawnote: See \cite{Das:2025:NMC}.
rawtitle: Correction
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul2020.bib

entry:
@Article{Anonymous:2025:Cd,
  author =       "Anonymous",
  title =        "Correction",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "95",
  number =       "15",
  pages =        "3397--3399",
  year =         "2025",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949655.2025.2525617",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Thu Oct 2 07:55:18 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul2020.bib",
  note =         "See \cite{Das:2025:NMC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
  onlinedate =   "16 Jul 2025",
}


bibtype: article
filename: elefunt.bib
label: Anton:2025:FER
author: Ramona Anton and Nicolae Mihalache and Francois Vigneron
title: Fast evaluation of real and complex polynomials
journal: j-NUM-MATH
volume: 157
number: 1
pages: 355--408
month: feb
monthnumber: 2
year: 2025
CODEN: NUMMA7
DOI: https://doi.org/10.1007/s00211-025-01454-x
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Sat Feb 1 09:47:51 MST 2025
bibtimestamp: 2025.02.01 09:47:51 MST
URL: https://link.springer.com/article/10.1007/s00211-025-01454-x
fjournal: Numerische Mathematik
keywords: Horner's nested form; number of multiplications to evaluate a polynomial
acknowledgement: ack-nhfb
ajournal: Num. Math.
journalURL: http://link.springer.com/journal/211
rawauthor: Ramona Anton and Nicolae Mihalache and Fran{\c{c}}ois Vigneron
rawtitle: Fast evaluation of real and complex polynomials
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/nummath2020.bib

entry:
@Article{Anton:2025:FER,
  author =       "Ramona Anton and Nicolae Mihalache and Fran{\c{c}}ois
                 Vigneron",
  title =        "Fast evaluation of real and complex polynomials",
  journal =      j-NUM-MATH,
  volume =       "157",
  number =       "1",
  pages =        "355--408",
  month =        feb,
  year =         "2025",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s00211-025-01454-x",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sat Feb 1 09:47:51 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath2020.bib",
  URL =          "https://link.springer.com/article/10.1007/s00211-025-01454-x",
  acknowledgement = ack-nhfb,
  ajournal =     "Num. Math.",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "Horner's nested form; number of multiplications to
                 evaluate a polynomial",
}


bibtype: article
filename: elefunt.bib
label: Das:2025:NMC
author: Abhranil Das
title: New methods to compute the generalized chi-square distribution
journal: j-J-STAT-COMPUT-SIMUL
volume: 95
number: 12
pages: 2608--2642
year: 2025
CODEN: JSCSAJ
DOI: https://doi.org/10.1080/00949655.2025.2501401
ISSNL: 0094-9655 OR 00949655
bibdate: Thu Aug 7 05:47:44 MDT 2025
bibtimestamp: 2025.08.07 05:47:44 MDT
note: See correction cite Anonymous:2025:Cd.
fjournal: Journal of Statistical Computation and Simulation
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/gscs20
onlinedate: 19 May 2025
rawauthor: Abhranil Das
rawnote: See correction \cite{Anonymous:2025:Cd}.
rawtitle: New methods to compute the generalized chi-square distribution
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul2020.bib

entry:
@Article{Das:2025:NMC,
  author =       "Abhranil Das",
  title =        "New methods to compute the generalized chi-square
                 distribution",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "95",
  number =       "12",
  pages =        "2608--2642",
  year =         "2025",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949655.2025.2501401",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Thu Aug 7 05:47:44 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul2020.bib",
  note =         "See correction \cite{Anonymous:2025:Cd}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
  onlinedate =   "19 May 2025",
}


bibtype: article
filename: elefunt.bib
label: Dronyuk:2025:ACG
author: Ivanna Dronyuk
title: Algorithms for Calculating Generalized Trigonometric Functions
journal: j-ALGORITHMS-BASEL
volume: 18
number: 2
pages: 2608--2642
month: feb
monthnumber: 2
year: 2025
CODEN: ALGOCH
DOI: https://doi.org/10.3390/a18020060
ISSN: 1999-4893 (electronic) OR 19994893 (electronic)
ISSNL: 1999-4893 OR 19994893
bibdate: Fri Feb 28 06:02:21 MST 2025
bibtimestamp: 2025.02.28 06:02:21 MST
URL: https://www.mdpi.com/1999-4893/18/2/60
fjournal: Algorithms (Basel)
remark: See cite Rosenberg:1963:FTP,Kowalenko:2024:AVT.
acknowledgement: ack-nhfb
articleno: 60
journalURL: https://www.mdpi.com/journal/algorithms
rawauthor: Ivanna Dronyuk
rawtitle: Algorithms for Calculating Generalized Trigonometric Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/algorithms.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Dronyuk:2025:ACG,
  author =       "Ivanna Dronyuk",
  title =        "Algorithms for Calculating Generalized Trigonometric
                 Functions",
  journal =      j-ALGORITHMS-BASEL,
  volume =       "18",
  number =       "2",
  month =        feb,
  year =         "2025",
  CODEN =        "ALGOCH",
  DOI =          "https://doi.org/10.3390/a18020060",
  ISSN =         "1999-4893 (electronic)",
  ISSN-L =       "1999-4893",
  bibdate =      "Fri Feb 28 06:02:21 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/algorithms.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.mdpi.com/1999-4893/18/2/60",
  acknowledgement = ack-nhfb,
  articleno =    "60",
  fjournal =     "Algorithms (Basel)",
  journal-URL =  "https://www.mdpi.com/journal/algorithms",
  pagecount =    "13",
  remark =       "See \cite{Rosenberg:1963:FTP,Kowalenko:2024:AVT}.",
}


bibtype: article
filename: elefunt.bib
label: Dunster:2025:NAC
author: T. M. Dunster and A. Gil and J. Segura
title: A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex plane
journal: j-BIT-NUM-MATH
volume: 65
number: 2
pages: ??--??
month: jun
monthnumber: 6
year: 2025
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/s10543-025-01065-w
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jul 16 14:17:01 MDT 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.07.16 14:17:01 MDT
URL: https://link.springer.com/article/10.1007/s10543-025-01065-w
fjournal: BIT Numerical Mathematics
acknowledgement: ack-nhfb
ajournal: Bit Num. Math.
articleno: 21
journalURL: http://link.springer.com/journal/10543
rawauthor: T. M. Dunster and A. Gil and J. Segura
rawtitle: A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex plane
entry:
@Article{Dunster:2025:NAC,
  author =       "T. M. Dunster and A. Gil and J. Segura",
  title =        "A numerical algorithm for computing the zeros of
                 parabolic cylinder functions in the complex plane",
  journal =      j-BIT-NUM-MATH,
  volume =       "65",
  number =       "2",
  pages =        "??--??",
  month =        jun,
  year =         "2025",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-025-01065-w",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jul 16 14:17:01 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://link.springer.com/article/10.1007/s10543-025-01065-w",
  acknowledgement = ack-nhfb,
  ajournal =     "Bit Num. Math.",
  articleno =    "21",
  fjournal =     "BIT Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: article
filename: elefunt.bib
label: Guseinov:2025:CEI
author: I. I. Guseinov and B. A. Mamedov
journal: j-J-MATH-CHEM
volume: 63
number: 2
pages: 650--650
month: feb
monthnumber: 2
year: 2025
CODEN: JMCHEG
DOI: https://doi.org/10.1007/s10910-024-01686-6
ISSN: 0259-9791 (print), 1572-8897 (electronic) OR 02599791 (print), 15728897 (electronic)
ISSNL: 0259-9791 OR 02599791
bibdate: Tue Mar 4 11:35:40 MST 2025
bibtimestamp: 2025.03.04 11:35:40 MST
note: See cite Guseinov:2004:EIG.
URL: https://link.springer.com/article/10.1007/s10910-024-01686-6
fjournal: Journal of Mathematical Chemistry
acknowledgement: ack-nhfb
ajournal: J. Math. Chem.
journalURL: http://link.springer.com/journal/10910
rawauthor: I. I. Guseinov and B. A. Mamedov
rawnote: See \cite{Guseinov:2004:EIG}.
title:
Correction to: Evaluation of incomplete gamma functions using downward recursion and analytical relations

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathchem.bib

rawtitle:
Correction to: {Evaluation} of incomplete gamma functions using downward recursion and analytical relations

entry:
@Article{Guseinov:2025:CEI,
  author =       "I. I. Guseinov and B. A. Mamedov",
  title =        "Correction to: {Evaluation} of incomplete gamma
                 functions using downward recursion and analytical
                 relations",
  journal =      j-J-MATH-CHEM,
  volume =       "63",
  number =       "2",
  pages =        "650--650",
  month =        feb,
  year =         "2025",
  CODEN =        "JMCHEG",
  DOI =          "https://doi.org/10.1007/s10910-024-01686-6",
  ISSN =         "0259-9791 (print), 1572-8897 (electronic)",
  ISSN-L =       "0259-9791",
  bibdate =      "Tue Mar 4 11:35:40 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathchem.bib",
  note =         "See \cite{Guseinov:2004:EIG}.",
  URL =          "https://link.springer.com/article/10.1007/s10910-024-01686-6",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Math. Chem.",
  fjournal =     "Journal of Mathematical Chemistry",
  journal-URL =  "http://link.springer.com/journal/10910",
}


bibtype: article
filename: elefunt.bib
label: Kokosinski:2025:FAA
author: Zbigniew Kokosinski and Pawel Gepner and Nataliia Gavkalova
title: Fast and accurate approximation algorithms for computing floating point square root
journal: j-NUMER-ALGORITHMS
volume: 99
number: 4
pages: 1791--1804
month: aug
monthnumber: 8
year: 2025
CODEN: NUALEG
DOI: https://doi.org/10.1007/s11075-024-01932-7
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Wed Jul 16 11:11:45 MDT 2025
bibtimestamp: 2025.07.16 11:11:45 MDT
URL: https://link.springer.com/article/10.1007/s11075-024-01932-7
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
ajournal: Numer. Algorithms
journalURL: http://link.springer.com/journal/11075
rawauthor: Zbigniew Kokosi{\'n}ski and Pawe{\l} Gepner and Nataliia Gavkalova
rawtitle: Fast and accurate approximation algorithms for computing floating point square root
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib

entry:
@Article{Kokosinski:2025:FAA,
  author =       "Zbigniew Kokosi{\'n}ski and Pawe{\l} Gepner and
                 Nataliia Gavkalova",
  title =        "Fast and accurate approximation algorithms for
                 computing floating point square root",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "99",
  number =       "4",
  pages =        "1791--1804",
  month =        aug,
  year =         "2025",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-024-01932-7",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Jul 16 11:11:45 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "https://link.springer.com/article/10.1007/s11075-024-01932-7",
  acknowledgement = ack-nhfb,
  ajournal =     "Numer. Algorithms",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}


bibtype: article
filename: elefunt.bib
label: Marcheva:2025:QCD
author: Plamena I. Marcheva and Ivan K. Ivanov and Stoil I. Ivanov
journal: j-ALGORITHMS-BASEL
volume: 18
number: 4
pages: 1791--1804
month: apr
monthnumber: 4
year: 2025
CODEN: ALGOCH
DOI: https://doi.org/10.3390/a18040205
ISSN: 1999-4893 (electronic) OR 19994893 (electronic)
ISSNL: 1999-4893 OR 19994893
bibdate: Mon Apr 28 09:25:31 MDT 2025
bibtimestamp: 2025.04.28 09:25:31 MDT
URL: https://www.mdpi.com/1999-4893/18/4/205
fjournal: Algorithms (Basel)
acknowledgement: ack-nhfb
articleno: 205
journalURL: https://www.mdpi.com/journal/algorithms
rawauthor: Plamena I. Marcheva and Ivan K. Ivanov and Stoil I. Ivanov
title:
On the Q-Convergence and Dynamics of a Modified Weierstrass Method for the Simultaneous Extraction of Polynomial Zeros

bibsource:
https://www.math.utah.edu/pub/tex/bib/algorithms.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
On the {Q}-Convergence and Dynamics of a Modified {Weierstrass} Method for the Simultaneous Extraction of Polynomial Zeros

entry:
@Article{Marcheva:2025:QCD,
  author =       "Plamena I. Marcheva and Ivan K. Ivanov and Stoil I.
                 Ivanov",
  title =        "On the {Q}-Convergence and Dynamics of a Modified
                 {Weierstrass} Method for the Simultaneous Extraction of
                 Polynomial Zeros",
  journal =      j-ALGORITHMS-BASEL,
  volume =       "18",
  number =       "4",
  month =        apr,
  year =         "2025",
  CODEN =        "ALGOCH",
  DOI =          "https://doi.org/10.3390/a18040205",
  ISSN =         "1999-4893 (electronic)",
  ISSN-L =       "1999-4893",
  bibdate =      "Mon Apr 28 09:25:31 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/algorithms.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.mdpi.com/1999-4893/18/4/205",
  acknowledgement = ack-nhfb,
  articleno =    "205",
  fjournal =     "Algorithms (Basel)",
  journal-URL =  "https://www.mdpi.com/journal/algorithms",
  pagecount =    "??",
}


bibtype: article
filename: elefunt.bib
label: Ozay:2025:CCS
author: S. Ozay and S. Akdemir and E. Oztekin
title: The coupling coefficients with six parameters and the generalized hypergeometric functions
journal: j-COMP-PHYS-COMM
volume: 315
pages: ??--??
month: oct
monthnumber: 10
year: 2025
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/j.cpc.2025.109656
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Aug 4 11:17:58 MDT 2025
bibtimestamp: 2025.08.04 11:17:58 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0010465525001584
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
ajournal: Comput. Phys. Commun.
articleno: 109656
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: S. {\"O}zay and S. Akdemir and E. {\"O}ztekin
rawtitle: The coupling coefficients with six parameters and the generalized hypergeometric functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib; https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathematica.bib

keywords:
angular momentum; binomial coefficients; Clebsch-Gordon coefficients; Gaunt coefficients; generalized hypergeometric functions; Mathematica; spherical harmonics; Wigner 3-j symbols; Wigner 6-j symbols; Wigner 9-j symbols

entry:
@Article{Ozay:2025:CCS,
  author =       "S. {\"O}zay and S. Akdemir and E. {\"O}ztekin",
  title =        "The coupling coefficients with six parameters and the
                 generalized hypergeometric functions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "315",
  number =       "??",
  pages =        "??--??",
  month =        oct,
  year =         "2025",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2025.109656",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Aug 4 11:17:58 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
                 https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465525001584",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys. Commun.",
  articleno =    "109656",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  keywords =     "angular momentum; binomial coefficients;
                 Clebsch-Gordon coefficients; Gaunt coefficients;
                 generalized hypergeometric functions; Mathematica;
                 spherical harmonics; Wigner 3-j symbols; Wigner 6-j
                 symbols; Wigner 9-j symbols",
}


bibtype: article
filename: elefunt.bib
label: Trim:2025:AEF
author: Sean J. Trim and Raymond J. Spiteri
journal: j-TOMS
volume: 51
number: 1
pages: 6:1--6:??
month: mar
monthnumber: 3
year: 2025
CODEN: ACMSCU
DOI: https://doi.org/10.1145/3709136
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Apr 10 08:03:40 MDT 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 2025.04.10 08:03:40 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
ajournal: ACM Trans. Math. Softw.
articleno: 6
journalURL: https://dl.acm.org/loi/toms
rawauthor: Sean J. Trim and Raymond J. Spiteri
title:
Algorithm 1054: pkg ellipFor, a Fortran Software Library for Legendre Elliptic Integrals and Jacobi Elliptic Functions with Generalized Input Arguments

abstract:
Legendre elliptic integrals and Jacobi elliptic functions arise in multiple applications within the physical sciences, including oscillations, celestial mechanics, and geodynamics. In this study, we describe the Fortran library ellipFor capable of evaluating the following for generalized input values: (1) the complete Legendre elliptic integrals of the first and second kinds, (2) the incomplete Legendre elliptic integrals of the first and second kinds, and (3) the principal Jacobi elliptic functions. Our software builds upon previously developed Fortran routines, which were designed with restrictions on input parameters that may be limiting in applications. Our routines apply multiple transformations to allow for more general input values, such as elliptic moduli greater than unity for points 1--3, arbitrary real Jacobi amplitudes for points 1--2, and complex first arguments for point 3. In addition, our routines are thread-safe, allowing for parallel computations. Our routines were compared with values from the computer algebra system SageMath over a wide range of input parameters. Values from ellipFor and SageMath agreed to within tolerances commensurate with the limitations of floating-point arithmetic used for the elliptic integrals and Jacobi elliptic functions listed in points 1, 2, and 3 above for generalized input arguments.

rawabstract:
Legendre elliptic integrals and Jacobi elliptic functions arise in multiple applications within the physical sciences, including oscillations, celestial mechanics, and geodynamics. In this study, we describe the Fortran library ellipFor capable of evaluating the following for generalized input values: (1) the complete Legendre elliptic integrals of the first and second kinds, (2) the incomplete Legendre elliptic integrals of the first and second kinds, and (3) the principal Jacobi elliptic functions. Our software builds upon previously developed Fortran routines, which were designed with restrictions on input parameters that may be limiting in applications. Our routines apply multiple transformations to allow for more general input values, such as elliptic moduli greater than unity for points 1--3, arbitrary real Jacobi amplitudes for points 1--2, and complex first arguments for point 3. In addition, our routines are thread-safe, allowing for parallel computations. Our routines were compared with values from the computer algebra system SageMath over a wide range of input parameters. Values from ellipFor and SageMath agreed to within tolerances commensurate with the limitations of floating-point arithmetic used for the elliptic integrals and Jacobi elliptic functions listed in points 1, 2, and 3 above for generalized input arguments.

rawtitle:
Algorithm 1054: \pkg{ellipFor}, a {Fortran} Software Library for {Legendre} Elliptic Integrals and {Jacobi} Elliptic Functions with Generalized Input Arguments

entry:
@Article{Trim:2025:AEF,
  author =       "Sean J. Trim and Raymond J. Spiteri",
  title =        "Algorithm 1054: \pkg{ellipFor}, a {Fortran} Software
                 Library for {Legendre} Elliptic Integrals and {Jacobi}
                 Elliptic Functions with Generalized Input Arguments",
  journal =      j-TOMS,
  volume =       "51",
  number =       "1",
  pages =        "6:1--6:??",
  month =        mar,
  year =         "2025",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3709136",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 10 08:03:40 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Legendre elliptic integrals and Jacobi elliptic
                 functions arise in multiple applications within the
                 physical sciences, including oscillations, celestial
                 mechanics, and geodynamics. In this study, we describe
                 the Fortran library ellipFor capable of evaluating the
                 following for generalized input values: (1) the
                 complete Legendre elliptic integrals of the first and
                 second kinds, (2) the incomplete Legendre elliptic
                 integrals of the first and second kinds, and (3) the
                 principal Jacobi elliptic functions. Our software
                 builds upon previously developed Fortran routines,
                 which were designed with restrictions on input
                 parameters that may be limiting in applications. Our
                 routines apply multiple transformations to allow for
                 more general input values, such as elliptic moduli
                 greater than unity for points 1--3, arbitrary real
                 Jacobi amplitudes for points 1--2, and complex first
                 arguments for point 3. In addition, our routines are
                 thread-safe, allowing for parallel computations. Our
                 routines were compared with values from the computer
                 algebra system SageMath over a wide range of input
                 parameters. Values from ellipFor and SageMath agreed to
                 within tolerances commensurate with the limitations of
                 floating-point arithmetic used for the elliptic
                 integrals and Jacobi elliptic functions listed in
                 points 1, 2, and 3 above for generalized input
                 arguments.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Walczyk:2025:OAX
author: Cezary J. Walczyk and Leonid V. Moroz and Volodymyr Samotyy and Jan L. Cieslinski
title: Optimal Approximation of the $ 1 / x $ Function using Chebyshev Polynomials and Magic Constants
journal: j-TOMS
volume: 51
number: 1
pages: 2:1--2:??
month: mar
monthnumber: 3
year: 2025
CODEN: ACMSCU
DOI: https://doi.org/10.1145/3708472
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Apr 10 08:03:40 MDT 2025
bibtimestamp: 2025.04.10 08:03:40 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
ajournal: ACM Trans. Math. Softw.
articleno: 2
journalURL: https://dl.acm.org/loi/toms
rawauthor: Cezary J. Walczyk and Leonid V. Moroz and Volodymyr Samotyy and Jan L. Cie{\'s}li{\'n}ski
rawtitle: Optimal Approximation of the $ 1 / x $ Function using {Chebyshev} Polynomials and Magic Constants
abstract:
In this article we analyze low-cost accurate approximation of the function $ 1 / x $ using Chebyshev polynomials of the first kind and minimizing number of elementary operations in computer codes (in particular, by using the so-called magic constants). It is shown that Newton-Raphson iterative method is not optimal and a new approach is proposed. We prove that optimal Chebyshev polynomials can be factorized in terms of Chebyshev polynomials of lower order which leads to new optimal iteration schemes. We also construct a family of new algorithms by dividing the considered interval into sub-intervals where different magic constants and multiplicative factors are used (in order to increase the accuracy). Theoretical considerations and proofs are completed with numerical tests on three types of microcontroller processors.

rawabstract:
In this article we analyze low-cost accurate approximation of the function $ 1 / x $ using Chebyshev polynomials of the first kind and minimizing number of elementary operations in computer codes (in particular, by using the so-called magic constants). It is shown that Newton-Raphson iterative method is not optimal and a new approach is proposed. We prove that optimal Chebyshev polynomials can be factorized in terms of Chebyshev polynomials of lower order which leads to new optimal iteration schemes. We also construct a family of new algorithms by dividing the considered interval into sub-intervals where different magic constants and multiplicative factors are used (in order to increase the accuracy). Theoretical considerations and proofs are completed with numerical tests on three types of microcontroller processors.

entry:
@Article{Walczyk:2025:OAX,
  author =       "Cezary J. Walczyk and Leonid V. Moroz and Volodymyr
                 Samotyy and Jan L. Cie{\'s}li{\'n}ski",
  title =        "Optimal Approximation of the $ 1 / x $ Function using
                 {Chebyshev} Polynomials and Magic Constants",
  journal =      j-TOMS,
  volume =       "51",
  number =       "1",
  pages =        "2:1--2:??",
  month =        mar,
  year =         "2025",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3708472",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 10 08:03:40 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this article we analyze low-cost accurate
                 approximation of the function $ 1 / x $ using Chebyshev
                 polynomials of the first kind and minimizing number of
                 elementary operations in computer codes (in particular,
                 by using the so-called magic constants). It is shown
                 that Newton-Raphson iterative method is not optimal and
                 a new approach is proposed. We prove that optimal
                 Chebyshev polynomials can be factorized in terms of
                 Chebyshev polynomials of lower order which leads to new
                 optimal iteration schemes. We also construct a family
                 of new algorithms by dividing the considered interval
                 into sub-intervals where different magic constants and
                 multiplicative factors are used (in order to increase
                 the accuracy). Theoretical considerations and proofs
                 are completed with numerical tests on three types of
                 microcontroller processors.",
  accepted =     "4 December 2024",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  received =     "3 September 2022",
  revised =      "25 September 2024",
}


bibtype: article
filename: elefunt.bib
label: Zhang:2025:RRH
author: Yangyi Zhang and Xianglong Wang and Lei Chen and Fengwei An
journal: j-IEEE-TRANS-VLSI-SYST
volume: 33
number: 10
pages: 2690--2701
year: 2025
CODEN: IEVSE9
DOI: https://doi.org/10.1109/TVLSI.2025.3566433
ISSN: 1063-8210 (print), 1557-9999 (electronic) OR 10638210 (print), 15579999 (electronic)
ISSNL: 1063-8210 OR 10638210
bibdate: Wed Oct 1 06:40:18 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.10.01 06:40:18 ???
fjournal: IEEE Transactions on Very Large Scale Integration (VLSI) Systems
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/issues?punumber=92
rawauthor: Yangyi Zhang and Xianglong Wang and Lei Chen and Fengwei An
title:
ReHIT: Reconfigurable High-Radix Iterative-Taylor Architecture for Ultraprecise Logarithm / Exponential Functions in FPGA-Based Softmax Accelerators

keywords:
Accuracy; Approximation algorithms; Architecture; Computer architecture; exponential function; Field programmable gate arrays; field-programmable gate array (FPGA); Hardware; logarithm function; Logic; Polynomials; softmax function; Table lookup; Taylor formula; Taylor series; Technological innovation

rawtitle:
{ReHIT}: Reconfigurable High-Radix Iterative-Taylor Architecture for Ultraprecise Logarithm\slash Exponential Functions in {FPGA}-Based {Softmax} Accelerators

entry:
@Article{Zhang:2025:RRH,
  author =       "Yangyi Zhang and Xianglong Wang and Lei Chen and
                 Fengwei An",
  title =        "{ReHIT}: Reconfigurable High-Radix Iterative-Taylor
                 Architecture for Ultraprecise Logarithm\slash
                 Exponential Functions in {FPGA}-Based {Softmax}
                 Accelerators",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "33",
  number =       "10",
  pages =        "2690--2701",
  year =         "2025",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2025.3566433",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
  keywords =     "Accuracy; Approximation algorithms; Architecture;
                 Computer architecture; exponential function; Field
                 programmable gate arrays; field-programmable gate array
                 (FPGA); Hardware; logarithm function; Logic;
                 Polynomials; softmax function; Table lookup; Taylor
                 formula; Taylor series; Technological innovation",
}


bibtype: article
filename: elefunt.bib
label: Zullo:2025:LFP
author: Federico Zullo
title: Lommel functions, Pade approximants and hypergeometric functions
journal: j-APPL-NUM-MATH
volume: 209
pages: 275--284
month: mar
monthnumber: 3
year: 2025
CODEN: ANMAEL
DOI: https://doi.org/10.1016/j.apnum.2024.11.003
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
bibdate: Sat Dec 28 08:12:54 MST 2024
bibtimestamp: 2024.12.28 08:12:54 MST
URL: http://www.sciencedirect.com/science/article/pii/S016892742400299X
fjournal: Applied Numerical Mathematics: Transactions of IMACS
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274
rawauthor: Federico Zullo
rawtitle: {Lommel} functions, {Pad{\'e}} approximants and hypergeometric functions
entry:
@Article{Zullo:2025:LFP,
  author =       "Federico Zullo",
  title =        "{Lommel} functions, {Pad{\'e}} approximants and
                 hypergeometric functions",
  journal =      j-APPL-NUM-MATH,
  volume =       "209",
  number =       "??",
  pages =        "275--284",
  month =        mar,
  year =         "2025",
  CODEN =        "ANMAEL",
  DOI =          "https://doi.org/10.1016/j.apnum.2024.11.003",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Sat Dec 28 08:12:54 MST 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S016892742400299X",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274",
}


bibtype: book
filename: elefunt.bib
label: Jones:1984:CFA
author: William B. (William Branham) Jones and Wolfgang J. Thron
booktitle: Continued Fractions: Analytic Theory and Applications
title: Continued Fractions: Analytic Theory and Applications
volume: 11
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: xxviii + 428
year: 1984
DOI: https://doi.org/10.1017/CBO9780511759550
ISBN: 0-521-30231-5 OR 0521302315
ISBN13: 978-0-521-30231-9 OR 9780521302319
LCCN: QA295 .J64 1984
bibdate: Sat Jul 10 09:47:15 MDT 2010
bibtimestamp: 2010.07.10 09:47:15 MDT
series: Encyclopedia of mathematics and its applications
acknowledgement: ack-nhfb
rawauthor: William B. (William Branham) Jones and Wolfgang J. Thron
rawbooktitle: Continued Fractions: Analytic Theory and Applications
rawtitle: Continued Fractions: Analytic Theory and Applications
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib; z3950.bibsys.no:2100/BIBSYS

TOC:
Editor's Statement Section Editor's Foreword Introduction by Peter Henrici Preface Symbols 1: Introduction 1.1 History 1.1.1 Beginnings 1.1.2 Number-Theoretic Results 1.1.3 Analytic Theory 1.2 Overview of Contents 2: Elementary Properties of Continued Fractions 2.1 Preliminaries 2.1.1 Basic Definitions and Theorems 2.1.2 Regular Continued Fractions 2.1.3 Other Continued-Fraction Expansions 2.1.4 Algorithms for Computing Approximants ldots 2.2 Sequences Generated by Linear Fractional Transformations 2.3 Equivalence Transformations 2.3.1 Equivalent Continued Fractions 2.3.2 Euler's [1748] Connection between Continued Fractions and Infinite Series 2.4 Contractions and Extensions 2.4.1 Contraction of Continued Fractions 2.4.2 Even Part of a Continued Fraction 2.4.3 Odd Part of a Continued Fraction 2.4.4 Extension of a Continued Fraction 3: Periodic Continued Fractions 3.1 Introduction 3.2 Convergence of Periodic Continued Fractions ldots 3.3 Dual Periodic Continued Fractions 4: Convergence of Continued Fractions 4.1 Introduction 4.2 Element Regions, Value Regions, and Sequences of Nested Circular Disks 4.3 Necessary Conditions for Convergence 4.3.1 Stern--Stolz Theorem 4.3.2 Necessary Conditions for Best Value Regions and Convergence Regions 4.4 Sufficient Conditions for Convergence: Constant Elements 4.4.1 Classical Results and Generalizations 4.4.2 Parabolic Convergence Regions 4.4.3 Convergence Neighborhoods for K(an/1) ldots 4.4.4 Twin Convergence Regions 4.4.5 Miscellaneous Convergence Criteria 4.5 Sufficient Conditions for Convergence Variable Elements 4.5.1 Introduction Classification of Continued Fractions 4.5.2 Regular C-fractions 4.5.3 Positive Definite/-fractions 4.5.4 General T-fractions 5: Methods for Representing Analytic Functions by Continued Fractions 5.1 Correspondence 5.2 Three-Term Recurrence Relations 5.3 Minimal Solutions of Three-Term Recurrence Relations 5.4 Uniform Convergence 5.5 Pade Table 5.5.1 Pade Approximants 5.5.2 Multiple-Point Pade Tables 6: Representations of Analytic Functions by Continued Fractions 6.1 Continued Fractions of Gauss 6.1.1 Hypergeometric Functions $F(a, b; c; z)$ ldots 6.1.2 Confluent Hypergeometric Functions $Phi (b; c; z)$ 6.1.3 Confluent Hypergeometric Functions $Psi (c; z)$ 6.1.4 Confluent Hypergeometric Functions $Omega (a, b; z)$ 6.2 Representations from Minimal Solutions 7: Types of Corresponding Continued Fractions and Related Algorithms 7.1 Regular $C$-Fractions 7.1.1 Correspondence of Regular $C$-Fractions 7.1.2 Quotient-Difference Algorithm 7.1.3 $g$-Fractions 7.2 Associated Continued Fractions and $J$-Fractions 7.2.1 Correspondence of Associated Continued Fractions 7.2.2 $J$-Fractions and Orthogonal Polynomials 7.3 General $T$-Fractions 7.3.1 Correspondence of General $T$-Fractions 7.3.2 FG Algorithms 7.3.3 Representation of Analytic Functions 7.4 Stable Polynomials 8: Truncation-Error Analysis 8.1 Introduction 8.2 General Theory of Inclusion Regions and Truncation Errors 8.3 Explicit Results on Inclusion Regions and Truncation-Error Bounds 8.4 Accelerating Convergence 9: Asymptotic Expansions and Moment Problems 9.1 Introduction 9.2 Moment Problems 9.3 Integral Representations of Continued Fractions 9.4 Asymptotic Expansions for Continued Fractions 9.5 Solutions of the Moment Problems 9.6 Representations of Analytic Functions 10: Numerical Stability in Evaluating Continued Fractions 10.1 General Estimates of Relative Roundoff Error 10.2 Methods for Estimating $g_^(n)$ 10.3 Applications 11: Application of Continued Fractions to Birth--Death Processes 11.1 Birth--Death Processes 11.2 Computational Procedures 12: Miscellaneous Results 12.1 $T$-Fraction Expansions for Families of Bounded Functions 12.2 $T$-Fractions Corresponding to Rational Functions 12.3 Location of Singular Points of Analytic Functions Represented by Continued Fractions 12.4 Univalence of Functions Represented by Continued Fractions Appendix A. Classification of Special Types of Continued Fractions Appendix B. Additional Results on Minimal Solutions of Three-Term Recurrence Relations Bibliography Author Index Subject Index

rawTOC:
Editor's Statement \\ Section Editor's Foreword \\ Introduction by Peter Henrici \\ Preface \\ Symbols \\ 1: Introduction \\ 1.1 History \\ 1.1.1 Beginnings \\ 1.1.2 Number-Theoretic Results \\ 1.1.3 Analytic Theory \\ 1.2 Overview of Contents \\ \\ 2: Elementary Properties of Continued Fractions \\ 2.1 Preliminaries \\ 2.1.1 Basic Definitions and Theorems \\ 2.1.2 Regular Continued Fractions \\ 2.1.3 Other Continued-Fraction Expansions \\ 2.1.4 Algorithms for Computing Approximants \ldots{} \\ 2.2 Sequences Generated by Linear Fractional Transformations \\ 2.3 Equivalence Transformations \\ 2.3.1 Equivalent Continued Fractions \\ 2.3.2 Euler's [1748] Connection between Continued Fractions and Infinite Series \\ 2.4 Contractions and Extensions \\ 2.4.1 Contraction of Continued Fractions \\ 2.4.2 Even Part of a Continued Fraction \\ 2.4.3 Odd Part of a Continued Fraction \\ 2.4.4 Extension of a Continued Fraction \\ \\ 3: Periodic Continued Fractions \\ 3.1 Introduction \\ 3.2 Convergence of Periodic Continued Fractions \ldots{} \\ 3.3 Dual Periodic Continued Fractions \\ \\ 4: Convergence of Continued Fractions \\ 4.1 Introduction \\ 4.2 Element Regions, Value Regions, and Sequences of Nested Circular Disks \\ 4.3 Necessary Conditions for Convergence \\ 4.3.1 Stern--Stolz Theorem \\ 4.3.2 Necessary Conditions for Best Value Regions and Convergence Regions \\ 4.4 Sufficient Conditions for Convergence: Constant Elements \\ 4.4.1 Classical Results and Generalizations \\ 4.4.2 Parabolic Convergence Regions \\ 4.4.3 Convergence Neighborhoods for K(an/1) \ldots{} \\ 4.4.4 Twin Convergence Regions \\ 4.4.5 Miscellaneous Convergence Criteria \\ 4.5 Sufficient Conditions for Convergence \\ Variable Elements \\ 4.5.1 Introduction \\ Classification of Continued Fractions \\ 4.5.2 Regular C-fractions \\ 4.5.3 Positive Definite/-fractions \\ 4.5.4 General T-fractions \\ \\ 5: Methods for Representing Analytic Functions by Continued Fractions \\ 5.1 Correspondence \\ 5.2 Three-Term Recurrence Relations \\ 5.3 Minimal Solutions of Three-Term Recurrence Relations \\ 5.4 Uniform Convergence \\ 5.5 Pad{\'e} Table \\ 5.5.1 Pad{\'e} Approximants \\ 5.5.2 Multiple-Point Pad{\'e} Tables \\ \\ 6: Representations of Analytic Functions by Continued Fractions \\ 6.1 Continued Fractions of Gauss \\ 6.1.1 Hypergeometric Functions $F(a, b; c; z)$ \ldots{} \\ 6.1.2 Confluent Hypergeometric Functions $\Phi(b; c; z)$ \\ 6.1.3 Confluent Hypergeometric Functions $\Psi(c; z)$ \\ 6.1.4 Confluent Hypergeometric Functions $\Omega(a, b; z)$ \\ 6.2 Representations from Minimal Solutions \\ \\ 7: Types of Corresponding Continued \\ Fractions and Related Algorithms \\ 7.1 Regular $C$-Fractions \\ 7.1.1 Correspondence of Regular $C$-Fractions \\ 7.1.2 Quotient-Difference Algorithm \\ 7.1.3 $g$-Fractions \\ 7.2 Associated Continued Fractions and $J$-Fractions \\ 7.2.1 Correspondence of Associated Continued Fractions \\ 7.2.2 $J$-Fractions and Orthogonal Polynomials \\ 7.3 General $T$-Fractions \\ 7.3.1 Correspondence of General $T$-Fractions \\ 7.3.2 FG Algorithms \\ 7.3.3 Representation of Analytic Functions \\ 7.4 Stable Polynomials \\ \\ 8: Truncation-Error Analysis \\ 8.1 Introduction \\ 8.2 General Theory of Inclusion Regions and Truncation Errors \\ 8.3 Explicit Results on Inclusion Regions and Truncation-Error Bounds \\ 8.4 Accelerating Convergence \\ \\ 9: Asymptotic Expansions and Moment Problems \\ 9.1 Introduction \\ 9.2 Moment Problems \\ 9.3 Integral Representations of Continued Fractions \\ 9.4 Asymptotic Expansions for Continued Fractions \\ 9.5 Solutions of the Moment Problems \\ 9.6 Representations of Analytic Functions \\ \\ 10: Numerical Stability in Evaluating Continued Fractions \\ 10.1 General Estimates of Relative Roundoff Error \\ 10.2 Methods for Estimating $g_^{(n)}$ \\ 10.3 Applications \\ \\ 11: Application of Continued Fractions to \\ Birth--Death Processes \\ 11.1 Birth--Death Processes \\ 11.2 Computational Procedures \\ \\ 12: Miscellaneous Results \\ 12.1 $T$-Fraction Expansions for Families of Bounded Functions \\ 12.2 $T$-Fractions Corresponding to Rational Functions \\ 12.3 Location of Singular Points of Analytic Functions Represented by Continued Fractions \\ 12.4 Univalence of Functions Represented by Continued Fractions \\ \\ Appendix A. Classification of Special Types of Continued Fractions \\ Appendix B. Additional Results on Minimal Solutions of Three-Term Recurrence Relations \\ Bibliography \\ Author Index \\ Subject Index

entry:
@Book{Jones:1984:CFA,
  author =       "William B. (William Branham) Jones and Wolfgang J.
                 Thron",
  booktitle =    "Continued Fractions: Analytic Theory and
                 Applications",
  title =        "Continued Fractions: Analytic Theory and
                 Applications",
  volume =       "11",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xxviii + 428",
  year =         "1984",
  DOI =          "https://doi.org/10.1017/CBO9780511759550",
  ISBN =         "0-521-30231-5",
  ISBN-13 =      "978-0-521-30231-9",
  LCCN =         "QA295 .J64 1984",
  bibdate =      "Sat Jul 10 09:47:15 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  series =       "Encyclopedia of mathematics and its applications",
  acknowledgement = ack-nhfb,
  tableofcontents = "Editor's Statement \\
                 Section Editor's Foreword \\
                 Introduction by Peter Henrici \\
                 Preface \\
                 Symbols \\
                 1: Introduction \\
                 1.1 History \\
                 1.1.1 Beginnings \\
                 1.1.2 Number-Theoretic Results \\
                 1.1.3 Analytic Theory \\
                 1.2 Overview of Contents \\
                 \\
                 2: Elementary Properties of Continued Fractions \\
                 2.1 Preliminaries \\
                 2.1.1 Basic Definitions and Theorems \\
                 2.1.2 Regular Continued Fractions \\
                 2.1.3 Other Continued-Fraction Expansions \\
                 2.1.4 Algorithms for Computing Approximants \ldots{}
                 \\
                 2.2 Sequences Generated by Linear Fractional
                 Transformations \\
                 2.3 Equivalence Transformations \\
                 2.3.1 Equivalent Continued Fractions \\
                 2.3.2 Euler's [1748] Connection between Continued
                 Fractions and Infinite Series \\
                 2.4 Contractions and Extensions \\
                 2.4.1 Contraction of Continued Fractions \\
                 2.4.2 Even Part of a Continued Fraction \\
                 2.4.3 Odd Part of a Continued Fraction \\
                 2.4.4 Extension of a Continued Fraction \\
                 \\
                 3: Periodic Continued Fractions \\
                 3.1 Introduction \\
                 3.2 Convergence of Periodic Continued Fractions
                 \ldots{} \\
                 3.3 Dual Periodic Continued Fractions \\
                 \\
                 4: Convergence of Continued Fractions \\
                 4.1 Introduction \\
                 4.2 Element Regions, Value Regions, and Sequences of
                 Nested Circular Disks \\
                 4.3 Necessary Conditions for Convergence \\
                 4.3.1 Stern--Stolz Theorem \\
                 4.3.2 Necessary Conditions for Best Value Regions and
                 Convergence Regions \\
                 4.4 Sufficient Conditions for Convergence: Constant
                 Elements \\
                 4.4.1 Classical Results and Generalizations \\
                 4.4.2 Parabolic Convergence Regions \\
                 4.4.3 Convergence Neighborhoods for K(an/1) \ldots{}
                 \\
                 4.4.4 Twin Convergence Regions \\
                 4.4.5 Miscellaneous Convergence Criteria \\
                 4.5 Sufficient Conditions for Convergence \\
                 Variable Elements \\
                 4.5.1 Introduction \\
                 Classification of Continued Fractions \\
                 4.5.2 Regular C-fractions \\
                 4.5.3 Positive Definite/-fractions \\
                 4.5.4 General T-fractions \\
                 \\
                 5: Methods for Representing Analytic Functions by
                 Continued Fractions \\
                 5.1 Correspondence \\
                 5.2 Three-Term Recurrence Relations \\
                 5.3 Minimal Solutions of Three-Term Recurrence
                 Relations \\
                 5.4 Uniform Convergence \\
                 5.5 Pad{\'e} Table \\
                 5.5.1 Pad{\'e} Approximants \\
                 5.5.2 Multiple-Point Pad{\'e} Tables \\
                 \\
                 6: Representations of Analytic Functions by Continued
                 Fractions \\
                 6.1 Continued Fractions of Gauss \\
                 6.1.1 Hypergeometric Functions $F(a, b; c; z)$ \ldots{}
                 \\
                 6.1.2 Confluent Hypergeometric Functions $\Phi(b; c;
                 z)$ \\
                 6.1.3 Confluent Hypergeometric Functions $\Psi(c; z)$
                 \\
                 6.1.4 Confluent Hypergeometric Functions $\Omega(a, b;
                 z)$ \\
                 6.2 Representations from Minimal Solutions \\
                 \\
                 7: Types of Corresponding Continued \\
                 Fractions and Related Algorithms \\
                 7.1 Regular $C$-Fractions \\
                 7.1.1 Correspondence of Regular $C$-Fractions \\
                 7.1.2 Quotient-Difference Algorithm \\
                 7.1.3 $g$-Fractions \\
                 7.2 Associated Continued Fractions and $J$-Fractions
                 \\
                 7.2.1 Correspondence of Associated Continued Fractions
                 \\
                 7.2.2 $J$-Fractions and Orthogonal Polynomials \\
                 7.3 General $T$-Fractions \\
                 7.3.1 Correspondence of General $T$-Fractions \\
                 7.3.2 FG Algorithms \\
                 7.3.3 Representation of Analytic Functions \\
                 7.4 Stable Polynomials \\
                 \\
                 8: Truncation-Error Analysis \\
                 8.1 Introduction \\
                 8.2 General Theory of Inclusion Regions and Truncation
                 Errors \\
                 8.3 Explicit Results on Inclusion Regions and
                 Truncation-Error Bounds \\
                 8.4 Accelerating Convergence \\
                 \\
                 9: Asymptotic Expansions and Moment Problems \\
                 9.1 Introduction \\
                 9.2 Moment Problems \\
                 9.3 Integral Representations of Continued Fractions \\
                 9.4 Asymptotic Expansions for Continued Fractions \\
                 9.5 Solutions of the Moment Problems \\
                 9.6 Representations of Analytic Functions \\
                 \\
                 10: Numerical Stability in Evaluating Continued
                 Fractions \\
                 10.1 General Estimates of Relative Roundoff Error \\
                 10.2 Methods for Estimating $g_^{(n)}$ \\
                 10.3 Applications \\
                 \\
                 11: Application of Continued Fractions to \\
                 Birth--Death Processes \\
                 11.1 Birth--Death Processes \\
                 11.2 Computational Procedures \\
                 \\
                 12: Miscellaneous Results \\
                 12.1 $T$-Fraction Expansions for Families of Bounded
                 Functions \\
                 12.2 $T$-Fractions Corresponding to Rational Functions
                 \\
                 12.3 Location of Singular Points of Analytic Functions
                 Represented by Continued Fractions \\
                 12.4 Univalence of Functions Represented by Continued
                 Fractions \\
                 \\
                 Appendix A. Classification of Special Types of
                 Continued Fractions \\
                 Appendix B. Additional Results on Minimal Solutions of
                 Three-Term Recurrence Relations \\
                 Bibliography \\
                 Author Index \\
                 Subject Index",
}


bibtype: proceedings
filename: elefunt.bib
label: Anonymous:1998:TIC
editor: Anonymous
volume: 147
publisher: Accademia Nazionale dei Lincei
address: Roma, Italy
pages: 322
year: 1998
ISSN: 0391-805X OR 0391805X
LCCN: QA299.6
bibdate: Fri May 31 16:34:38 MDT 2024
bibtimestamp: 2024.05.31 16:34:38 MDT
series: Atti dei convegni Lincei
acknowledgement: ack-nhfb
raweditor: Anonymous
booktitle:
Tricomi's ideas and contemporary applied mathematics: (Roma, 28--29 novembre --- Torino, 1--2 dicembre 1997)

title:
Tricomi's ideas and contemporary applied mathematics: (Roma, 28--29 novembre --- Torino, 1--2 dicembre 1997)

bibsource:
fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawbooktitle:
{Tricomi's ideas and contemporary applied mathematics: (Roma, 28--29 novembre --- Torino, 1--2 dicembre 1997)}

rawtitle:
{Tricomi's ideas and contemporary applied mathematics: (Roma, 28--29 novembre --- Torino, 1--2 dicembre 1997)}

entry:
@Proceedings{Anonymous:1998:TIC,
  editor =       "Anonymous",
  booktitle =    "{Tricomi's ideas and contemporary applied mathematics:
                 (Roma, 28--29 novembre --- Torino, 1--2 dicembre
                 1997)}",
  title =        "{Tricomi's ideas and contemporary applied mathematics:
                 (Roma, 28--29 novembre --- Torino, 1--2 dicembre
                 1997)}",
  volume =       "147",
  publisher =    "Accademia Nazionale dei Lincei",
  address =      "Roma, Italy",
  pages =        "322",
  year =         "1998",
  ISSN =         "0391-805X",
  LCCN =         "QA299.6",
  bibdate =      "Fri May 31 16:34:38 MDT 2024",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Atti dei convegni Lincei",
  acknowledgement = ack-nhfb,
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bibtype: book
filename: elefunt.bib
label: Knuth:1998:SA
author: Donald E. Knuth
title: Seminumerical Algorithms
volume: 2
publisher: pub-AW
address: pub-AW:adr
edition: Third
pages: xiii + 762
year: 1998
ISBN: 0-201-89684-2 OR 0201896842
ISBN13: 978-0-201-89684-8 OR 9780201896848
LCCN: QA76.6 .K64 1997
bibdate: Fri Jul 11 15:41:22 1997
bibtimestamp: 1997.07.11 15:41:22 ???
series: The Art of Computer Programming
acknowledgement: ack-nhfb
rawauthor: Donald E. Knuth
rawtitle: Seminumerical Algorithms
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/css.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/texbook2.bib

TOC:
3: Random Numbers / 1 3.1. Introduction / 1 3.2. Generating Uniform Random Numbers / 10 3.2.1. The Linear Congruential Method / 10 3.2 1.1. Choice of modulus / 12 3.2.1.2 Choice of multiplier / 16 3.2.1.3. Potency / 23 3.2.2. Other Methods / 26 3.3. Statistical Tests / 41 3.3.1. General Test Procedures for Studying Random Data / 41 3.3.2. Empirical Tests / 61 *3.3.3. Theoretical Tests / 80 3.3.4. The Spectral Test / 93 3.4. Other Types of Random Quantities / 119 3.4 1. Numerical Distributions / 119 3.4.2. Random Sampling and Shuffling / 142 *3.5. What Is a Random Sequence? / 149 3.6. Summary / 184 4: Arithmetic / 194 4.1. Positional Number Systems / 195 4.2. Floating Point Arithmetic / 214 4.2.1. Single-Precision Calculations / 214 4.2 2. Accuracy of Floating Point Arithmetic / 229 *4.2.3. Double-Precision Calculations / 246 4.2.4. Distribution of Floating Point Numbers / 253 4.3 Multiple Precision Arithmetic / 265 4.3.1. The Classical Algorithms / 265 *4.3.2. Modular Arithmetic / 284 *4.3.3. How Fast Can We Multiply? / 294 4.4. Radix Conversion / 319 4.5. Rational Arithmetic / 330 4.5.1. Fractions / 330 4.5.2. The Greatest Common Divisor / 333 *4.5.3. Analysis of Euclid's Algorithm / 356 4.5.4. Factoring into Primes / 379 4.6. Polynomial Arithmetic / 418 4.6.1. Division of Polynomials / 420 *4.6.2. Factorization of Polynomials / 439 4.6.3. Evaluation of Powers / 461 4.6.4. Evaluation of Polynomials / 485 *4.7. Manipulation of Power Series / 525 Answers to Exercises / 538 Appendix A: Tables of Numerical Quantities / 726 1. Fundamental Constants (decimal) / 726 2; Fundamental Constants ( octal) / 727 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers / 728 Appendix B: Index to Notations / 730 Index and Glossary / 735

rawTOC:
3: Random Numbers / 1 \\ 3.1. Introduction / 1 \\ 3.2. Generating Uniform Random Numbers / 10 \\ 3.2.1. The Linear Congruential Method / 10 \\ 3.2 1.1. Choice of modulus / 12 \\ 3.2.1.2 Choice of multiplier / 16 \\ 3.2.1.3. Potency / 23 \\ 3.2.2. Other Methods / 26 \\ 3.3. Statistical Tests / 41 \\ 3.3.1. General Test Procedures for Studying Random Data / 41 \\ 3.3.2. Empirical Tests / 61 \\ *3.3.3. Theoretical Tests / 80 \\ 3.3.4. The Spectral Test / 93 \\ 3.4. Other Types of Random Quantities / 119 \\ 3.4 1. Numerical Distributions / 119 \\ 3.4.2. Random Sampling and Shuffling / 142 \\ *3.5. What Is a Random Sequence? / 149 \\ 3.6. Summary / 184 \\ 4: Arithmetic / 194 \\ 4.1. Positional Number Systems / 195 \\ 4.2. Floating Point Arithmetic / 214 \\ 4.2.1. Single-Precision Calculations / 214 \\ 4.2 2. Accuracy of Floating Point Arithmetic / 229 \\ *4.2.3. Double-Precision Calculations / 246 \\ 4.2.4. Distribution of Floating Point Numbers / 253 \\ 4.3 Multiple Precision Arithmetic / 265 \\ 4.3.1. The Classical Algorithms / 265 \\ *4.3.2. Modular Arithmetic / 284 \\ *4.3.3. How Fast Can We Multiply? / 294 \\ 4.4. Radix Conversion / 319 \\ 4.5. Rational Arithmetic / 330 \\ 4.5.1. Fractions / 330 \\ 4.5.2. The Greatest Common Divisor / 333 \\ *4.5.3. Analysis of Euclid's Algorithm / 356 \\ 4.5.4. Factoring into Primes / 379 \\ 4.6. Polynomial Arithmetic / 418 \\ 4.6.1. Division of Polynomials / 420 \\ *4.6.2. Factorization of Polynomials / 439 \\ 4.6.3. Evaluation of Powers / 461 \\ 4.6.4. Evaluation of Polynomials / 485 \\ *4.7. Manipulation of Power Series / 525 \\ Answers to Exercises / 538 \\ Appendix A: Tables of Numerical Quantities / 726 \\ 1. Fundamental Constants (decimal) / 726 \\ 2; Fundamental Constants ( octal) / 727 \\ 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers / 728 \\ Appendix B: Index to Notations / 730 \\ Index and Glossary / 735

entry:
@Book{Knuth:1998:SA,
  author =       "Donald E. Knuth",
  title =        "Seminumerical Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Third",
  pages =        "xiii + 762",
  year =         "1998",
  ISBN =         "0-201-89684-2",
  ISBN-13 =      "978-0-201-89684-8",
  LCCN =         "QA76.6 .K64 1997",
  bibdate =      "Fri Jul 11 15:41:22 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/css.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
  price =        "US\$52.75",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nhfb,
  tableofcontents = "3: Random Numbers / 1 \\
                 3.1. Introduction / 1 \\
                 3.2. Generating Uniform Random Numbers / 10 \\
                 3.2.1. The Linear Congruential Method / 10 \\
                 3.2 1.1. Choice of modulus / 12 \\
                 3.2.1.2 Choice of multiplier / 16 \\
                 3.2.1.3. Potency / 23 \\
                 3.2.2. Other Methods / 26 \\
                 3.3. Statistical Tests / 41 \\
                 3.3.1. General Test Procedures for Studying Random Data
                 / 41 \\
                 3.3.2. Empirical Tests / 61 \\
                 *3.3.3. Theoretical Tests / 80 \\
                 3.3.4. The Spectral Test / 93 \\
                 3.4. Other Types of Random Quantities / 119 \\
                 3.4 1. Numerical Distributions / 119 \\
                 3.4.2. Random Sampling and Shuffling / 142 \\
                 *3.5. What Is a Random Sequence? / 149 \\
                 3.6. Summary / 184 \\
                 4: Arithmetic / 194 \\
                 4.1. Positional Number Systems / 195 \\
                 4.2. Floating Point Arithmetic / 214 \\
                 4.2.1. Single-Precision Calculations / 214 \\
                 4.2 2. Accuracy of Floating Point Arithmetic / 229 \\
                 *4.2.3. Double-Precision Calculations / 246 \\
                 4.2.4. Distribution of Floating Point Numbers / 253 \\
                 4.3 Multiple Precision Arithmetic / 265 \\
                 4.3.1. The Classical Algorithms / 265 \\
                 *4.3.2. Modular Arithmetic / 284 \\
                 *4.3.3. How Fast Can We Multiply? / 294 \\
                 4.4. Radix Conversion / 319 \\
                 4.5. Rational Arithmetic / 330 \\
                 4.5.1. Fractions / 330 \\
                 4.5.2. The Greatest Common Divisor / 333 \\
                 *4.5.3. Analysis of Euclid's Algorithm / 356 \\
                 4.5.4. Factoring into Primes / 379 \\
                 4.6. Polynomial Arithmetic / 418 \\
                 4.6.1. Division of Polynomials / 420 \\
                 *4.6.2. Factorization of Polynomials / 439 \\
                 4.6.3. Evaluation of Powers / 461 \\
                 4.6.4. Evaluation of Polynomials / 485 \\
                 *4.7. Manipulation of Power Series / 525 \\
                 Answers to Exercises / 538 \\
                 Appendix A: Tables of Numerical Quantities / 726 \\
                 1. Fundamental Constants (decimal) / 726 \\
                 2; Fundamental Constants ( octal) / 727 \\
                 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
                 Numbers / 728 \\
                 Appendix B: Index to Notations / 730 \\
                 Index and Glossary / 735",
}


bibtype: book
filename: elefunt.bib
label: Borwein:2007:RHR
editor: Peter Borwein and Stephen Choi and Brendan Rooney and Andrea Weirathmueller and others
title: The Riemann Hypothesis: a resource for the afficionado and virtuoso alike
volume: 27
publisher: Springer Science+Business Media, LLC
address: New York, NY, USA
pages: xiv + 533
year: 2007
DOI: https://doi.org/10.1007/978-0-387-72126-2
ISBN: 0-387-72125-8 (hardcover), 0-387-72126-6 (e-book) OR 0387721258 (hardcover), 0387721266 (ebook)
LCCN: QA246 .R53 2008
bibdate: Thu Sep 1 07:07:49 MDT 2022
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2022.09.01 07:07:49 MDT
series: CMS books in mathematics
URL: http://libanswers.liverpool.ac.uk/faq/182315
acknowledgement: ack-nhfb
raweditor: Peter Borwein and Stephen Choi and Brendan Rooney and Andrea Weirathmueller and others
rawtitle: The {Riemann Hypothesis}: a resource for the afficionado and virtuoso alike
ISBN13:
978-0-387-72125-5 (hardcover), 978-0-387-72126-2 (e-book) OR 9780387721255 (hardcover), 9780387721262 (ebook)

abstract:
This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis. The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.

subject:
Mathematics; History; Number theory; Mathematiques; Histoire; Theorie des nombres; Mathematics.; Number theory.

TOC:
Part 1: Introduction to the Riemann hypothesis 1: Why this book 1.1: The Holy Grail 1.2: Riemann's zeta and Liouville's lambda 1.3: The prime number theorem 2: Analytic preliminaries 2.1: The Riemann zeta function 2.2: Zero-free region 2.3: Counting the zeros of [cedilla](s) 2.4: Hardy's theorem 3: Algorithms for calculating [cedilla](s) 3.1: Euler--MacLaurin summation 3.2: Backlund 3.3: Hardy's function 3.4: The Riemann--Siegel formula 3.5: Gram's law 3.6: Turing 3.7: The Odlyzko--Schonhage algorithm 3.8: A simple algorithm for the zeta function 3.9: Further reading 4: Empirical evidence 4.1: Verification in an interval 4.2: A brief history of computational evidence 4.3: The Riemann hypothesis and random matrices 4.4: The Skewes number 5: Equivalent statements 5.1: Number-theoretic equivalences 5.2: Analytic equivalences 5.3: Other equivalences 6: Extensions of the Riemann hypothesis 6.1: The Riemann hypothesis 6.2: The generalized Riemann hypothesis 6.3: The extended Riemann hypothesis 6.4: An equivalent extended Riemann hypothesis 6.5: Another extended Riemann hypothesis 6.6: The Grand Riemann hypothesis 7: Assuming the Riemann hypothesis and its extensions 7.1: Another proof of the prime number theorem 7.2: Goldbach's conjecture 7.3: More Goldbach 7.4: Primes in a given interval 7.5: The least prime in arithmetic progressions 7.6: Primality testing 7.7: Artin's primitive root conjecture 7.8: Bounds on Dirichlet $L$-series 7.9: The Lindelof hypothesis 7.10: Titchmarsh's [delta](T) function 7.11: Mean values of [cedilla](s)8: Failed attempts at proof 8.1: Stieltjes and Mertens' conjecture 8.2: Hans Rademacher and false hopes 8.3: Turan's condition 8.4: Louis de Branges's approach 8.5: No really good idea 9: Formulas 10: Timeline pt. 2: Original papers 11: Expert witnesses 11. 1: E. Bombieri (2000--2001) 11.2: P. Sarnak (2004) 11.3: J.B. Conrey (2003) 11.4: A. Ivic (2003) 12: The experts speak for themselves 12.1: P.L. Chebyshev (1852) 12.2: B. Riemann (1859) 12.3: J. Hadamard (1896) 12.4: C. de la Vallee Poussin (1899) 12.5: G.H. Hardy (1914) 12.6: G.H. Hardy (1915) 12.7: G.H. Hardy and J.E. Littlewood (1915) 12.8: A. Weil (1941) 12.9: P. Turan (1948) 12.10: A. Selberg (1949) 12.11: P. Erdo$cdot $s (1949) 12.12: S. Skewes (1955) 12.13: C.B. Haselgrove (1958) 12.14: H. Montgomery (1973) 12.15: D.J. Newman (1980) 12.16: J. Korevaar (1982) 12.17: H. Daboussi (1984) 12.18: A. Hildebrand (1986) 12.19: D. Goldston and H. Montgomery (1987) 12.20: M. Agrawal, N. Kayal, and N. Saxena (2004) References References Index

rawabstract:
This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis. The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.

shortTOC:
To the Riemann Hypothesis Why This Book Analytic Preliminaries Algorithms for Calculating ?(s) Empirical Evidence Equivalent Statements Extensions of the Riemann Hypothesis Assuming the Riemann Hypothesis and Its Extensions ldots Failed Attempts at Proof Formulas Timeline Original Papers Expert Witnesses The Experts Speak for Themselves

rawshortTOC:
To the Riemann Hypothesis \\ Why This Book \\ Analytic Preliminaries \\ Algorithms for Calculating ?(s) \\ Empirical Evidence \\ Equivalent Statements \\ Extensions of the Riemann Hypothesis \\ Assuming the Riemann Hypothesis and Its Extensions \ldots{} \\ Failed Attempts at Proof \\ Formulas \\ Timeline \\ Original Papers \\ Expert Witnesses \\ The Experts Speak for Themselves

rawTOC:
Part 1: Introduction to the Riemann hypothesis \\ 1: Why this book \\ 1.1: The Holy Grail \\ 1.2: Riemann's zeta and Liouville's lambda \\ 1.3: The prime number theorem \\ 2: Analytic preliminaries \\ 2.1: The Riemann zeta function \\ 2.2: Zero-free region \\ 2.3: Counting the zeros of [cedilla](s) \\ 2.4: Hardy's theorem \\ 3: Algorithms for calculating [cedilla](s) \\ 3.1: Euler--MacLaurin summation \\ 3.2: Backlund \\ 3.3: Hardy's function \\ 3.4: The Riemann--Siegel formula \\ 3.5: Gram's law \\ 3.6: Turing \\ 3.7: The Odlyzko--Sch{\"o}nhage algorithm \\ 3.8: A simple algorithm for the zeta function \\ 3.9: Further reading \\ 4: Empirical evidence \\ 4.1: Verification in an interval \\ 4.2: A brief history of computational evidence \\ 4.3: The Riemann hypothesis and random matrices \\ 4.4: The Skewes number \\ 5: Equivalent statements \\ 5.1: Number-theoretic equivalences \\ 5.2: Analytic equivalences \\ 5.3: Other equivalences \\ 6: Extensions of the Riemann hypothesis \\ 6.1: The Riemann hypothesis \\ 6.2: The generalized Riemann hypothesis \\ 6.3: The extended Riemann hypothesis \\ 6.4: An equivalent extended Riemann hypothesis \\ 6.5: Another extended Riemann hypothesis \\ 6.6: The Grand Riemann hypothesis \\ 7: Assuming the Riemann hypothesis and its extensions \\ 7.1: Another proof of the prime number theorem \\ 7.2: Goldbach's conjecture \\ 7.3: More Goldbach \\ 7.4: Primes in a given interval \\ 7.5: The least prime in arithmetic progressions \\ 7.6: Primality testing \\ 7.7: Artin's primitive root conjecture \\ 7.8: Bounds on Dirichlet $L$-series \\ 7.9: The Lindel{\"o}f hypothesis \\ 7.10: Titchmarsh's [delta](T) function \\ 7.11: Mean values of [cedilla](s)8: Failed attempts at proof \\ 8.1: Stieltjes and Mertens' conjecture \\ 8.2: Hans Rademacher and false hopes \\ 8.3: Tur{\'a}n's condition \\ 8.4: Louis de Branges's approach \\ 8.5: No really good idea \\ 9: Formulas \\ 10: Timeline \\ pt. 2: Original papers \\ 11: Expert witnesses \\ 11. 1: E. Bombieri (2000--2001) \\ 11.2: P. Sarnak (2004) \\ 11.3: J.B. Conrey (2003) \\ 11.4: A. Ivi{\'c} (2003) \\ 12: The experts speak for themselves \\ 12.1: P.L. Chebyshev (1852) \\ 12.2: B. Riemann (1859) \\ 12.3: J. Hadamard (1896) \\ 12.4: C. de la Vall{\'e}e Poussin (1899) \\ 12.5: G.H. Hardy (1914) \\ 12.6: G.H. Hardy (1915) \\ 12.7: G.H. Hardy and J.E. Littlewood (1915) \\ 12.8: A. Weil (1941) \\ 12.9: P. Tur{\'a}n (1948) \\ 12.10: A. Selberg (1949) \\ 12.11: P. Erdo$\cdot$s (1949) \\ 12.12: S. Skewes (1955) \\ 12.13: C.B. Haselgrove (1958) \\ 12.14: H. Montgomery (1973) \\ 12.15: D.J. Newman (1980) \\ 12.16: J. Korevaar (1982) \\ 12.17: H. Daboussi (1984) \\ 12.18: A. Hildebrand (1986) \\ 12.19: D. Goldston and H. Montgomery (1987) \\ 12.20: M. Agrawal, N. Kayal, and N. Saxena (2004) \\ References \\ References \\ Index

entry:
@Book{Borwein:2007:RHR,
  editor =       "Peter Borwein and Stephen Choi and Brendan Rooney and
                 Andrea Weirathmueller and others",
  title =        "The {Riemann Hypothesis}: a resource for the
                 afficionado and virtuoso alike",
  volume =       "27",
  publisher =    "Springer Science+Business Media, LLC",
  address =      "New York, NY, USA",
  pages =        "xiv + 533",
  year =         "2007",
  DOI =          "https://doi.org/10.1007/978-0-387-72126-2",
  ISBN =         "0-387-72125-8 (hardcover), 0-387-72126-6 (e-book)",
  ISBN-13 =      "978-0-387-72125-5 (hardcover), 978-0-387-72126-2
                 (e-book)",
  LCCN =         "QA246 .R53 2008",
  bibdate =      "Thu Sep 1 07:07:49 MDT 2022",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "CMS books in mathematics",
  URL =          "http://libanswers.liverpool.ac.uk/faq/182315",
  abstract =     "This book is an introduction to the theory surrounding
                 the Riemann Hypothesis. Part I serves as a compendium
                 of known results and as a primer for the material
                 presented in the 20 original papers contained in Part
                 II. The original papers place the material into
                 historical context and illustrate the motivations for
                 research on and around the Riemann Hypothesis. Several
                 of these papers focus on computation of the zeta
                 function, while others give proofs of the Prime Number
                 Theorem, since the Prime Number Theorem is so closely
                 connected to the Riemann Hypothesis. The text is
                 suitable for a graduate course or seminar or simply as
                 a reference for anyone interested in this extraordinary
                 conjecture.",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "To the Riemann Hypothesis \\
                 Why This Book \\
                 Analytic Preliminaries \\
                 Algorithms for Calculating ?(s) \\
                 Empirical Evidence \\
                 Equivalent Statements \\
                 Extensions of the Riemann Hypothesis \\
                 Assuming the Riemann Hypothesis and Its Extensions
                 \ldots{} \\
                 Failed Attempts at Proof \\
                 Formulas \\
                 Timeline \\
                 Original Papers \\
                 Expert Witnesses \\
                 The Experts Speak for Themselves",
  subject =      "Mathematics; History; Number theory;
                 Math{\'e}matiques; Histoire; Th{\'e}orie des nombres;
                 Mathematics.; Number theory.",
  tableofcontents = "Part 1: Introduction to the Riemann hypothesis \\
                 1: Why this book \\
                 1.1: The Holy Grail \\
                 1.2: Riemann's zeta and Liouville's lambda \\
                 1.3: The prime number theorem \\
                 2: Analytic preliminaries \\
                 2.1: The Riemann zeta function \\
                 2.2: Zero-free region \\
                 2.3: Counting the zeros of [cedilla](s) \\
                 2.4: Hardy's theorem \\
                 3: Algorithms for calculating [cedilla](s) \\
                 3.1: Euler--MacLaurin summation \\
                 3.2: Backlund \\
                 3.3: Hardy's function \\
                 3.4: The Riemann--Siegel formula \\
                 3.5: Gram's law \\
                 3.6: Turing \\
                 3.7: The Odlyzko--Sch{\"o}nhage algorithm \\
                 3.8: A simple algorithm for the zeta function \\
                 3.9: Further reading \\
                 4: Empirical evidence \\
                 4.1: Verification in an interval \\
                 4.2: A brief history of computational evidence \\
                 4.3: The Riemann hypothesis and random matrices \\
                 4.4: The Skewes number \\
                 5: Equivalent statements \\
                 5.1: Number-theoretic equivalences \\
                 5.2: Analytic equivalences \\
                 5.3: Other equivalences \\
                 6: Extensions of the Riemann hypothesis \\
                 6.1: The Riemann hypothesis \\
                 6.2: The generalized Riemann hypothesis \\
                 6.3: The extended Riemann hypothesis \\
                 6.4: An equivalent extended Riemann hypothesis \\
                 6.5: Another extended Riemann hypothesis \\
                 6.6: The Grand Riemann hypothesis \\
                 7: Assuming the Riemann hypothesis and its extensions
                 \\
                 7.1: Another proof of the prime number theorem \\
                 7.2: Goldbach's conjecture \\
                 7.3: More Goldbach \\
                 7.4: Primes in a given interval \\
                 7.5: The least prime in arithmetic progressions \\
                 7.6: Primality testing \\
                 7.7: Artin's primitive root conjecture \\
                 7.8: Bounds on Dirichlet $L$-series \\
                 7.9: The Lindel{\"o}f hypothesis \\
                 7.10: Titchmarsh's [delta](T) function \\
                 7.11: Mean values of [cedilla](s)8: Failed attempts at
                 proof \\
                 8.1: Stieltjes and Mertens' conjecture \\
                 8.2: Hans Rademacher and false hopes \\
                 8.3: Tur{\'a}n's condition \\
                 8.4: Louis de Branges's approach \\
                 8.5: No really good idea \\
                 9: Formulas \\
                 10: Timeline \\
                 pt. 2: Original papers \\
                 11: Expert witnesses \\
                 11. 1: E. Bombieri (2000--2001) \\
                 11.2: P. Sarnak (2004) \\
                 11.3: J.B. Conrey (2003) \\
                 11.4: A. Ivi{\'c} (2003) \\
                 12: The experts speak for themselves \\
                 12.1: P.L. Chebyshev (1852) \\
                 12.2: B. Riemann (1859) \\
                 12.3: J. Hadamard (1896) \\
                 12.4: C. de la Vall{\'e}e Poussin (1899) \\
                 12.5: G.H. Hardy (1914) \\
                 12.6: G.H. Hardy (1915) \\
                 12.7: G.H. Hardy and J.E. Littlewood (1915) \\
                 12.8: A. Weil (1941) \\
                 12.9: P. Tur{\'a}n (1948) \\
                 12.10: A. Selberg (1949) \\
                 12.11: P. Erdo$\cdot$s (1949) \\
                 12.12: S. Skewes (1955) \\
                 12.13: C.B. Haselgrove (1958) \\
                 12.14: H. Montgomery (1973) \\
                 12.15: D.J. Newman (1980) \\
                 12.16: J. Korevaar (1982) \\
                 12.17: H. Daboussi (1984) \\
                 12.18: A. Hildebrand (1986) \\
                 12.19: D. Goldston and H. Montgomery (1987) \\
                 12.20: M. Agrawal, N. Kayal, and N. Saxena (2004) \\
                 References \\
                 References \\
                 Index",
}


bibtype: article
filename: elefunt.bib
label: Dunster:2024:CPC
author: T. M. Dunster and A. Gil and J. Segura
title: Computation of parabolic cylinder functions having complex argument
journal: j-APPL-NUM-MATH
volume: 197
pages: 230--242
month: mar
monthnumber: 3
year: 2024
CODEN: ANMAEL
DOI: https://doi.org/10.1016/j.apnum.2023.11.017
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
bibdate: Mon Dec 18 15:47:31 MST 2023
bibtimestamp: 2023.12.18 15:47:31 MST
URL: http://www.sciencedirect.com/science/article/pii/S0168927423002969
fjournal: Applied Numerical Mathematics: Transactions of IMACS
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274
rawauthor: T. M. Dunster and A. Gil and J. Segura
rawtitle: Computation of parabolic cylinder functions having complex argument
entry:
@Article{Dunster:2024:CPC,
  author =       "T. M. Dunster and A. Gil and J. Segura",
  title =        "Computation of parabolic cylinder functions having
                 complex argument",
  journal =      j-APPL-NUM-MATH,
  volume =       "197",
  number =       "??",
  pages =        "230--242",
  month =        mar,
  year =         "2024",
  CODEN =        "ANMAEL",
  DOI =          "https://doi.org/10.1016/j.apnum.2023.11.017",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Mon Dec 18 15:47:31 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0168927423002969",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274",
}


bibtype: proceedings
filename: elefunt.bib
label: Bowden:1953:FTT
editor: Baron Bertram Vivian Bowden
booktitle: Faster Than Thought: a Symposium on Digital Computing Machines
title: Faster Than Thought: a Symposium on Digital Computing Machines
publisher: Sir Isaac Pitman and Sons, Ltd.
address: London, UK
pages: xix + 416 + 21
year: 1953
LCCN: QA76.5 .B66
bibdate: Sun May 15 10:03:12 MDT 2011
bibtimestamp: 2011.05.15 10:03:12 MDT
note: With a foreword by the Right Honourable the Earl of Halsbury.
URL: https://archive.org/details/FasterThanThought
subject: Electronic digital computers
acknowledgement: ack-nhfb
rawbooktitle: Faster Than Thought: a Symposium on Digital Computing Machines
raweditor: {Baron} Bertram Vivian Bowden
rawnote: With a foreword by the Right Honourable the Earl of Halsbury.
rawtitle: Faster Than Thought: a Symposium on Digital Computing Machines
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib; https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib; https://www.math.utah.edu/pub/tex/bib/adabooks.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager

TOC:
Foreword / v Preface / vii List of Contributors / xv Part One: The History and Theory of Computing Machines 1. A Brief History of Computation / B. V. Bowden / 3 2. The Circuit Components of Digital Computers / B. V. Bowden and B. W. Pollard / 32 3. The Organization of a Typical Machine / B. V. Bowden / 67 4. The Construction, Performance and Maintenance of Digital Computers / B. V. Bowden / 78 5. Programming For High-Speed Digital Calculating Machines / J. M. Bennett and A. E. Glennie / 101 Part Two: Electronic Computing Machines in Britain and America / 6. The University of Manchester Computing Machine / T. Kilburn and F. C. Williams / 117 7. Calculating Machine Development at Cambridge / 130 8. Automatic Computation at the National Physical Laboratory / 135 9. The Harwell Electronic Digital Computer / E. H. Cooke-Yarborough / 140 10. The Telecommunications Research Establishment Parallel Electronic Digital Computer / R. H. A. Carter and A. M. Uttley / 144 11. The Imperial College Computing Engine / S. Michaelson and K. D. Tocher / 161 12. The Royal Aircraft Establishment Sequence-Controlled Calculator / S. H. Hollingdale / 165 13. Calculating Machines at the Birkbeck College Computation Laboratory / A. D. Booth / 170 14. Computers in America / B. V. Bowden / 173 Part Three: Applications of Electronic Computing Machines 15. Machines for the Solution of Logical Problems / D. G. Prinz and J. B. Smith / 181 16. Special-Purpose Automatic Computers / R. Stuart-Williams / 199 17. Digital Computation and the Crystallographer / J. M. Bennett and M. V. Wilkes / 203 18. The Use of High-Speed Computing Machines in Meteorology / R. S. Scorer / 210 19. An Application to Ballistics / A. E. Glennie / 216 20. Digital Computers and the Engineer / J. M. Bennett / 223 21. Machines in Government Calculations / B. B. Swann / 234 22. The Application of Digital Computers to Business and Commerce / B. V. Bowden / 246 23. Electronic Machines and Economics / G. Morton / 272 24. Problems of Dynamical Astronomy / Cicely M. Popplewell / 282 25. Digital Computers Applied to Games / M. Audrey Bates, B. V. Bowden, C. Strachey, and A. M. Turing / 286 26. Thought and Machine Processes / B. V. Bowden / 311 Appendix 1: Extracts From booktitle Taylor's Scientific Memoirs, Vol. III / 341 Appendix 2: Extracts From the booktitle Lovelace Papers / 409 Glossary / 411 Index / 415 Insets Flow Sheet For P.A.Y.E. Calculation / 254 Computation of Bernoulli Numbers / 404

rawTOC:
Foreword / v \\ Preface / vii \\ List of Contributors / xv \\ Part One: The History and Theory of Computing Machines \\ 1. A Brief History of Computation / B. V. Bowden / 3 \\ 2. The Circuit Components of Digital Computers / B. V. Bowden and B. W. Pollard / 32 \\ 3. The Organization of a Typical Machine / B. V. Bowden / 67 \\ 4. The Construction, Performance and Maintenance of Digital Computers / B. V. Bowden / 78 \\ 5. Programming For High-Speed Digital Calculating Machines / J. M. Bennett and A. E. Glennie / 101 \\ Part Two: Electronic Computing Machines in Britain and America / \\ 6. The University of Manchester Computing Machine / T. Kilburn and F. C. Williams / 117 \\ 7. Calculating Machine Development at Cambridge / 130 \\ 8. Automatic Computation at the National Physical Laboratory / 135 \\ 9. The Harwell Electronic Digital Computer / E. H. Cooke-Yarborough / 140 \\ 10. The Telecommunications Research Establishment Parallel Electronic Digital Computer / R. H. A. Carter and A. M. Uttley / 144 \\ 11. The Imperial College Computing Engine / S. Michaelson and K. D. Tocher / 161 \\ 12. The Royal Aircraft Establishment Sequence-Controlled Calculator / S. H. Hollingdale / 165 \\ 13. Calculating Machines at the Birkbeck College Computation Laboratory / A. D. Booth / 170 \\ 14. Computers in America / B. V. Bowden / 173 \\ Part Three: Applications of Electronic Computing Machines \\ 15. Machines for the Solution of Logical Problems / D. G. Prinz and J. B. Smith / 181 \\ 16. Special-Purpose Automatic Computers / R. Stuart-Williams / 199 \\ 17. Digital Computation and the Crystallographer / J. M. Bennett and M. V. Wilkes / 203 \\ 18. The Use of High-Speed Computing Machines in Meteorology / R. S. Scorer / 210 \\ 19. An Application to Ballistics / A. E. Glennie / 216 \\ 20. Digital Computers and the Engineer / J. M. Bennett / 223 \\ 21. Machines in Government Calculations / B. B. Swann / 234 \\ 22. The Application of Digital Computers to Business and Commerce / B. V. Bowden / 246 \\ 23. Electronic Machines and Economics / G. Morton / 272 \\ 24. Problems of Dynamical Astronomy / Cicely M. Popplewell / 282 \\ 25. Digital Computers Applied to Games / M. Audrey Bates, B. V. Bowden, C. Strachey, and A. M. Turing / 286 \\ 26. Thought and Machine Processes / B. V. Bowden / 311 \\ Appendix 1: Extracts From \booktitle{Taylor's Scientific Memoirs}, Vol. III / 341 \\ Appendix 2: Extracts From the \booktitle{Lovelace Papers} / 409 \\ Glossary / 411 \\ Index / 415 \\ Insets \\ Flow Sheet For P.A.Y.E. Calculation / 254 \\ Computation of Bernoulli Numbers / 404

entry:
@Proceedings{Bowden:1953:FTT,
  editor =       "{Baron} Bertram Vivian Bowden",
  booktitle =    "Faster Than Thought: a Symposium on Digital Computing
                 Machines",
  title =        "Faster Than Thought: a Symposium on Digital Computing
                 Machines",
  publisher =    "Sir Isaac Pitman and Sons, Ltd.",
  address =      "London, UK",
  pages =        "xix + 416 + 21",
  year =         "1953",
  LCCN =         "QA76.5 .B66",
  bibdate =      "Sun May 15 10:03:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "With a foreword by the Right Honourable the Earl of
                 Halsbury.",
  URL =          "https://archive.org/details/FasterThanThought",
  acknowledgement = ack-nhfb,
  listofcontributors = "Miss M. Audrey Bates, Ferranti Ltd., Moston,
                 Manchester (Chapter 25) \\
                 Dr. J. M. Bennett, Ferranti Ltd., Moston, Manchester
                 (Chapters 5, 17, 20) \\
                 Dr. A. D. Booth, Director of the Electronic Computation
                 Laboratory, Birkbeck College, London (Chapter 13) \\
                 Dr. B. V. Bowden, Ferranti Ltd., Moston, Manchester
                 (Chapters 1--4, 14, 22, 25, 26) \\
                 Mr. R. H. A. Carter, Telecommunications Research
                 Establishment, Malvern (M.O.S.) (Chapter 10) \\
                 Mr. E. H. Cooke-Yarborough, Atomic Energy Research
                 Establishment, Harwell (M.O.S.) (Chapter 9) \\
                 Mr. A. E. Glennie, Research Establishment, Fort
                 Halstead (M.O.S.) (Chapters 5, 19) \\
                 Dr. S. H. Hollingdale, Head of the Mathematical
                 Services Department, Royal Aircraft Establishment,
                 Farnborough (M.O.S.) \\
                 (Chapter 12) \\
                 Dr. T. Kilburn, Senior Lecturer, Electrical Engineering
                 Dept., Manchester University (Chapter 6) \\
                 Mr. S. Michaelson, Imperial College of Science and
                 Technology, London (Chapter 11) \\
                 Dr. G. Morton, Lecturer In Economics, London School of
                 Economics And Political Science (Chapter 23) \\
                 Mr. B. W. Pollard, Ferranti Ltd., Moston, Manchester
                 (Chapter 2) \\
                 Miss Cicely M. Popplewell, Staff Member of the Royal
                 Society Computing Laboratory, Manchester University
                 (Chapter 24) \\
                 Dr. D. G. Prinz, Ferranti Ltd., Moston, Manchester
                 (Chapter 15) \\
                 Dr. R. S. Scorer, Lecturer, Department of Meteorology,
                 Imperial College of Science and Technology, London
                 (Chapter 18) \\
                 Mr. J. B. Smith, Ferranti Ltd., Crewe Toll, Edinburgh
                 (Chapter 15) \\
                 Mr. R. Stuart-Williams, Sometime of Ferranti Ltd.,
                 Moston, Manchester, now at the R.C.A. Research
                 Laboratories, Princeton, New Jersey, U.S.A. (Chapter
                 16) \\
                 Mr. B. B. Swann, Ferranti Ltd., Moston, Manchester
                 (Chapter 21) \\
                 Mr. C. Strachey, National Research Development
                 Corporation (Chapter 25) \\
                 Dr. K. D. Tocher, Imperial College of Science and
                 Technology, London (Chapter 11) \\
                 Dr. A. M. Turing, F.R.S., Assistant Director of the
                 Royal Society Computing Laboratory, Manchester
                 University (Chapter 25) \\
                 Dr. A. M. Uttley, Telecommunications Research
                 Establishment, Malvern (M.O.S.) (Chapter 10) \\
                 Dr. M. V. Wilkes, Director of the University
                 Mathematical Laboratory, Cambridge (Chapter 17) \\
                 Professor F. C. Williams, O.B.E., F.R.S. (Professor of
                 Electrical Engineering) Director of the Royal Society
                 Computing Laboratory, Manchester University (Chapter 6)
                 \\
                 Chapter 8 is reprinted from \booktitle{Engineering} by
                 kind permission of the Publishers",
  listofplates = "Ada Augusta, Countess of Lovelace / Frontispiece \\
                 I. Charles Babbage / 12 \\
                 II. Part of Babbage's Difference Engine / 28 \\
                 III. Two Hollerith Punch Cards of the Type Used in the
                 A.C.E. / 29 \\
                 IV. The Magnetic Drum of the Manchester Machine / 60
                 \\
                 V. The Photo-Electric Tape-Reader of the Manchester
                 Machine / 112 \\
                 VI. A Typical Stored Pattern on a Cathode-Ray-Tube
                 Screen / 120 \\
                 VII. The First Manchester University Computer / 121 \\
                 VIII. A General View of the Manchester University
                 Computer Without Covers / 124 \\
                 IX. A General View of the Manchester University
                 Computer and Control Desk / 126 \\
                 X. The Control Desk of the Manchester University
                 Computer, Showing the Console / 127 \\
                 XI. A General View of the E.D.S.A.C. / 132 \\
                 XII. One Unit of the A.C.E. / 136 \\
                 XIII. A View of the A.C.E. Showing Delay Units / 138
                 \\
                 XIV. A View of the A.C.E. Showing the Hollerith
                 Equipment Used for Input and Output / 139 \\
                 XV. A Cathode-Ray-Tube Store Pattern / 148 \\
                 XVI. The Ferranti (Edinburgh) Logical Computer and
                 Feedback Computer / 188 \\
                 XVII. ``Nimrod'' at the Science Exhibition, South
                 Kensington / 200 \\
                 XVIII. The $b$ Patterson Projection of Whale Myoglobin
                 Printed in Contour Form / 204",
  remark-01 =    "Portrait of Ada Augusta, Countess of Lovelace, faces
                 title page.",
  remark-02 =    "Chapter authors are credited only in the List of
                 Contributors on page xv; their names, and order, fail
                 to appear on chapter papers. No author is credited for
                 Chapters 7 and 8",
  remark-03 =    "From page ix: ``The principles on which all modern
                 computing machines are based were enunciated more than
                 a hundred years ago by a Cambridge mathematician named
                 Charles Babbage, who devoted his life and fortune to an
                 unsuccessful attempt to construct one. Modern
                 developments in electronics have made his dream come
                 true in the last decade, and there are now a dozen or
                 more machines in the world which do all and more than
                 he expected.",
  remark-04 =    "From page ix: ``A rough count showed that about 150
                 digital computers are being built at this moment, most
                 of them in universities and other research
                 establishments. It will be interesting to see if these
                 machines play in the next decade the part of the
                 cyclotrons and high voltage generators in the
                 `thirties'.''",
  remark-05 =    "From page x: ``It seems probable that we shall have a
                 second Industrial Revolution on our hands before long.
                 The first one replaced men's muscles by machines, and
                 eve1y worker in England now has an average of more than
                 3 horse power to help him. In the next revolution
                 machines may replace men's brains and relieve them of
                 much of the drudgery and boredom which is now the lot
                 of so many white collar workers.''",
  remark-06 =    "From page x: ``Nowadays many of these dedicated men
                 spend their time in computing prime numbers. The search
                 for the largest known prime is a hobby which is at
                 least as useful and interesting as playing bridge, and
                 computing machines have helped enormously. The reader
                 will not be surprised to hear that nowadays the biggest
                 primes are found in America. The largest which has been
                 discovered so far (January, 1953) consists of 2281
                 consecutive `ones,' when it is expressed in the binary
                 scale (see page 33).''",
  remark-07 =    "From page xi: ``The early history of these machines
                 and the story of poor Babbage's struggles is very
                 interesting. We owe our best account of Babbage's
                 `Engines' to the Countess of Lovelace, who was a
                 mathematician of great competence and one of the very
                 few people who understood what Babbage was trying to
                 do. Her ideas are so modern that they have become of
                 great topical interest once again, and since her paper
                 has long been out of print (it appeared more than a
                 hundred years ago) it has been reproduced as an
                 appendix to this book. Lady Lovelace's grand-daughter,
                 the Right Hon. Lady Wentworth, has very kindly allowed
                 me to read many of Lady Lovelace's most interesting
                 papers; I was so surprised by the connexion that I
                 found between digital computers and thoroughbred horses
                 that I have given a brief account of the story, for
                 further details of which the reader is referred to Lady
                 Wentworth's own books.''",
  remark-08 =    "From page xi: ``After I had finished the book, I saw a
                 microfilm of a life of Babbage which had been written
                 by his executor, the late Mr. L. H. D. Buxton. Mr.
                 Whitwell of the Powers Samas Company found the
                 manuscript in the Museum of the History of Science in
                 Oxford. It contains a more detailed account of the
                 construction of Babbage's Engines than any I have seen
                 elsewhere, and it is to be hoped that the material will
                 some day be published.''",
  remark-09 =    "From page xiii: ``Much of this book derives from the
                 work of those prolific authors `Anon' and `Ibid' who
                 have done so much to put our English platitudes on a
                 sound literary basis.''",
  remark-10 =    "From page xiii: ``I must express my thanks to all my
                 collaborators; to Lord Halsbury for writing the
                 foreword; to Lady Wentworth who gave me so much
                 information about Lady Lovelace, and who allowed me to
                 reproduce the portrait which has been used as a
                 frontispiece. I am also indebted to Miss Draper who
                 read all the Lovelace paper; and gave me a great deal
                 of help. I must thank Miss Dyke for preparing the flow
                 sheets which I used in Chapter 22. Dr. Gilles and Mr.
                 Whitewell told me the story of Dr. Comrie; Dr. Bullard
                 found some of Babbage's writing in the archives of the
                 National Physical Laboratory; and Professor Aitken, Mr.
                 W. Klein, Dr. van Wijngaarden, Dr. Stokvis, Mr. Seeber,
                 Mr. Ferris and Dr. Gabor gave me much of the
                 information on which Chapter 26 is based. The Portrait
                 of Babbage is included by courtesy of the Director of
                 the Science Museum, South Kensington.''",
  remark-11 =    "From glossary entry on page 411: ``{\em Computor}.
                 `Bad spelling of Computer' --- Oxford English
                 Dictionary.''",
  remark-12 =    "From glossary entry on page 411: ``{\em Cybernetics}.
                 A word invented by Professor Wiener to describe the
                 field of control and communication theory, whether in
                 the machine or in the animal. None of the authors quite
                 understands what the word means, so it has not been
                 used in this book.",
  remark-13 =    "From glossary entry on page 412: ``{\em Hartree
                 Constant}. The time which is expected to elapse before
                 a particular electronic computing machine is finished
                 and working. It was Professor Hartree who first pointed
                 out that this estimated time usually remains constant
                 at about six months for a period of several years
                 during the development of a machine. This phenomenon
                 was well known to Babbage. Few engineers are worried
                 unless the `constant' shows signs of increasing
                 monotonically as the years go by.''",
  remark-14 =    "From glossary entry on page 413: ``{\em Mill}.
                 Babbage's name for the arithmetic unit of his
                 machine.''",
  remark-15 =    "From glossary entry on page 414: ``{\em Programmer}.
                 One who prepares programmes for a machine, `a harmless
                 drudge'.''",
  remark-16 =    "From glossary entry on page 414: ``{\em T{\"u}ring
                 Machine}. In 1936 Dr. Turing wrote a paper on the
                 design and the limitations of computing machines. For
                 this reason they are sometimes known by his name. The
                 umlaut is an unearned and undesirable addition, due,
                 presumably, to an impression that anything so
                 incomprehensible must be Teutonic.''",
  subject =      "Electronic digital computers",
  tableofcontents = "Foreword / v \\
                 Preface / vii \\
                 List of Contributors / xv \\
                 Part One: The History and Theory of Computing Machines
                 \\
                 1. A Brief History of Computation / B. V. Bowden / 3
                 \\
                 2. The Circuit Components of Digital Computers / B. V.
                 Bowden and B. W. Pollard / 32 \\
                 3. The Organization of a Typical Machine / B. V. Bowden
                 / 67 \\
                 4. The Construction, Performance and Maintenance of
                 Digital Computers / B. V. Bowden / 78 \\
                 5. Programming For High-Speed Digital Calculating
                 Machines / J. M. Bennett and A. E. Glennie / 101 \\
                 Part Two: Electronic Computing Machines in Britain and
                 America / \\
                 6. The University of Manchester Computing Machine / T.
                 Kilburn and F. C. Williams / 117 \\
                 7. Calculating Machine Development at Cambridge / 130
                 \\
                 8. Automatic Computation at the National Physical
                 Laboratory / 135 \\
                 9. The Harwell Electronic Digital Computer / E. H.
                 Cooke-Yarborough / 140 \\
                 10. The Telecommunications Research Establishment
                 Parallel Electronic Digital Computer / R. H. A. Carter
                 and A. M. Uttley / 144 \\
                 11. The Imperial College Computing Engine / S.
                 Michaelson and K. D. Tocher / 161 \\
                 12. The Royal Aircraft Establishment
                 Sequence-Controlled Calculator / S. H. Hollingdale /
                 165 \\
                 13. Calculating Machines at the Birkbeck College
                 Computation Laboratory / A. D. Booth / 170 \\
                 14. Computers in America / B. V. Bowden / 173 \\
                 Part Three: Applications of Electronic Computing
                 Machines \\
                 15. Machines for the Solution of Logical Problems / D.
                 G. Prinz and J. B. Smith / 181 \\
                 16. Special-Purpose Automatic Computers / R.
                 Stuart-Williams / 199 \\
                 17. Digital Computation and the Crystallographer / J.
                 M. Bennett and M. V. Wilkes / 203 \\
                 18. The Use of High-Speed Computing Machines in
                 Meteorology / R. S. Scorer / 210 \\
                 19. An Application to Ballistics / A. E. Glennie / 216
                 \\
                 20. Digital Computers and the Engineer / J. M. Bennett
                 / 223 \\
                 21. Machines in Government Calculations / B. B. Swann /
                 234 \\
                 22. The Application of Digital Computers to Business
                 and Commerce / B. V. Bowden / 246 \\
                 23. Electronic Machines and Economics / G. Morton / 272
                 \\
                 24. Problems of Dynamical Astronomy / Cicely M.
                 Popplewell / 282 \\
                 25. Digital Computers Applied to Games / M. Audrey
                 Bates, B. V. Bowden, C. Strachey, and A. M. Turing /
                 286 \\
                 26. Thought and Machine Processes / B. V. Bowden / 311
                 \\
                 Appendix 1: Extracts From \booktitle{Taylor's
                 Scientific Memoirs}, Vol. III / 341 \\
                 Appendix 2: Extracts From the \booktitle{Lovelace
                 Papers} / 409 \\
                 Glossary / 411 \\
                 Index / 415 \\
                 Insets \\
                 Flow Sheet For P.A.Y.E. Calculation / 254 \\
                 Computation of Bernoulli Numbers / 404",
}


bibtype: book
filename: elefunt.bib
label: Birkhoff:1954:SMM
editor: Garrett Birkhoff
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: ix + 353
year: 1954
ISBN: 1-4832-6356-8 OR 1483263568
ISBN13: 978-1-4832-6356-4 OR 9781483263564
LCCN: QA3 .S853
bibdate: Fri Oct 20 10:13:10 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.20 10:13:10 ???
acknowledgement: ack-nhfb
subjectdates: Richard von Mises (1883--1953)
raweditor: Garrett Birkhoff
booktitle:
Studies in Mathematics and Mechanics Presented to Richard von Mises by friends, colleagues, and pupils

title:
Studies in Mathematics and Mechanics Presented to Richard von Mises by friends, colleagues, and pupils

abstract:
Studies in Mathematics and Mechanics is a collection of studies presented to Professor Richard von Mises as a token of reverence and appreciation on the occasion of his seventieth birthday which occurred on April 19, 1953. von Mises' thought has been a stimulus in many seemingly unconnected fields of mathematics, science, and philosophy, to which he has contributed decisive results and new formulations of fundamental concepts. The book contains 42 chapters organized into five parts. Part I contains papers on algebra, number theory and geometry. These include a study of Poincare's representation of a hyperbolic space on an Euclidean half-space and elementary estimates for the least primitive root. Part II on analysis includes papers on a generalization of Green's Formula and its application to the Cauchy problem for a hyperbolic equation, and the fundamental solutions of a singular Beltrami operator. Part III deals with theoretical mechanics and covers topics such as turbulent flow, axially symmetric flow, and oscillating wakes. The papers in Part IV focus on applied mechanics. These include studies on plastic flow under high stresses and the problem of inelastic thermal stresses. Part V presents studies on probability and statistics, including a finite frequency theory of probability and the problem of expansion of clusters of galaxies.

rawabstract:
Studies in Mathematics and Mechanics is a collection of studies presented to Professor Richard von Mises as a token of reverence and appreciation on the occasion of his seventieth birthday which occurred on April 19, 1953. von Mises' thought has been a stimulus in many seemingly unconnected fields of mathematics, science, and philosophy, to which he has contributed decisive results and new formulations of fundamental concepts. The book contains 42 chapters organized into five parts. Part I contains papers on algebra, number theory and geometry. These include a study of Poincar{\'e}'s representation of a hyperbolic space on an Euclidean half-space and elementary estimates for the least primitive root. Part II on analysis includes papers on a generalization of Green's Formula and its application to the Cauchy problem for a hyperbolic equation, and the fundamental solutions of a singular Beltrami operator. Part III deals with theoretical mechanics and covers topics such as turbulent flow, axially symmetric flow, and oscillating wakes. The papers in Part IV focus on applied mechanics. These include studies on plastic flow under high stresses and the problem of inelastic thermal stresses. Part V presents studies on probability and statistics, including a finite frequency theory of probability and the problem of expansion of clusters of galaxies.

rawbooktitle:
Studies in Mathematics and Mechanics Presented to {Richard von Mises} by friends, colleagues, and pupils

rawtitle:
Studies in Mathematics and Mechanics Presented to {Richard von Mises} by friends, colleagues, and pupils

entry:
@Book{Birkhoff:1954:SMM,
  editor =       "Garrett Birkhoff",
  booktitle =    "Studies in Mathematics and Mechanics Presented to
                 {Richard von Mises} by friends, colleagues, and
                 pupils",
  title =        "Studies in Mathematics and Mechanics Presented to
                 {Richard von Mises} by friends, colleagues, and
                 pupils",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "ix + 353",
  year =         "1954",
  ISBN =         "1-4832-6356-8",
  ISBN-13 =      "978-1-4832-6356-4",
  LCCN =         "QA3 .S853",
  bibdate =      "Fri Oct 20 10:13:10 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Studies in Mathematics and Mechanics is a collection
                 of studies presented to Professor Richard von Mises as
                 a token of reverence and appreciation on the occasion
                 of his seventieth birthday which occurred on April 19,
                 1953. von Mises' thought has been a stimulus in many
                 seemingly unconnected fields of mathematics, science,
                 and philosophy, to which he has contributed decisive
                 results and new formulations of fundamental concepts.
                 The book contains 42 chapters organized into five
                 parts. Part I contains papers on algebra, number theory
                 and geometry. These include a study of Poincar{\'e}'s
                 representation of a hyperbolic space on an Euclidean
                 half-space and elementary estimates for the least
                 primitive root. Part II on analysis includes papers on
                 a generalization of Green's Formula and its application
                 to the Cauchy problem for a hyperbolic equation, and
                 the fundamental solutions of a singular Beltrami
                 operator. Part III deals with theoretical mechanics and
                 covers topics such as turbulent flow, axially symmetric
                 flow, and oscillating wakes. The papers in Part IV
                 focus on applied mechanics. These include studies on
                 plastic flow under high stresses and the problem of
                 inelastic thermal stresses. Part V presents studies on
                 probability and statistics, including a finite
                 frequency theory of probability and the problem of
                 expansion of clusters of galaxies.",
  acknowledgement = ack-nhfb,
  subject-dates = "Richard von Mises (1883--1953)",
}


bibtype: book
filename: elefunt.bib
label: Langer:1959:NAP
editor: R. E. Langer
booktitle: On numerical approximation. Proceedings of a Symposium, Madison, April 21--23, 1958
title: On numerical approximation. Proceedings of a Symposium, Madison, April 21--23, 1958
publisher: The University of Wisconsin Press
address: Madison, WI, USA
pages: x + 462
year: 1959
LCCN: QA3 .U45 no. 1
bibdate: Tue Jun 19 06:45:47 2018
bibtimestamp: 2018.06.19 06:45:47 ???
note: Publication no. 1 of the Mathematics Research Center, U.S. Army, the University of Wisconsin.
acknowledgement: ack-nhfb
rawbooktitle: On numerical approximation. {Proceedings of a Symposium, Madison, April 21--23, 1958}
raweditor: R. E. Langer
rawnote: Publication no. 1 of the Mathematics Research Center, U.S. Army, the University of Wisconsin.
rawtitle: On numerical approximation. {Proceedings of a Symposium, Madison, April 21--23, 1958}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib; https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

TOC:
1. On trends and problems in numerical approximation / Ostrowski 2. Linear spaces and approximation theory / Buck 3. Operational methods in numerical analysis based on rational approximations / Kopal 4. On the numerical integration of periodic analytic functions / Davis S. Some new divided difference algorithms in two variables / Salzer 6. Numerical evaluation of multiple integrals / Hammer 7. Optimal approximation and error bounds / Golomb and Weinberger 8. The rationale of approximation / Sard 9. On extremal approximations / Walsh 10. Numerical methods of Tchebycheff approximation / Stiefel 11. Minimax methods in table construction / Fox 12. Existence of essentially nonlinear families suitable for oscillatory approximation / Motzkin 13. On variation diminishing approximation methods / Schoenberg 14. Approximation by functions of fewer variables / Golomb 15. Extremal approximations --- a summary / Miller 16. Survey of recent Russian literature on approximation / Buck 17. The quotient--difference and epsilon algorithms / Bauer 18. Some sufficient conditions for the existence of an asymptotic formula or an asymptotic expansion / Rosser 19. The estimation of (power) spectra and related quantities / Tukey 20. Approximation in partial differential equations / Collatz 21. Special polynomials in numerical analysis / Todd

rawTOC:
1. On trends and problems in numerical approximation / Ostrowski \\ 2. Linear spaces and approximation theory / Buck \\ 3. Operational methods in numerical analysis based on rational approximations / Kopal \\ 4. On the numerical integration of periodic analytic functions / Davis \\ S. Some new divided difference algorithms in two variables / Salzer \\ 6. Numerical evaluation of multiple integrals / Hammer \\ 7. Optimal approximation and error bounds / Golomb and Weinberger \\ 8. The rationale of approximation / Sard \\ 9. On extremal approximations / Walsh \\ 10. Numerical methods of Tchebycheff approximation / Stiefel \\ 11. Minimax methods in table construction / Fox \\ 12. Existence of essentially nonlinear families suitable for oscillatory approximation / Motzkin \\ 13. On variation diminishing approximation methods / Schoenberg \\ 14. Approximation by functions of fewer variables / Golomb \\ 15. Extremal approximations --- a summary / Miller \\ 16. Survey of recent Russian literature on approximation / Buck \\ 17. The quotient--difference and epsilon algorithms / Bauer \\ 18. Some sufficient conditions for the existence of an asymptotic formula or an asymptotic expansion / Rosser \\ 19. The estimation of (power) spectra and related quantities / Tukey \\ 20. Approximation in partial differential equations / Collatz \\ 21. Special polynomials in numerical analysis / Todd

entry:
@Book{Langer:1959:NAP,
  editor =       "R. E. Langer",
  booktitle =    "On numerical approximation. {Proceedings of a
                 Symposium, Madison, April 21--23, 1958}",
  title =        "On numerical approximation. {Proceedings of a
                 Symposium, Madison, April 21--23, 1958}",
  publisher =    "The University of Wisconsin Press",
  address =      "Madison, WI, USA",
  pages =        "x + 462",
  year =         "1959",
  LCCN =         "QA3 .U45 no. 1",
  bibdate =      "Tue Jun 19 06:45:47 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Publication no. 1 of the Mathematics Research Center,
                 U.S. Army, the University of Wisconsin.",
  acknowledgement = ack-nhfb,
  subjects =     "statistics",
  tableofcontents = "1. On trends and problems in numerical
                 approximation / Ostrowski \\
                 2. Linear spaces and approximation theory / Buck \\
                 3. Operational methods in numerical analysis based on
                 rational approximations / Kopal \\
                 4. On the numerical integration of periodic analytic
                 functions / Davis \\
                 S. Some new divided difference algorithms in two
                 variables / Salzer \\
                 6. Numerical evaluation of multiple integrals / Hammer
                 \\
                 7. Optimal approximation and error bounds / Golomb and
                 Weinberger \\
                 8. The rationale of approximation / Sard \\
                 9. On extremal approximations / Walsh \\
                 10. Numerical methods of Tchebycheff approximation /
                 Stiefel \\
                 11. Minimax methods in table construction / Fox \\
                 12. Existence of essentially nonlinear families
                 suitable for oscillatory approximation / Motzkin \\
                 13. On variation diminishing approximation methods /
                 Schoenberg \\
                 14. Approximation by functions of fewer variables /
                 Golomb \\
                 15. Extremal approximations --- a summary / Miller \\
                 16. Survey of recent Russian literature on
                 approximation / Buck \\
                 17. The quotient--difference and epsilon algorithms /
                 Bauer \\
                 18. Some sufficient conditions for the existence of an
                 asymptotic formula or an asymptotic expansion / Rosser
                 \\
                 19. The estimation of (power) spectra and related
                 quantities / Tukey \\
                 20. Approximation in partial differential equations /
                 Collatz \\
                 21. Special polynomials in numerical analysis / Todd",
}


bibtype: book
filename: elefunt.bib
label: Ralston:1960:MMD
editor: Anthony Ralston and Herbert S. Wilf
booktitle: Mathematical methods for digital computers
title: Mathematical methods for digital computers
publisher: pub-WILEY
address: pub-WILEY:adr
pages: various
year: 1960 -- 1977
ISBN: 0-471-70690-6 OR 0471706906
ISBN13: 978-0-471-70690-8 OR 9780471706908
LCCN: QA39 .R26
bibdate: Mon Jan 13 10:36:06 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.13 10:36:06 ???
note: Three volumes.
acknowledgement: ack-nhfb
rawbooktitle: Mathematical methods for digital computers
raweditor: Anthony Ralston and Herbert S. Wilf
rawnote: Three volumes.
rawtitle: Mathematical methods for digital computers
entry:
@Book{Ralston:1960:MMD,
  editor =       "Anthony Ralston and Herbert S. Wilf",
  booktitle =    "Mathematical methods for digital computers",
  title =        "Mathematical methods for digital computers",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "various",
  year =         "1960--1977",
  ISBN =         "0-471-70690-6",
  ISBN-13 =      "978-0-471-70690-8",
  LCCN =         "QA39 .R26",
  bibdate =      "Mon Jan 13 10:36:06 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Three volumes.",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Abramowitz:1964:HMF
editor: Milton Abramowitz and Irene A. Stegun
booktitle: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
title: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
volume: 55
publisher: U. S. Department of Commerce
address: Washington, DC, USA
pages: xiv + 1046
year: 1964
LCCN: QA47.A161 1972; QA 55 A16h 1972
bibdate: Thu Jan 27 07:58:12 2000
bibtimestamp: 2000.01.27 07:58:12 ???
series: Applied mathematics series
acknowledgement: ack-nhfb
key: NBS
rawbooktitle: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
raweditor: Milton Abramowitz and Irene A. Stegun
rawtitle: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
bibsource:
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

note:
Tenth printing, with corrections (December 1972). This book is also available online at path =http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP= in bitmap image format.

abstract:
This book is a compendium of mathematical formulas, tables, and graphs. It contains a table of analytical integrals, differential equations, and numerical series; and includes tables of trigonometric and hyperbolic functions, tables for numerical integration, rules for differentiation and integration, and techniques for point interpolation and function approximation. Additionally, it devotes a entire section to mathematical and physical constants as fractions and powers of Pi, e, and prime numbers; and discusses statistics by presenting combinatorial analysis and probability functions.

TOC:
Mathematical constants / David S. Liepman Physical constants and conversion factors / A. G. McNish Elementary analytical methods / Milton Abramowitz Elementary transcendental functions: logarithmic, exponential, circular and hyperbolic functions / Ruth Zucker Exponential integral and related functions / Walter Gautschi and William F. Cahill Gamma function and related functions / Philip J. Davis Error function and Fresnel integrals / Walter Gautschi Legendre functions / Irene A. Stegun Bessel functions of integer order / F. W. J. Olver Bessell functions of fractional order / H. A. Antosiewicz Integrals of Bessel functions / Yudell L. Luke Struve functions and related functions / Milton Abramowitz Confluent hypergeometric functions / Lucy Joan Slater Coulomb wave functions / Milton Abramowitz Hypergeometric functions / Fritz Oberhettinger Jacobian elliptic functions and theta functions; Elliptic integrals / L. M. Milne-Thomson Weierstrass elliptic and related functions / Thomas H. Southard Parabolic cylinder functions / J. C. P. Millerldots Mathieu functions / Gertrude Blanch Spheroidal wave functions / Arnold N. Lowan Orthogonal polynomials / Urs W. Hochstrasser Bernoulli and Euler polynomials, Riemann zeta function / Emilie V. Haynesworth and Karl Goldberg Combinatorial analysis / K. Goldberg, M. Newman and E. Haynesworth Numerical interpolation, differentiation and integration / Philip J. Davis and Ivan Polonsky Probability functions / Marvin Zelen and Norman C. Severo Miscellaneous functions / Irene A. Stegun Scales of notation / S. Peavy and A. Schopf Laplace transforms

rawabstract:
This book is a compendium of mathematical formulas, tables, and graphs. It contains a table of analytical integrals, differential equations, and numerical series; and includes tables of trigonometric and hyperbolic functions, tables for numerical integration, rules for differentiation and integration, and techniques for point interpolation and function approximation. Additionally, it devotes a entire section to mathematical and physical constants as fractions and powers of Pi, e, and prime numbers; and discusses statistics by presenting combinatorial analysis and probability functions.

rawnote:
Tenth printing, with corrections (December 1972). This book is also available online at \path=http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP= in bitmap image format.

rawTOC:
Mathematical constants / David S. Liepman \\ Physical constants and conversion factors / A. G. McNish \\ Elementary analytical methods / Milton Abramowitz \\ Elementary transcendental functions: logarithmic, exponential, circular and hyperbolic functions / Ruth Zucker \\ Exponential integral and related functions / Walter Gautschi and William F. Cahill \\ Gamma function and related functions / Philip J. Davis \\ Error function and Fresnel integrals / Walter Gautschi \\ Legendre functions / Irene A. Stegun \\ Bessel functions of integer order / F. W. J. Olver \\ Bessell functions of fractional order / H. A. Antosiewicz \\ Integrals of Bessel functions / Yudell L. Luke \\ Struve functions and related functions / Milton Abramowitz \\ Confluent hypergeometric functions / Lucy Joan Slater \\ Coulomb wave functions / Milton Abramowitz \\ Hypergeometric functions / Fritz Oberhettinger \\ Jacobian elliptic functions and theta functions; Elliptic integrals / L. M. Milne-Thomson \\ Weierstrass elliptic and related functions / Thomas H. Southard \\ Parabolic cylinder functions / J. C. P. Miller\ldots{} Mathieu functions / Gertrude Blanch \\ Spheroidal wave functions / Arnold N. Lowan \\ Orthogonal polynomials / Urs W. Hochstrasser \\ Bernoulli and Euler polynomials, Riemann zeta function / Emilie V. Haynesworth and Karl Goldberg \\ Combinatorial analysis / K. Goldberg, M. Newman and E. Haynesworth \\ Numerical interpolation, differentiation and integration / Philip J. Davis and Ivan Polonsky \\ Probability functions / Marvin Zelen and Norman C. Severo \\ Miscellaneous functions / Irene A. Stegun \\ Scales of notation / S. Peavy and A. Schopf \\ Laplace transforms

entry:
@Book{Abramowitz:1964:HMF,
  editor =       "Milton Abramowitz and Irene A. Stegun",
  key =          "NBS",
  booktitle =    "Handbook of Mathematical Functions with Formulas,
                 Graphs, and Mathematical Tables",
  title =        "Handbook of Mathematical Functions with Formulas,
                 Graphs, and Mathematical Tables",
  volume =       "55",
  publisher =    "U. S. Department of Commerce",
  address =      "Washington, DC, USA",
  pages =        "xiv + 1046",
  year =         "1964",
  LCCN =         "QA47.A161 1972; QA 55 A16h 1972",
  bibdate =      "Thu Jan 27 07:58:12 2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Tenth printing, with corrections (December 1972). This
                 book is also available online at
                 \path=http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP=
                 in bitmap image format.",
  series =       "Applied mathematics series",
  abstract =     "This book is a compendium of mathematical formulas,
                 tables, and graphs. It contains a table of analytical
                 integrals, differential equations, and numerical
                 series; and includes tables of trigonometric and
                 hyperbolic functions, tables for numerical integration,
                 rules for differentiation and integration, and
                 techniques for point interpolation and function
                 approximation. Additionally, it devotes a entire
                 section to mathematical and physical constants as
                 fractions and powers of Pi, e, and prime numbers; and
                 discusses statistics by presenting combinatorial
                 analysis and probability functions.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Mathematical constants / David S. Liepman \\
                 Physical constants and conversion factors / A. G.
                 McNish \\
                 Elementary analytical methods / Milton Abramowitz \\
                 Elementary transcendental functions: logarithmic,
                 exponential, circular and hyperbolic functions / Ruth
                 Zucker \\
                 Exponential integral and related functions / Walter
                 Gautschi and William F. Cahill \\
                 Gamma function and related functions / Philip J. Davis
                 \\
                 Error function and Fresnel integrals / Walter Gautschi
                 \\
                 Legendre functions / Irene A. Stegun \\
                 Bessel functions of integer order / F. W. J. Olver \\
                 Bessell functions of fractional order / H. A.
                 Antosiewicz \\
                 Integrals of Bessel functions / Yudell L. Luke \\
                 Struve functions and related functions / Milton
                 Abramowitz \\
                 Confluent hypergeometric functions / Lucy Joan Slater
                 \\
                 Coulomb wave functions / Milton Abramowitz \\
                 Hypergeometric functions / Fritz Oberhettinger \\
                 Jacobian elliptic functions and theta functions;
                 Elliptic integrals / L. M. Milne-Thomson \\
                 Weierstrass elliptic and related functions / Thomas H.
                 Southard \\
                 Parabolic cylinder functions / J. C. P. Miller\ldots{}
                 Mathieu functions / Gertrude Blanch \\
                 Spheroidal wave functions / Arnold N. Lowan \\
                 Orthogonal polynomials / Urs W. Hochstrasser \\
                 Bernoulli and Euler polynomials, Riemann zeta function
                 / Emilie V. Haynesworth and Karl Goldberg \\
                 Combinatorial analysis / K. Goldberg, M. Newman and E.
                 Haynesworth \\
                 Numerical interpolation, differentiation and
                 integration / Philip J. Davis and Ivan Polonsky \\
                 Probability functions / Marvin Zelen and Norman C.
                 Severo \\
                 Miscellaneous functions / Irene A. Stegun \\
                 Scales of notation / S. Peavy and A. Schopf \\
                 Laplace transforms",
}


bibtype: book
filename: elefunt.bib
label: Magnus:1966:FTS
author: Wilhelm Magnus and Fritz Oberhettinger and Raj Pal Soni
booktitle: Formulas and theorems for the special functions of mathematical physics
title: Formulas and theorems for the special functions of mathematical physics
publisher: pub-SV
address: pub-SV:adr
edition: Third
pages: viii + 508
year: 1966
LCCN: QA1 G88 v. 52, 1966
bibdate: Sat Oct 30 18:23:25 2010
bibtimestamp: 2010.10.30 18:23:25 ???
note: See errata cite Cohl:2012:TEF,Szmytkowski:2013:EBT.
acknowledgement: ack-nhfb
rawauthor: Wilhelm Magnus and Fritz Oberhettinger and Raj Pal Soni
rawbooktitle: Formulas and theorems for the special functions of mathematical physics
rawnote: See errata \cite{Cohl:2012:TEF,Szmytkowski:2013:EBT}.
rawtitle: Formulas and theorems for the special functions of mathematical physics
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib

entry:
@Book{Magnus:1966:FTS,
  author =       "Wilhelm Magnus and Fritz Oberhettinger and Raj Pal
                 Soni",
  booktitle =    "Formulas and theorems for the special functions of
                 mathematical physics",
  title =        "Formulas and theorems for the special functions of
                 mathematical physics",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Third",
  pages =        "viii + 508",
  year =         "1966",
  LCCN =         "QA1 G88 v. 52, 1966",
  bibdate =      "Sat Oct 30 18:23:25 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  note =         "See errata
                 \cite{Cohl:2012:TEF,Szmytkowski:2013:EBT}.",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: AFIPS:1969:ACPb
booktitle: 1969 Fall Joint Computer Conference, November 18--20, 1969, Las Vegas, Nevada
title: 1969 Fall Joint Computer Conference, November 18--20, 1969, Las Vegas, Nevada
volume: 35
publisher: pub-AFIPS
address: pub-AFIPS:adr
pages: 807
year: 1969
LCCN: TK7885.A1 J6 1969
bibdate: Sat Sep 24 01:06:00 1994
bibtimestamp: 1994.09.24 01:06:00 ???
series: AFIPS conference proceedings
acknowledgement: ack-nhfb
key: AFIPS FJCC '69
rawbooktitle: 1969 Fall Joint Computer Conference, November 18--20, 1969, Las Vegas, Nevada
rawtitle: 1969 Fall Joint Computer Conference, November 18--20, 1969, Las Vegas, Nevada
entry:
@Proceedings{AFIPS:1969:ACPb,
  key =          "AFIPS FJCC '69",
  booktitle =    "1969 Fall Joint Computer Conference, November 18--20,
                 1969, Las Vegas, Nevada",
  title =        "1969 Fall Joint Computer Conference, November 18--20,
                 1969, Las Vegas, Nevada",
  volume =       "35",
  publisher =    pub-AFIPS,
  address =      pub-AFIPS:adr,
  pages =        "807",
  year =         "1969",
  LCCN =         "TK7885.A1 J6 1969",
  bibdate =      "Sat Sep 24 01:06:00 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "AFIPS conference proceedings",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: AFIPS:1971:ACP
booktitle: 1971 Spring Joint Computer Conference, May 18--20, 1971, Atlantic City, New Jersey
title: 1971 Spring Joint Computer Conference, May 18--20, 1971, Atlantic City, New Jersey
volume: 38
publisher: pub-AFIPS
address: pub-AFIPS:adr
pages: 631
year: 1971
bibdate: Fri Sep 16 10:47:01 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.16 10:47:01 ???
series: AFIPS conference proceedings
acknowledgement: ack-nj
key: AFIPS SJCC '71
rawbooktitle: 1971 Spring Joint Computer Conference, May 18--20, 1971, Atlantic City, New Jersey
rawtitle: 1971 Spring Joint Computer Conference, May 18--20, 1971, Atlantic City, New Jersey
entry:
@Proceedings{AFIPS:1971:ACP,
  key =          "AFIPS SJCC '71",
  booktitle =    "1971 Spring Joint Computer Conference, May 18--20,
                 1971, Atlantic City, New Jersey",
  title =        "1971 Spring Joint Computer Conference, May 18--20,
                 1971, Atlantic City, New Jersey",
  volume =       "38",
  publisher =    pub-AFIPS,
  address =      pub-AFIPS:adr,
  pages =        "631",
  year =         "1971",
  LCCN =         "????",
  bibdate =      "Fri Sep 16 10:47:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "AFIPS conference proceedings",
  acknowledgement = ack-nj # " and " # ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Rice:1971:MS
author: John R. Rice
booktitle: Mathematical Software
title: Mathematical Software
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xvii + 515
year: 1971
ISBN: 0-12-587250-X OR 012587250X
ISBN13: 978-0-12-587250-8 OR 9780125872508
LCCN: QA1 .M26
bibdate: Thu Sep 15 18:56:52 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.15 18:56:52 ???
acknowledgement: ack-nhfb
rawauthor: John R. Rice
rawbooktitle: Mathematical Software
rawtitle: Mathematical Software
note:
Based on the proceedings of the Mathematical Software Symposium held at Purdue University, Lafayette, Indiana, USA, April 1--3, 1970.

rawnote:
Based on the proceedings of the Mathematical Software Symposium held at Purdue University, Lafayette, Indiana, USA, April 1--3, 1970.

entry:
@Book{Rice:1971:MS,
  author =       "John R. Rice",
  booktitle =    "Mathematical Software",
  title =        "Mathematical Software",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xvii + 515",
  year =         "1971",
  ISBN =         "0-12-587250-X",
  ISBN-13 =      "978-0-12-587250-8",
  LCCN =         "QA1 .M26",
  bibdate =      "Thu Sep 15 18:56:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Based on the proceedings of the Mathematical Software
                 Symposium held at Purdue University, Lafayette,
                 Indiana, USA, April 1--3, 1970.",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Askey:1975:TAS
editor: Richard Askey
number: 35
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xi + 560
year: 1975
ISBN: 0-12-064850-4 OR 0120648504
ISBN13: 978-0-12-064850-4 OR 9780120648504
LCCN: QA3 .U45 no. 35 QA351
bibdate: Sat Oct 30 07:41:32 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 07:41:32 MDT
series: Publication of the Mathematics Research Center, the University of Wisconsin
subject: Functions, Special; Congresses
acknowledgement: ack-nhfb
raweditor: Richard Askey
booktitle:
Theory and application of special functions: proceedings of an advanced seminar sponsored by the Mathematics Research Center, the University of Wisconsin-Madison, March 31--April 2, 1975

title:
Theory and application of special functions: proceedings of an advanced seminar sponsored by the Mathematics Research Center, the University of Wisconsin-Madison, March 31--April 2, 1975

rawbooktitle:
{Theory and application of special functions: proceedings of an advanced seminar sponsored by the Mathematics Research Center, the University of Wisconsin-Madison, March 31--April 2, 1975}

rawtitle:
{Theory and application of special functions: proceedings of an advanced seminar sponsored by the Mathematics Research Center, the University of Wisconsin-Madison, March 31--April 2, 1975}

entry:
@Proceedings{Askey:1975:TAS,
  editor =       "Richard Askey",
  booktitle =    "{Theory and application of special functions:
                 proceedings of an advanced seminar sponsored by the
                 Mathematics Research Center, the University of
                 Wisconsin-Madison, March 31--April 2, 1975}",
  title =        "{Theory and application of special functions:
                 proceedings of an advanced seminar sponsored by the
                 Mathematics Research Center, the University of
                 Wisconsin-Madison, March 31--April 2, 1975}",
  number =       "35",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xi + 560",
  year =         "1975",
  ISBN =         "0-12-064850-4",
  ISBN-13 =      "978-0-12-064850-4",
  LCCN =         "QA3 .U45 no. 35 QA351",
  bibdate =      "Sat Oct 30 07:41:32 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Publication of the Mathematics Research Center, the
                 University of Wisconsin",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  meetingname =  "Advanced Seminar on Special Functions, Madison, Wis.,
                 1975.",
  subject =      "Functions, Special; Congresses",
}


bibtype: proceedings
filename: elefunt.bib
label: Miller:1975:TNA
editor: John J. H. Miller
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: various
year: 1975
ISBN: 0-12-496950-X OR 012496950X
ISBN13: 978-0-12-496950-6 OR 9780124969506
LCCN: QA297 .R69 1973
bibdate: Mon Jan 13 10:41:13 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.13 10:41:13 ???
acknowledgement: ack-nhfb
raweditor: John J. H. Miller
booktitle:
Topics in numerical analysis: proceedings of the Royal Irish Academy Conference on Numerical Analysis, 1972, 1974, 1976

title:
Topics in numerical analysis: proceedings of the Royal Irish Academy Conference on Numerical Analysis, 1972, 1974, 1976

rawbooktitle:
Topics in numerical analysis: proceedings of the Royal Irish Academy Conference on Numerical Analysis, 1972, 1974, 1976

entry:
@Proceedings{Miller:1975:TNA,
  editor =       "John J. H. Miller",
  booktitle =    "Topics in numerical analysis: proceedings of the Royal
                 Irish Academy Conference on Numerical Analysis, 1972,
                 1974, 1976",
  title =        "Topics in numerical analysis: proceedings of the Royal
                 Irish Academy Conference on Numerical Analysis, 1972,
                 1974, 1976",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "various",
  year =         "1975",
  ISBN =         "0-12-496950-X",
  ISBN-13 =      "978-0-12-496950-6",
  LCCN =         "QA297 .R69 1973",
  bibdate =      "Mon Jan 13 10:41:13 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Traub:1976:ACC
editor: J. F. (Joseph Frederick) Traub
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: ix + 239
year: 1976
ISBN: 0-12-697560-4 OR 0126975604
ISBN13: 978-0-12-697560-4 OR 9780126975604
LCCN: QA297.S9151 1975
bibdate: Mon Jan 13 10:18:33 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.13 10:18:33 ???
acknowledgement: ack-nhfb
raweditor: J. F. (Joseph Frederick) Traub
booktitle:
Analytic computational complexity: Proceedings of the Symposium on Analytic Computational Complexity, held by the Computer Science Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania, on April 7--8, 1975

title:
Analytic computational complexity: Proceedings of the Symposium on Analytic Computational Complexity, held by the Computer Science Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania, on April 7--8, 1975

rawbooktitle:
{Analytic computational complexity: Proceedings of the Symposium on Analytic Computational Complexity, held by the Computer Science Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania, on April 7--8, 1975}

rawtitle:
{Analytic computational complexity: Proceedings of the Symposium on Analytic Computational Complexity, held by the Computer Science Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania, on April 7--8, 1975}

entry:
@Proceedings{Traub:1976:ACC,
  editor =       "J. F. (Joseph Frederick) Traub",
  booktitle =    "{Analytic computational complexity: Proceedings of the
                 Symposium on Analytic Computational Complexity, held by
                 the Computer Science Department, Carnegie-Mellon
                 University, Pittsburgh, Pennsylvania, on April 7--8,
                 1975}",
  title =        "{Analytic computational complexity: Proceedings of the
                 Symposium on Analytic Computational Complexity, held by
                 the Computer Science Department, Carnegie-Mellon
                 University, Pittsburgh, Pennsylvania, on April 7--8,
                 1975}",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "ix + 239",
  year =         "1976",
  ISBN =         "0-12-697560-4",
  ISBN-13 =      "978-0-12-697560-4",
  LCCN =         "QA297.S9151 1975",
  bibdate =      "Mon Jan 13 10:18:33 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Cowell:1977:PMS
editor: Wayne Cowell
booktitle: Portability of Numerical Software Workshop, Oak Brook, Illinois, June 21--23, 1976
title: Portability of Numerical Software Workshop, Oak Brook, Illinois, June 21--23, 1976
volume: 57
publisher: pub-SV
address: pub-SV:adr
pages: viii + 539
year: 1977
ISBN: 0-387-08446-0 OR 0387084460
ISBN13: 978-0-387-08446-6 OR 9780387084466
LCCN: QA297 .W65 1976
bibdate: Sat Sep 24 00:24:09 1994
bibtimestamp: 1994.09.24 00:24:09 ???
series: Lecture Notes in Computer Science
remark: Workshop organized by Argonne National Laboratory.
acknowledgement: ack-nhfb
rawbooktitle: {Portability of Numerical Software Workshop, Oak Brook, Illinois, June 21--23, 1976}
raweditor: Wayne Cowell
rawtitle: {Portability of Numerical Software Workshop, Oak Brook, Illinois, June 21--23, 1976}
entry:
@Proceedings{Cowell:1977:PMS,
  editor =       "Wayne Cowell",
  booktitle =    "{Portability of Numerical Software Workshop, Oak
                 Brook, Illinois, June 21--23, 1976}",
  title =        "{Portability of Numerical Software Workshop, Oak
                 Brook, Illinois, June 21--23, 1976}",
  volume =       "57",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 539",
  year =         "1977",
  ISBN =         "0-387-08446-0",
  ISBN-13 =      "978-0-387-08446-6",
  LCCN =         "QA297 .W65 1976",
  bibdate =      "Sat Sep 24 00:24:09 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Lecture Notes in Computer Science",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  remark =       "Workshop organized by Argonne National Laboratory.",
}


bibtype: proceedings
filename: elefunt.bib
label: IEEE:1978:PSC
editor: IEEE
booktitle: Proceedings of the Symposium on Computer Arithmetic (4th: 1978: Santa Monica, CA)
title: Proceedings of the Symposium on Computer Arithmetic (4th: 1978: Santa Monica, CA)
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xi + 274
year: 1978
ISSN: 1063-6889 OR 10636889
LCCN: QA76.6 .S919a
bibdate: Mon May 19 15:22:15 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.05.19 15:22:15 ???
note: IEEE catalog no. 78 CH1412-6C.
acknowledgement: ack-nhfb
rawbooktitle: Proceedings of the Symposium on Computer Arithmetic {(4th: 1978: Santa Monica, CA)}
raweditor: {IEEE}
rawnote: IEEE catalog no. 78 CH1412-6C.
rawtitle: Proceedings of the Symposium on Computer Arithmetic {(4th: 1978: Santa Monica, CA)}
keywords:
Computer arithmetic --- Congresses.; Electronic digital computers --- Programming --- Congresses.; Floating-point arithmetic --- Congresses.

entry:
@Proceedings{IEEE:1978:PSC,
  editor =       "{IEEE}",
  booktitle =    "Proceedings of the Symposium on Computer Arithmetic
                 {(4th: 1978: Santa Monica, CA)}",
  title =        "Proceedings of the Symposium on Computer Arithmetic
                 {(4th: 1978: Santa Monica, CA)}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 274",
  year =         "1978",
  ISSN =         "1063-6889",
  LCCN =         "QA76.6 .S919a",
  bibdate =      "Mon May 19 15:22:15 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "IEEE catalog no. 78 CH1412-6C.",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic --- Congresses.; Electronic
                 digital computers --- Programming --- Congresses.;
                 Floating-point arithmetic --- Congresses.",
}


bibtype: proceedings
filename: elefunt.bib
label: Alefeld:1980:PSE
editor: G. Alefeld and R. D. Grigorieff and R. Albrecht and U. Kulisch and F. Stummel
volume: 2
publisher: pub-SV
address: pub-SV:adr
pages: 229
year: 1980
ISBN: 0-387-81566-X OR 038781566X
ISBN13: 978-0-387-81566-4 OR 9780387815664
ISSN: 0344-8029 OR 03448029
LCCN: QA297 .F84
bibdate: Mon Jan 13 10:20:47 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.13 10:20:47 ???
series: Computing. Supplementum
acknowledgement: ack-nhfb
raweditor: G. Alefeld and R. D. Grigorieff and R. Albrecht and U. Kulisch and F. Stummel
booktitle:
Fundamentals of numerical computation (computer-oriented numerical analysis). Proceedings of a conference held June 5--8, 1979, on the occasion of the centennial of the Technical University of Berlin

title:
Fundamentals of numerical computation (computer-oriented numerical analysis). Proceedings of a conference held June 5--8, 1979, on the occasion of the centennial of the Technical University of Berlin

rawbooktitle:
{Fundamentals of numerical computation (computer-oriented numerical analysis). Proceedings of a conference held June 5--8, 1979, on the occasion of the centennial of the Technical University of Berlin}

rawtitle:
{Fundamentals of numerical computation (computer-oriented numerical analysis). Proceedings of a conference held June 5--8, 1979, on the occasion of the centennial of the Technical University of Berlin}

entry:
@Proceedings{Alefeld:1980:PSE,
  editor =       "G. Alefeld and R. D. Grigorieff and R. Albrecht and U.
                 Kulisch and F. Stummel",
  booktitle =    "{Fundamentals of numerical computation
                 (computer-oriented numerical analysis). Proceedings of
                 a conference held June 5--8, 1979, on the occasion of
                 the centennial of the Technical University of Berlin}",
  title =        "{Fundamentals of numerical computation
                 (computer-oriented numerical analysis). Proceedings of
                 a conference held June 5--8, 1979, on the occasion of
                 the centennial of the Technical University of Berlin}",
  volume =       "2",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "229",
  year =         "1980",
  ISBN =         "0-387-81566-X",
  ISBN-13 =      "978-0-387-81566-4",
  ISSN =         "0344-8029",
  LCCN =         "QA297 .F84",
  bibdate =      "Mon Jan 13 10:20:47 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Computing. Supplementum",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Dieudonne:1980:SFL
editor: Jean Dieudonne
booktitle: Special functions and linear representations of Lie groups
title: Special functions and linear representations of Lie groups
volume: 42
address: Providence, RI, USA
pages: iii + 59
year: 1980
ISBN: 0-8218-1692-6 OR 0821816926
ISBN13: 978-0-8218-1692-9 OR 9780821816929
bibdate: Sat Oct 30 17:14:47 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.bibsys.no:2100/BIBSYS
bibtimestamp: 2010.10.30 17:14:47 MDT
series: Regional conference series in mathematics
acknowledgement: ack-nhfb
rawbooktitle: {Special functions and linear representations of Lie groups}
raweditor: Jean Dieudonn{\'e}
rawtitle: {Special functions and linear representations of Lie groups}
publisher:
Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society

remark:
Expository lectures from the CBMS regional conference held at East Carolina University, March 5--9, 1979.

entry:
@Proceedings{Dieudonne:1980:SFL,
  editor =       "Jean Dieudonn{\'e}",
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                 groups}",
  title =        "{Special functions and linear representations of Lie
                 groups}",
  volume =       "42",
  publisher =    "Published for the Conference Board of the Mathematical
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  address =      "Providence, RI, USA",
  pages =        "iii + 59",
  year =         "1980",
  ISBN =         "0-8218-1692-6",
  ISBN-13 =      "978-0-8218-1692-9",
  LCCN =         "????",
  bibdate =      "Sat Oct 30 17:14:47 MDT 2010",
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  acknowledgement = ack-nhfb,
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}


bibtype: proceedings
filename: elefunt.bib
label: Lavington:1980:IPP
editor: Simon Hugh Lavington
publisher: pub-ENH
address: pub-ENH:adr
pages: xiii + 1070
year: 1980
ISBN: 0-444-86034-7 OR 0444860347
ISBN13: 978-0-444-86034-7 OR 9780444860347
LCCN: QA 75.5 I57 1980
bibdate: Thu Sep 01 23:09:20 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.01 23:09:20 ???
acknowledgement: ack-nhfb
raweditor: Simon Hugh Lavington
booktitle:
Information Processing 80: Proceedings of IFIP Congress 80, Tokyo, Japan, October 6--9, 1980, Melbourne, Australia, October 14--17, 1980

title:
Information Processing 80: Proceedings of IFIP Congress 80, Tokyo, Japan, October 6--9, 1980, Melbourne, Australia, October 14--17, 1980

rawbooktitle:
Information Processing 80: Proceedings of {IFIP} Congress 80, Tokyo, Japan, October 6--9, 1980, Melbourne, Australia, October 14--17, 1980

rawtitle:
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  editor =       "Simon Hugh Lavington",
  booktitle =    "Information Processing 80: Proceedings of {IFIP}
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  title =        "Information Processing 80: Proceedings of {IFIP}
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  address =      pub-ENH:adr,
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  bibdate =      "Thu Sep 01 23:09:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
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bibtype: proceedings
filename: elefunt.bib
label: IEEE:1981:PIS
editor: IEEE
publisher: pub-IEEE
address: pub-IEEE:adr
pages: vii + 278
year: 1981
LCCN: QA76.9.C62 S95 1981
bibdate: Mon May 19 13:17:13 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.05.19 13:17:13 ???
note: IEEE Catalog No. 81CH1630-3. Computer Society Order No. 347.
acknowledgement: ack-nhfb
raweditor: {IEEE}
rawnote: IEEE Catalog No. 81CH1630-3. Computer Society Order No. 347.
booktitle:
Proceedings: 5th Symposium on Computer Arithmetic, May 18-19, 1981, University of Michigan, Ann Arbor, Michigan

title:
Proceedings: 5th Symposium on Computer Arithmetic, May 18-19, 1981, University of Michigan, Ann Arbor, Michigan

rawbooktitle:
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  title =        "Proceedings: 5th Symposium on Computer Arithmetic, May
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  address =      pub-IEEE:adr,
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  xxISBN =       "none",
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bibtype: proceedings
filename: elefunt.bib
label: IEEE:1981:PSC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: vii + 278
year: 1981
LCCN: QA 76.6 S985t 1981
bibdate: Sat Feb 24 15:01:45 MST 1996
bibtimestamp: 1996.02.24 15:01:45 MST
note: IEEE catalog number 81CH1630-C.
acknowledgement: ack-nhfb
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booktitle:
Proceedings: 5th Symposium on Computer Arithmetic, May 18--19, 1981, University of Michigan, Ann Arbor, Michigan

title:
Proceedings: 5th Symposium on Computer Arithmetic: May 18--19, 1981, University of Michigan, Ann Arbor, Michigan

keywords:
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bibtype: proceedings
filename: elefunt.bib
label: Mulvey:1982:EMP
editor: J. M. Mulvey
volume: 199
publisher: pub-SV
address: pub-SV:adr
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ISBN: 0-387-11495-5 OR 0387114955
ISBN13: 978-0-387-11495-8 OR 9780387114958
LCCN: QA402.5 .E94 1982
bibdate: Thu Nov 17 06:36:49 1994
bibtimestamp: 1994.11.17 06:36:49 ???
series: Lecture Notes in Economics and Mathematical Systems
acknowledgement: ack-nhfb
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booktitle:
Evaluating Mathematical Programming Techniques: Proceedings of a Conference Held at the National Bureau of Standards, Boulder, Colorado, January 5--6, 1981

title:
Evaluating Mathematical Programming Techniques: Proceedings of a Conference Held at the National Bureau of Standards, Boulder, Colorado, January 5--6, 1981

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  title =        "{Evaluating Mathematical Programming Techniques:
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bibtype: proceedings
filename: elefunt.bib
label: Hwang:1985:PSC
editor: Kai Hwang
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xi + 343
year: 1985
LCCN: QA76.9.C62 S95 1985
bibdate: Thu Sep 08 00:11:41 1994
bibtimestamp: 1994.09.08 00:11:41 ???
note: IEEE catalog number 85CH2146-9. IEEE Computer Society order number 632.
keywords: ARITH-7
acknowledgement: ack-nj
raweditor: Kai Hwang
rawnote: IEEE catalog number 85CH2146-9. IEEE Computer Society order number 632.
booktitle:
Proceedings: 7th Symposium on Computer Arithmetic, June 4--6, 1985, University of Illinois, Urbana, Illinois

title:
Proceedings: 7th Symposium on Computer Arithmetic, June 4--6, 1985, University of Illinois, Urbana, Illinois

ISBN:
0-8186-0632-0 (paperback), 0-8186-8632-4 (hard), 0-8186-4632-2 (microfiche) OR 0818606320 (paperback), 0818686324 (hard), 0818646322 (microfiche)

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  title =        "Proceedings: 7th Symposium on Computer Arithmetic,
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  address =      pub-IEEE:adr,
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bibtype: proceedings
filename: elefunt.bib
label: IEEE:1985:ERC
booktitle: 1985 IEEE Region 5 Conference, March 13--15, 1985, Holiday Inn Civic Center, Lubbock, Texas
title: 1985 IEEE Region 5 Conference, March 13--15, 1985, Holiday Inn Civic Center, Lubbock, Texas
publisher: pub-IEEE
address: pub-IEEE:adr
pages: vi + 71
year: 1985
LCCN: TK 7801 N56 1985
bibdate: Thu Sep 15 18:50:54 1994
bibtimestamp: 1994.09.15 18:50:54 ???
acknowledgement: ack-nhfb
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  title =        "1985 {IEEE} Region 5 Conference, March 13--15, 1985,
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  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "vi + 71",
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  LCCN =         "TK 7801 N56 1985",
  bibdate =      "Thu Sep 15 18:50:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
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  acknowledgement = ack-nhfb,
  xxISBN =       "(none)",
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bibtype: proceedings
filename: elefunt.bib
label: Marron:1985:FEP
editor: J. S. Marron
booktitle: Function estimates: proceedings of a conference held July 28--August 3, 1985
title: Function estimates: proceedings of a conference held July 28--August 3, 1985
volume: 59
publisher: pub-AMS
address: pub-AMS:adr
pages: ix + 178
year: 1985
ISBN: 0-8218-5062-8 OR 0821850628
ISBN13: 978-0-8218-5062-6 OR 9780821850626
ISSN: 0271-4132 (print), 1098-3627 (electronic) OR 02714132 (print), 10983627 (electronic)
LCCN: QA276.8 .C651 1985
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
note: Held at Humboldt State University, Arcata, California.
series: Contemporary mathematics (American Mathematical Society)
subject: G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS
acknowledgement: ack-nhfb
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bibtype: proceedings
filename: elefunt.bib
label: Miranker:1985:ASC
editor: Willard L. Miranker and Richard A. Toupin
booktitle: Accurate Scientific Computations: Symposium, Bad Neuenahr, FRG, March 12--14, 1985: Proceedings
title: Accurate Scientific Computations: Symposium, Bad Neuenahr, FRG, March 12--14, 1985: Proceedings
volume: 235
publisher: pub-SV
address: pub-SV:adr
pages: x + 205
year: 1985
DOI: https://doi.org/10.1007/3-540-16798-6
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ISBN13: 978-0-387-16798-5 OR 9780387167985
LCCN: QA76.95 .A231 1986
bibdate: Sat Sep 03 12:24:08 1994
bibtimestamp: 1994.09.03 12:24:08 ???
series: ser-LNCS
acknowledgement: ack-nhfb
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bibtype: proceedings
filename: elefunt.bib
label: Miranker:1986:ASC
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publisher: pub-SV
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ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
LCCN: QA76.95 .A231 1986
bibdate: Fri Apr 12 07:14:49 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.04.12 07:14:49 ???
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bibtype: proceedings
filename: elefunt.bib
label: ACM:1987:UAA
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publisher: pub-ACM
address: pub-ACM:adr
pages: viii + 240
year: 1987
ISBN: 0-89791-243-8 OR 0897912438
ISBN13: 978-0-89791-243-3 OR 9780897912433
LCCN: QA 76.73 A35 U85 1987
bibdate: Mon May 19 13:18:54 1997
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bibtype: proceedings
filename: elefunt.bib
label: Iserles:1987:SAN
editor: A. Iserles and M. J. D. Powell
publisher: pub-OXFORD
address: pub-OXFORD:adr
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year: 1987
ISBN: 0-19-853614-3 OR 0198536143
ISBN13: 978-0-19-853614-7 OR 9780198536147
LCCN: QA297 .S781 1987
bibdate: Thu Sep 08 00:41:24 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.08 00:41:24 ???
acknowledgement: ack-nj
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booktitle:
The State of the Art in Numerical Analysis: Proceedings of the Joint IMA / SIAM Conference on the State of the Art in Numerical Analysis held at the University of Birmingham, 14--18 April 1986

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The State of the Art in Numerical Analysis: Proceedings of the Joint IMA / SIAM Conference on the State of the Art in Numerical Analysis held at the University of Birmingham, 14--18 April 1986

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bibtype: proceedings
filename: elefunt.bib
label: Mason:1987:AAB
editor: J. C. Mason and M. G. Cox
volume: 10
publisher: pub-CLARENDON
address: pub-CLARENDON:adr
pages: xvi + 694 + 8
year: 1987
ISBN: 0-19-853612-7 OR 0198536127
ISBN13: 978-0-19-853612-3 OR 9780198536123
LCCN: QA221 .A5361 1987; QA221 .I47 1985
bibdate: Fri Nov 8 18:01:57 MST 2002
bibtimestamp: 2002.11.08 18:01:57 MST
series: The Institute of Mathematics and Its Applications conference series, new series
acknowledgement: ack-nhfb
raweditor: J. C. Mason and M. G. Cox
booktitle:
Algorithms for approximation: based on the proceedings of the IMA Conference on Algorithms for the Approximation of Functions and Data, held at the Royal Military College of Science, Shrivenham, July 1985

title:
Algorithms for approximation: based on the proceedings of the IMA Conference on Algorithms for the Approximation of Functions and Data, held at the Royal Military College of Science, Shrivenham, July 1985

bibsource:
ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib; https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib; https://www.math.utah.edu/pub/bibnet/authors/r/ruhe-axel.bib; https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager

subject:
Approximation theory; Data processing; Congresses; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

TOC:
Preface / v Contributors / xiii I Development of Algorithms 1. Spline Approximation and Smoothing G. T. Anthony and M. G. Cox / The fitting of extremely large data sets by bivariate splines / 5 W. Dahmen / Subdivision algorithms --- recent results, some extensions and further developments / 21 P. Dierckx / Fast algorithms for smoothing data over a disc or a sphere using tensor product splines / 51 T. Lyche and K. Morken / A discrete approach to knot removal and degree reduction algorithms for splines / 67 R. H. J. Gmelig Meyling / On algorithms and applications for bivariate B-splines / 83 2. Spline Interpolation and Shape Preservation R. E. Carlson / Shape preserving interpolation / 97 M. G. Cox and H. M. Jones / Shape preserving spline approximation in the $ell _1$-norm / 115 J. A. Gregory / A review of curve interpolation with shape control / 131 3. Multivariate Interpolation M. J. D. Powell / Radial basis functions for multivariable interpolation: a review / 143 R. A. Lorentz / On the determinant of a bivariate Birkhoff interpolation problem / 169 A. Le Mehaute / Interpolation with piecewise polynomials in more than one variable / 181 4. Least Square Methods R. Farwig / Multivariate interpolation of scattered data by moving least squares methods / 193 F. Yoshimoto / Least squares approximation by one-pass methods with piecewise polynomials / 213 5. Rational Approximation L. N. Trefethen and M. H. Gutknecht / Pade, stable Pade, and Chebyshev--Pade approximation / 227 P. T. Breuer / A new method for real rational uniform approximation / 265 C. B. Dunham / Rationals with repeated poles / 285 A. Iserles and S. P. Norsett / Error control of rational approximation with a matrix argument / 293 6. Complex and Nonlinear Approximation K. Madsen / General algorithms for discrete non-linear parameter estimation / 309 G. Opfer / Complex rational approximation with numerical experiments / 327 G. A. Watson / Data fitting by positive sums of exponentials / 337 J. C. Mason and P. Owen / Some simple algorithms for constrained complex and rational approximation / 357 7. Computer-Aided Design and Blending L. L. Schumaker / Numerical aspects of spaces of piecewise polynomials on triangulations / 373 M. V. Golitschek / The $H$-sets of the blending functions / 407 D. Levin / Multidimensional reconstruction by set-valued approximations/ 421 II Applications 8. Applications in Numerical Analysis H. P. Blatt, A, Iserles and E. B. Saff / Remarks on the behaviour of zeros of best approximating polynomials and rational functions / 437 J. Gilbert and W. A. Light / Multigrid methods and the alternating algorithm / 447 K. Jetter and J. Stockler / On the computation of Gauss--Birkhoff quadrature formulas / 459 E. Schock / Error bounds for the solution of integral equations by Galerkin-like methods / 471 N. M. Temme / On the computation of the incomplete gamma functions for large values of the parameters / 479 9. Applications in Partial Differential Equations J. R. Rice / Adaptive tensor product grids for singular problems / 493 W. Freeden / Harmonic splines for solving boundary value problems of potential theory / 507 D. C. Hanscomb / Recovery of fluid flow fields / 531 L. Reichel / The selection of subspace and collocation points in the boundary collocation method for some plane elliptic boundary problems / 541 10. Applications in Other Disciplines L. Andersson, K. Holmstrom and A. Ruhe / Complex formation constants --- a problem from solution chemistry / 557 D. E. Roberts and P. R. Graves-Morris / The application of generalised inverse rational interpolants in the model analysis of vibrating structures I / 573 A. Daman and J. C. Mason / A generalised cross-validation method for meteorological data with gaps / 595 K. P. Jackson and J. C. Mason / The approximation by complex functions of stresses in cracked domains / 611 J. H. McDonnell / Equally spaced cubic splines for representing time histories / 623 B. L. Rahimi and S. W. Ellacott / Dynamic phase analysis of heart anomalies / 641 III Software J. G. Hayes / NAG algorithms for the approximation of functions and data / 653 G. T. Anthony and M. G. Cox / The National Physical Laboratory's Data Approximation Subroutine Library / 669 M. G. Cox (editor) / Panel Discussion / 689

rawbooktitle:
{Algorithms for approximation: based on the proceedings of the IMA Conference on Algorithms for the Approximation of Functions and Data, held at the Royal Military College of Science, Shrivenham, July 1985}

rawtitle:
{Algorithms for approximation: based on the proceedings of the IMA Conference on Algorithms for the Approximation of Functions and Data, held at the Royal Military College of Science, Shrivenham, July 1985}

rawTOC:
Preface / v \\ Contributors / xiii \\ \\ I Development of Algorithms \\ \\ 1. Spline Approximation and Smoothing \\ \\ G. T. Anthony and M. G. Cox / The fitting of extremely large data sets by bivariate splines / 5 \\ W. Dahmen / Subdivision algorithms --- recent results, some extensions and further developments / 21 \\ P. Dierckx / Fast algorithms for smoothing data over a disc or a sphere using tensor product splines / 51 \\ T. Lyche and K. M{\o}rken / A discrete approach to knot removal and degree reduction algorithms for splines / 67 \\ R. H. J. Gmelig Meyling / On algorithms and applications for bivariate B-splines / 83 \\ \\ 2. Spline Interpolation and Shape Preservation \\ \\ R. E. Carlson / Shape preserving interpolation / 97 \\ M. G. Cox and H. M. Jones / Shape preserving spline approximation in the $\ell_1$-norm / 115 \\ J. A. Gregory / A review of curve interpolation with shape control / 131 \\ \\ 3. Multivariate Interpolation \\ \\ M. J. D. Powell / Radial basis functions for multivariable interpolation: a review / 143 \\ R. A. Lorentz / On the determinant of a bivariate Birkhoff interpolation problem / 169 \\ A. Le Mehaute / Interpolation with piecewise polynomials in more than one variable / 181 \\ \\ 4. Least Square Methods \\ \\ R. Farwig / Multivariate interpolation of scattered data by moving least squares methods / 193 \\ F. Yoshimoto / Least squares approximation by one-pass methods with piecewise polynomials / 213 \\ \\ 5. Rational Approximation \\ \\ L. N. Trefethen and M. H. Gutknecht / Pad{\'e}, stable Pad{\'e}, and Chebyshev--Pad{\'e} approximation / 227 \\ P. T. Breuer / A new method for real rational uniform approximation / 265 \\ C. B. Dunham / Rationals with repeated poles / 285 \\ A. Iserles and S. P. N{\o}rsett / Error control of rational approximation with a matrix argument / 293 \\ \\ 6. Complex and Nonlinear Approximation \\ \\ K. Madsen / General algorithms for discrete non-linear parameter estimation / 309 \\ G. Opfer / Complex rational approximation with numerical experiments / 327 \\ G. A. Watson / Data fitting by positive sums of exponentials / 337 \\ J. C. Mason and P. Owen / Some simple algorithms for constrained complex and rational approximation / 357 \\ \\ 7. Computer-Aided Design and Blending \\ \\ L. L. Schumaker / Numerical aspects of spaces of piecewise polynomials on triangulations / 373 \\ M. V. Golitschek / The $H$-sets of the blending functions / 407 \\ D. Levin / Multidimensional reconstruction by set-valued approximations/ 421 \\ \\ II Applications \\ \\ 8. Applications in Numerical Analysis \\ \\ H. P. Blatt, A, Iserles and E. B. Saff / Remarks on the behaviour of zeros of best approximating polynomials and rational functions / 437 \\ J. Gilbert and W. A. Light / Multigrid methods and the alternating algorithm / 447 \\ K. Jetter and J. St{\"o}ckler / On the computation of Gauss--Birkhoff quadrature formulas / 459 \\ E. Schock / Error bounds for the solution of integral equations by Galerkin-like methods / 471 \\ N. M. Temme / On the computation of the incomplete gamma functions for large values of the parameters / 479 \\ \\ 9. Applications in Partial Differential Equations \\ \\ J. R. Rice / Adaptive tensor product grids for singular problems / 493 \\ W. Freeden / Harmonic splines for solving boundary value problems of potential theory / 507 \\ D. C. Hanscomb / Recovery of fluid flow fields / 531 \\ L. Reichel / The selection of subspace and collocation points in the boundary collocation method for some plane elliptic boundary problems / 541 \\ \\ 10. Applications in Other Disciplines \\ \\ L. Andersson, K. Holmstr{\"o}m and A. Ruhe / Complex formation constants --- a problem from solution chemistry / 557 \\ D. E. Roberts and P. R. Graves-Morris / The application of generalised inverse rational interpolants in the model analysis of vibrating structures I / 573 \\ A. Daman and J. C. Mason / A generalised cross-validation method for meteorological data with gaps / 595 \\ K. P. Jackson and J. C. Mason / The approximation by complex functions of stresses in cracked domains / 611 \\ J. H. McDonnell / Equally spaced cubic splines for representing time histories / 623 \\ B. L. Rahimi and S. W. Ellacott / Dynamic phase analysis of heart anomalies / 641 \\ \\ III Software \\ \\ J. G. Hayes / NAG algorithms for the approximation of functions and data / 653 \\ G. T. Anthony and M. G. Cox / The National Physical Laboratory's Data Approximation Subroutine Library / 669 \\ \\ M. G. Cox (editor) / Panel Discussion / 689

entry:
@Proceedings{Mason:1987:AAB,
  editor =       "J. C. Mason and M. G. Cox",
  booktitle =    "{Algorithms for approximation: based on the
                 proceedings of the IMA Conference on Algorithms for the
                 Approximation of Functions and Data, held at the Royal
                 Military College of Science, Shrivenham, July 1985}",
  title =        "{Algorithms for approximation: based on the
                 proceedings of the IMA Conference on Algorithms for the
                 Approximation of Functions and Data, held at the Royal
                 Military College of Science, Shrivenham, July 1985}",
  volume =       "10",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
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  year =         "1987",
  ISBN =         "0-19-853612-7",
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  LCCN =         "QA221 .A5361 1987; QA221 .I47 1985",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/r/ruhe-axel.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$90",
  series =       "The Institute of Mathematics and Its Applications
                 conference series, new series",
  acknowledgement = ack-nhfb,
  bibno =        "39820",
  catcode =      "G.1.2; G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Approximation; G.1.2
                 Elementary function approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "theory; algorithms",
  guideno =      "1987-16080",
  meetingname =  "IMA Conference on Algorithms for the Approximation of
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                 Science, Shrivenham)",
  procdate =     "The Institute of mathematics and its applications
                 conference series; 10 July 1985",
  procloc =      "Shrivenham, UK",
  sub =          "Proceedings of the IMA Conference on Algorithms for
                 the approximation of functions",
  subject =      "Approximation theory; Data processing; Congresses; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
  tableofcontents = "Preface / v \\
                 Contributors / xiii \\
                 \\
                 I Development of Algorithms \\
                 \\
                 1. Spline Approximation and Smoothing \\
                 \\
                 G. T. Anthony and M. G. Cox / The fitting of extremely
                 large data sets by bivariate splines / 5 \\
                 W. Dahmen / Subdivision algorithms --- recent results,
                 some extensions and further developments / 21 \\
                 P. Dierckx / Fast algorithms for smoothing data over a
                 disc or a sphere using tensor product splines / 51 \\
                 T. Lyche and K. M{\o}rken / A discrete approach to knot
                 removal and degree reduction algorithms for splines /
                 67 \\
                 R. H. J. Gmelig Meyling / On algorithms and
                 applications for bivariate B-splines / 83 \\
                 \\
                 2. Spline Interpolation and Shape Preservation \\
                 \\
                 R. E. Carlson / Shape preserving interpolation / 97 \\
                 M. G. Cox and H. M. Jones / Shape preserving spline
                 approximation in the $\ell_1$-norm / 115 \\
                 J. A. Gregory / A review of curve interpolation with
                 shape control / 131 \\
                 \\
                 3. Multivariate Interpolation \\
                 \\
                 M. J. D. Powell / Radial basis functions for
                 multivariable interpolation: a review / 143 \\
                 R. A. Lorentz / On the determinant of a bivariate
                 Birkhoff interpolation problem / 169 \\
                 A. Le Mehaute / Interpolation with piecewise
                 polynomials in more than one variable / 181 \\
                 \\
                 4. Least Square Methods \\
                 \\
                 R. Farwig / Multivariate interpolation of scattered
                 data by moving least squares methods / 193 \\
                 F. Yoshimoto / Least squares approximation by one-pass
                 methods with piecewise polynomials / 213 \\
                 \\
                 5. Rational Approximation \\
                 \\
                 L. N. Trefethen and M. H. Gutknecht / Pad{\'e}, stable
                 Pad{\'e}, and Chebyshev--Pad{\'e} approximation / 227
                 \\
                 P. T. Breuer / A new method for real rational uniform
                 approximation / 265 \\
                 C. B. Dunham / Rationals with repeated poles / 285 \\
                 A. Iserles and S. P. N{\o}rsett / Error control of
                 rational approximation with a matrix argument / 293 \\
                 \\
                 6. Complex and Nonlinear Approximation \\
                 \\
                 K. Madsen / General algorithms for discrete non-linear
                 parameter estimation / 309 \\
                 G. Opfer / Complex rational approximation with
                 numerical experiments / 327 \\
                 G. A. Watson / Data fitting by positive sums of
                 exponentials / 337 \\
                 J. C. Mason and P. Owen / Some simple algorithms for
                 constrained complex and rational approximation / 357
                 \\
                 \\
                 7. Computer-Aided Design and Blending \\
                 \\
                 L. L. Schumaker / Numerical aspects of spaces of
                 piecewise polynomials on triangulations / 373 \\
                 M. V. Golitschek / The $H$-sets of the blending
                 functions / 407 \\
                 D. Levin / Multidimensional reconstruction by
                 set-valued approximations/ 421 \\
                 \\
                 II Applications \\
                 \\
                 8. Applications in Numerical Analysis \\
                 \\
                 H. P. Blatt, A, Iserles and E. B. Saff / Remarks on the
                 behaviour of zeros of best approximating polynomials
                 and rational functions / 437 \\
                 J. Gilbert and W. A. Light / Multigrid methods and the
                 alternating algorithm / 447 \\
                 K. Jetter and J. St{\"o}ckler / On the computation of
                 Gauss--Birkhoff quadrature formulas / 459 \\
                 E. Schock / Error bounds for the solution of integral
                 equations by Galerkin-like methods / 471 \\
                 N. M. Temme / On the computation of the incomplete
                 gamma functions for large values of the parameters /
                 479 \\
                 \\
                 9. Applications in Partial Differential Equations \\
                 \\
                 J. R. Rice / Adaptive tensor product grids for singular
                 problems / 493 \\
                 W. Freeden / Harmonic splines for solving boundary
                 value problems of potential theory / 507 \\
                 D. C. Hanscomb / Recovery of fluid flow fields / 531
                 \\
                 L. Reichel / The selection of subspace and collocation
                 points in the boundary collocation method for some
                 plane elliptic boundary problems / 541 \\
                 \\
                 10. Applications in Other Disciplines \\
                 \\
                 L. Andersson, K. Holmstr{\"o}m and A. Ruhe / Complex
                 formation constants --- a problem from solution
                 chemistry / 557 \\
                 D. E. Roberts and P. R. Graves-Morris / The application
                 of generalised inverse rational interpolants in the
                 model analysis of vibrating structures I / 573 \\
                 A. Daman and J. C. Mason / A generalised
                 cross-validation method for meteorological data with
                 gaps / 595 \\
                 K. P. Jackson and J. C. Mason / The approximation by
                 complex functions of stresses in cracked domains / 611
                 \\
                 J. H. McDonnell / Equally spaced cubic splines for
                 representing time histories / 623 \\
                 B. L. Rahimi and S. W. Ellacott / Dynamic phase
                 analysis of heart anomalies / 641 \\
                 \\
                 III Software \\
                 \\
                 J. G. Hayes / NAG algorithms for the approximation of
                 functions and data / 653 \\
                 G. T. Anthony and M. G. Cox / The National Physical
                 Laboratory's Data Approximation Subroutine Library /
                 669 \\
                 \\
                 M. G. Cox (editor) / Panel Discussion / 689",
}


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bibdate: Sun Feb 18 07:46:09 MST 1996
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LCCN: QA76.95.I59 1989
bibdate: Tue Sep 17 06:46:18 MDT 1996
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bibtype: book
filename: elefunt.bib
label: Campbell-Kelly:1989:WCB-3
editor: Martin Campbell-Kelly
booktitle: The works of Charles Babbage, Vol. 3, The analytical engine and mechanical notation
title: The works of Charles Babbage, Vol. 3, The analytical engine and mechanical notation
publisher: William Pickering
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MRnumber: 998151 (90g:01064)
MRreviewer: A. D. Booth
bibdate: Sat Jan 12 22:42:35 MST 2013
bibtimestamp: 2013.01.12 22:42:35 MST
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bibtype: proceedings
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label: Ercegovac:1989:PSC
editor: Milos D. Ercegovac and Earl E. Swartzlander, Jr.
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bibdate: Thu Sep 01 22:36:52 1994
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note: IEEE catalog no. 89CH2757-3.
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Proceedings: 9th Symposium on Computer Arithmetic: September 6--8, 1989, Santa Monica, California, USA

title:
Proceedings: 9th Symposium on Computer Arithmetic: September 6--8, 1989, Santa Monica, California, USA

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address: pub-IEE:adr
pages: xv + 247
year: 1989
ISBN: 0-85296-383-1 OR 0852963831
ISBN13: 978-0-85296-383-8 OR 9780852963838
bibdate: Sat Nov 29 08:19:35 2003
bibtimestamp: 2003.11.29 08:19:35 ???
note: Conference publication no. 308.
acknowledgement: ack-nhfb
bookpages: xviii + 680
raweditor: {IEE}
rawnote: Conference publication no. 308.
booktitle:
ECCTD 89: European Conference on Circuit Theory and Design, 5--8 September 1989: venue, University of Sussex, Brighton, United Kingdom

title:
ECCTD 89: European Conference on Circuit Theory and Design, 5--8 September 1989: venue, University of Sussex, Brighton, United Kingdom

rawbooktitle:
{ECCTD 89}: European Conference on Circuit Theory and Design, 5--8 September 1989: venue, University of Sussex, Brighton, United Kingdom

rawtitle:
{ECCTD} 89: European Conference on Circuit Theory and Design, 5--8 September 1989: venue, University of Sussex, Brighton, United Kingdom

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  booktitle =    "{ECCTD 89}: European Conference on Circuit Theory and
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  title =        "{ECCTD} 89: European Conference on Circuit Theory and
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bibtype: proceedings
filename: elefunt.bib
label: IEEE:1989:ASF
editor: IEEE
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xvii + 632
year: 1989
CODEN: ASFPDV
ISSN: 0272-5428 OR 02725428
LCCN: QA 76 S979 1989; TK7885.A1 S92 1989
bibdate: Thu Dec 3 07:11:18 MST 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.12.03 07:11:18 MST
acknowledgement: ack-nhfb
raweditor: {IEEE}
booktitle:
30th annual Symposium on Foundations of Computer Science, October 30--November 1, 1989, Research Triangle Park, North Carolina

title:
30th annual Symposium on Foundations of Computer Science, October 30--November 1, 1989, Research Triangle Park, North Carolina

ISBN:
0-8186-1982-1 (casebound), 0-8186-5982-3 (microfiche) OR 0818619821 (casebound), 0818659823 (microfiche)

ISBN13:
978-0-8186-1982-3 (casebound), 978-0-8186-5982-9 (microfiche) OR 9780818619823 (casebound), 9780818659829 (microfiche)

note:
Formerly called the Annual Symposium on Switching and Automata Theory. IEEE catalog no. 89CH2808-4. Computer Society order no. 1982.

keywords:
computational complexity --- congresses; electronic data processing --- congresses; machine theory --- congresses

rawbooktitle:
30th annual Symposium on Foundations of Computer Science, October 30--November 1, 1989, Research Triangle Park, North Carolina

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Formerly called the Annual Symposium on Switching and Automata Theory. IEEE catalog no. 89CH2808-4. Computer Society order no. 1982.

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  booktitle =    "30th annual Symposium on Foundations of Computer
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  title =        "30th annual Symposium on Foundations of Computer
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  publisher =    pub-IEEE,
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  note =         "Formerly called the Annual Symposium on Switching and
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  acknowledgement = ack-nhfb,
  keywords =     "computational complexity --- congresses; electronic
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}


bibtype: proceedings
filename: elefunt.bib
label: IEEE:1989:PII
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xvii + 587
year: 1989
LCCN: TK 7888.4 I23 1989
bibdate: Wed Dec 13 18:26:58 1995
bibtimestamp: 1995.12.13 18:26:58 ???
note: IEEE catalog number 89CH2794-6.
acknowledgement: ack-nj
key: IEEE ICCD '89
rawnote: IEEE catalog number 89CH2794-6.
booktitle:
Proceedings: 1989 IEEE International Conference on Computer Design: VLSI in Computer and Processors, ICCD '89, Hyatt Regency Cambridge, Cambridge, Massachusetts, October 2--4, 1989

title:
Proceedings: 1989 IEEE International Conference on Computer Design: VLSI in Computer and Processors, ICCD '89, Hyatt Regency Cambridge, Cambridge, Massachusetts, October 2--4, 1989

ISBN:
0-8186-1971-6 (paper), 0-8186-5971-8 (microfiche), 0-8186-8971-4 (case) OR 0818619716 (paper), 0818659718 (microfiche), 0818689714 (case)

ISBN13:
978-0-8186-1971-7 (paper), 978-0-8186-5971-3 (microfiche), 978-0-8186-8971-0 (case) OR 9780818619717 (paper), 9780818659713 (microfiche), 9780818689710 (case)

rawbooktitle:
Proceedings: 1989 {IEEE} International Conference on Computer Design: {VLSI} in Computer and Processors, {ICCD} '89, Hyatt Regency Cambridge, Cambridge, Massachusetts, October 2--4, 1989

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Proceedings: 1989 {IEEE} International Conference on Computer Design: {VLSI} in Computer and Processors, {ICCD} '89, Hyatt Regency Cambridge, Cambridge, Massachusetts, October 2--4, 1989

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  title =        "Proceedings: 1989 {IEEE} International Conference on
                 Computer Design: {VLSI} in Computer and Processors,
                 {ICCD} '89, Hyatt Regency Cambridge, Cambridge,
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bibtype: proceedings
filename: elefunt.bib
label: MacNair:1989:WSC
editor: Edward A. MacNair and Kenneth J. Musselman and Philip Heidelberger
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xx + 1139
year: 1989
ISBN: 0-911801-58-8 OR 0911801588
ISBN13: 978-0-911801-58-3 OR 9780911801583
LCCN: QA76.9.C65 W56 1989
bibdate: Fri Nov 8 18:01:57 MST 2002
bibtimestamp: 2002.11.08 18:01:57 MST
note: IEEE order number 89CH2778-9.
URL: http://ieeexplore.ieee.org/servlet/opac?punumber=5823
acknowledgement: ack-nhfb
bookpages: xx + 1139
raweditor: Edward A. MacNair and Kenneth J. Musselman and Philip Heidelberger
rawnote: IEEE order number 89CH2778-9.
booktitle:
1989 Winter Simulation Conference proceedings: December 4--6, 1989, the Capital Hilton Hotel, Washington, DC

title:
1989 Winter Simulation Conference proceedings: December 4--6, 1989, the Capital Hilton Hotel, Washington, DC

bibsource:
ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib

subject:
I. Computing Methodologies; I.6 SIMULATION AND MODELING; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

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  title =        "{1989 Winter Simulation Conference proceedings:
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                 Washington, DC}",
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bibtype: proceedings
filename: elefunt.bib
label: Megiddo:1989:PMP
editor: N. Megiddo
booktitle: Progress in Mathematical Programming: Interior-Point and Related Methods
title: Progress in Mathematical Programming: Interior-Point and Related Methods
publisher: pub-SV
address: pub-SV:adr
pages: x + 158
year: 1989
ISBN: 0-387-96847-4 OR 0387968474
ISBN13: 978-0-387-96847-6 OR 9780387968476
LCCN: QA402.5 .P7851 1989
bibdate: Sat Nov 09 07:07:37 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.09 07:07:37 ???
acknowledgement: ack-nhfb
rawbooktitle: Progress in Mathematical Programming: Interior-Point and Related Methods
raweditor: N. Megiddo
rawtitle: Progress in Mathematical Programming: Interior-Point and Related Methods
note:
Proceedings of the conference held at the Asilomar conference center in Pacific Grove, California, March 1--4, 1987.

rawnote:
Proceedings of the conference held at the Asilomar conference center in Pacific Grove, California, March 1--4, 1987.

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  editor =       "N. Megiddo",
  booktitle =    "Progress in Mathematical Programming: Interior-Point
                 and Related Methods",
  title =        "Progress in Mathematical Programming: Interior-Point
                 and Related Methods",
  publisher =    pub-SV,
  address =      pub-SV:adr,
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  bibdate =      "Sat Nov 09 07:07:37 2002",
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  note =         "Proceedings of the conference held at the Asilomar
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  acknowledgement = ack-nhfb,
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bibtype: book
filename: elefunt.bib
label: Srivastava:1989:UFF
editor: H. M. Srivastava and Shigeyoshi Owa
booktitle: Univalent functions, fractional calculus, and their applications (Koriyama, 1988)
title: Univalent functions, fractional calculus, and their applications (Koriyama, 1988)
publisher: pub-ELLIS-HORWOOD
address: pub-ELLIS-HORWOOD:adr
pages: 404
year: 1989
ISBN: 0-470-21630-1, 0-7458-0701-1 OR 0470216301, 0745807011
ISBN13: 978-0-470-21630-9, 978-0-7458-0701-0 OR 9780470216309, 9780745807010
LCCN: QA331 .U55 1989
bibdate: Mon Jan 13 09:52:29 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.13 09:52:29 ???
acknowledgement: ack-nhfb
rawbooktitle: Univalent functions, fractional calculus, and their applications (K{\=o}riyama, 1988)
raweditor: H. M. Srivastava and Shigeyoshi Owa
rawtitle: Univalent functions, fractional calculus, and their applications ({K}{\=o}riyama, 1988)
entry:
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  LCCN =         "QA331 .U55 1989",
  bibdate =      "Mon Jan 13 09:52:29 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  price =        "UK\pounds 39.95",
  acknowledgement = ack-nhfb,
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bibtype: proceedings
filename: elefunt.bib
label: Cray:1990:PCU
booktitle: Proceedings Cray User Group
title: Proceedings Cray User Group
month: Spring
year: 1990
bibdate: Thu Sep 08 08:56:01 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.08 08:56:01 ???
acknowledgement: ack-nj
key: Cray UG '90
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  month =        "Spring",
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  ISBN =         "????",
  ISBN-13 =      "????",
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  bibdate =      "Thu Sep 08 08:56:01 1994",
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bibtype: proceedings
filename: elefunt.bib
label: Mason:1990:AAI
editor: J. C. Mason and M. G. Cox
publisher: pub-CHAPMAN-HALL
address: pub-CHAPMAN-HALL:adr
pages: 514
year: 1990
ISBN: 0-412-34580-3 OR 0412345803
ISBN13: 978-0-412-34580-7 OR 9780412345807
LCCN: QA221 .I54 1988
bibdate: Thu Sep 01 23:55:44 1994
bibtimestamp: 1994.09.01 23:55:44 ???
subject: Approximation theory; Data processing; Congresses
acknowledgement: ack-nhfb
raweditor: J. C. Mason and M. G. Cox
booktitle:
Algorithms for approximation II: based on the proceedings of the Second International Conference on Algorithms for Approximation, held at Royal Military College of Science, Shrivenham, July 1988

title:
Algorithms for approximation II: based on the proceedings of the Second International Conference on Algorithms for Approximation, held at Royal Military College of Science, Shrivenham, July 1988

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib; https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib; https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager

TOC:
Part One: Development of Algorithms / 1 1. Spline Approximation / 3 E. Arge, M. Dcehlen, T. Lyche and K. Morken / Constrained spline approximation of functions and data based on constrained knot removal / 4 G. T. Anthony and M. G. Cox / Near real-time spline fitting of long sequences of uniformly-spaced data / 21 M. Bozzini and F. de Tisi / An algorithm for knot location in bivariate least squares spline approximation / 30 M. G. Cox, P. M. Harris and H. M. Jones / A knot placement strategy for least squares spline fitting based on the use of local polynomial approximations / 37 G. Opfer / An algorithm for nonlinear splines with non-negativity constraints / 46 C. Potier and C. Vercken / Spline curve fitting of digitized contours / 54 C. Rabut / A B-spline approximation algorithm for quasi-interpolation or filtering / 62 P. W. Smith / On knots and nodes for spline interpolation / 72 2. Polynomial and Piecewise Polynomial Approximation / 79 W. Dahmen / A basis for certain spaces of multivariate polynomials and exponentials / 80 F. N. Fritschi / Monotone piecewise cubic data fitting / 99 M. Heilmann and M. W. Muller / Direct and converse results on simultaneous approximation by the method of Bernstein--Durrmeyer operators / 107 A. Iserles, P. E. Koch, S. P. Norsett and J. M. Sanz-Serna / Orthogonality and approximation in a Sobolev space / 117 M. A. Lachance / Piecewise polynomial approximation of polynomial curves / 125 E. Quak and L. L. Schumaker / Calculation of the energy of a piecewise polynomial surface / 134 3. Interpolation / 145 M. D. Buhmann and M. J. D. Powell / Radial basis function interpolation on an infinite regular grid / 146 L. Brutman / The Fourier operator of even order and its application to an extremum problem in interpolation / 170 N. Dyn and A. Ron / On multivariate polynomial interpolation / 177 N. Dyn, D. Levin and S. Rippen / Algorithms for the construction of data dependent triangulations / 185 C. Rademacher and K. Scherer / Algorithms for computing best parametric cubic interpolation / 193 4. Smoothing and Constraint Methods / 209 M. Von Golitschek and L. L. Schumaker / Data fitting by penalized least squares / 210 K. W. Bosworth / A semiinfinite programming algorithm for constrained best approximation / 228 M. Bozzini and L. Lenarduzzi / Inference region for a method of local approximation by using the residuals / 236 5. Complex Approximation / 245 G. A. Watson / Numerical methods for Chebyshev approximation of complex-valued functions / 246 P. T. P. Tang / A fast algorithm for linear complex Chebyshev approximation / 265 Part Two: Applications / 275 6. Computer Aided Design and Geometric Modelling / 277 N. Dyn, J. A. Gregory and D. Levin / Uniform subdivision algorithms for curves and surfaces / 278 T. B. Boffey, M. G. Cox, L. M. Delves and C. J. Pursglove / Approximation by spheres / 296 T. A. Foley / Interpolation of scattered data on a spherical domain / 303 A. B. Forbes / Least squares best fit geometric elements / 311 W. Freeden and J. C. Mason / Uniform piecewise approximation on the sphere / 320 7. Applications in Numerical Analysis / 335 L. N. Trefethen / Approximation theory and numerical linear algebra / 336 M. Frontini, G. Rodriguez and S. Seatzu / An algorithm for computing minimum norm solutions of the finite moment problem / 361 R. H. J. Gmelig Meyling / Numerical solution of the biharmonic equation using different types of bivariate spline functions / 369 G. O. Olaofe / Quadrature solution of integral equations: a uniform treatment of Fredholm and Volterra equations / 377 G. Walz / Increasing the convergence modulus of an asymptotic expansion: an algorithm for numerical differentiation / 387 J. Williams / Approximation and parameter estimation in ordinary differential equations / 395 8. Applications in Other Disciplines / 405 C. Zala and I. Barrodale / Applications of discrete $L_1$ methods in science and engineering / 406 J. C. Mason, A. E. Trefethen and S. J. Wilde / Constrained complex approximation algorithms in communication engineering / 424 R. W. Allen and J. G. Metcalfe / Integration of absolute amplitude from a decibel B-spline fit / 449 M. G. Cox and H. M. Jones / A nonlinear least squares data fitting problem arising in microwave measurement / 458 J. C. Mason and S. J. Wilde / A complex minimax algorithm for phase-only adaptation in antenna arrays / 466 Part Three: Catalogue of Algorithms / 477 E. Grosse / A catalogue of algorithms for approximation / 479

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{Algorithms for approximation II: based on the proceedings of the Second International Conference on Algorithms for Approximation, held at Royal Military College of Science, Shrivenham, July 1988}

rawtitle:
{Algorithms for approximation II: based on the proceedings of the Second International Conference on Algorithms for Approximation, held at Royal Military College of Science, Shrivenham, July 1988}

rawTOC:
Part One: Development of Algorithms / 1 \\ 1. Spline Approximation / 3 \\ E. Arge, M. Dcehlen, T. Lyche and K. Morken / Constrained spline approximation of functions and data based on constrained knot removal / 4 \\ G. T. Anthony and M. G. Cox / Near real-time spline fitting of long sequences of uniformly-spaced data / 21 \\ M. Bozzini and F. de Tisi / An algorithm for knot location in bivariate least squares spline approximation / 30 \\ M. G. Cox, P. M. Harris and H. M. Jones / A knot placement strategy for least squares spline fitting based on the use of local polynomial approximations / 37 \\ G. Opfer / An algorithm for nonlinear splines with non-negativity constraints / 46 \\ C. Potier and C. Vercken / Spline curve fitting of digitized contours / 54 \\ C. Rabut / A B-spline approximation algorithm for quasi-interpolation or filtering / 62 \\ P. W. Smith / On knots and nodes for spline interpolation / 72 \\ 2. Polynomial and Piecewise Polynomial Approximation / 79 \\ W. Dahmen / A basis for certain spaces of multivariate polynomials and exponentials / 80 \\ F. N. Fritschi / Monotone piecewise cubic data fitting / 99 \\ M. Heilmann and M. W. M{\"u}ller / Direct and converse results on simultaneous approximation by the method of Bernstein--Durrmeyer operators / 107 \\ A. Iserles, P. E. Koch, S. P. N{\o}rsett and J. M. Sanz-Serna / Orthogonality and approximation in a Sobolev space / 117 \\ M. A. Lachance / Piecewise polynomial approximation of polynomial curves / 125 \\ E. Quak and L. L. Schumaker / Calculation of the energy of a piecewise polynomial surface / 134 \\ 3. Interpolation / 145 \\ M. D. Buhmann and M. J. D. Powell / Radial basis function interpolation on an infinite regular grid / 146 \\ L. Brutman / The Fourier operator of even order and its application to an extremum problem in interpolation / 170 \\ N. Dyn and A. Ron / On multivariate polynomial interpolation / 177 \\ N. Dyn, D. Levin and S. Rippen / Algorithms for the construction of data dependent triangulations / 185 \\ C. Rademacher and K. Scherer / Algorithms for computing best parametric cubic interpolation / 193 \\ 4. Smoothing and Constraint Methods / 209 \\ M. Von Golitschek and L. L. Schumaker / Data fitting by penalized least squares / 210 \\ K. W. Bosworth / A semiinfinite programming algorithm for constrained best approximation / 228 \\ M. Bozzini and L. Lenarduzzi / Inference region for a method of local approximation by using the residuals / 236 \\ 5. Complex Approximation / 245 \\ G. A. Watson / Numerical methods for Chebyshev approximation of complex-valued functions / 246 \\ P. T. P. Tang / A fast algorithm for linear complex Chebyshev approximation / 265 \\ Part Two: Applications / 275 \\ 6. Computer Aided Design and Geometric Modelling / 277 \\ N. Dyn, J. A. Gregory and D. Levin / Uniform subdivision algorithms for curves and surfaces / 278 \\ T. B. Boffey, M. G. Cox, L. M. Delves and C. J. Pursglove / Approximation by spheres / 296 \\ T. A. Foley / Interpolation of scattered data on a spherical domain / 303 \\ A. B. Forbes / Least squares best fit geometric elements / 311 \\ W. Freeden and J. C. Mason / Uniform piecewise approximation on the sphere / 320 \\ 7. Applications in Numerical Analysis / 335 \\ L. N. Trefethen / Approximation theory and numerical linear algebra / 336 \\ M. Frontini, G. Rodriguez and S. Seatzu / An algorithm for computing minimum norm solutions of the finite moment problem / 361 \\ R. H. J. Gmelig Meyling / Numerical solution of the biharmonic equation using different types of bivariate spline functions / 369 \\ G. O. Olaofe / Quadrature solution of integral equations: a uniform treatment of Fredholm and Volterra equations / 377 \\ G. Walz / Increasing the convergence modulus of an asymptotic expansion: an algorithm for numerical differentiation / 387 \\ J. Williams / Approximation and parameter estimation in ordinary differential equations / 395 \\ 8. Applications in Other Disciplines / 405 \\ C. Zala and I. Barrodale / Applications of discrete $L_1$ methods in science and engineering / 406 \\ J. C. Mason, A. E. Trefethen and S. J. Wilde / Constrained complex approximation algorithms in communication engineering / 424 \\ R. W. Allen and J. G. Metcalfe / Integration of absolute amplitude from a decibel B-spline fit / 449 \\ M. G. Cox and H. M. Jones / A nonlinear least squares data fitting problem arising in microwave measurement / 458 \\ J. C. Mason and S. J. Wilde / A complex minimax algorithm for phase-only adaptation in antenna arrays / 466 \\ Part Three: Catalogue of Algorithms / 477 \\ E. Grosse / A catalogue of algorithms for approximation / 479

entry:
@Proceedings{Mason:1990:AAI,
  editor =       "J. C. Mason and M. G. Cox",
  booktitle =    "{Algorithms for approximation II: based on the
                 proceedings of the Second International Conference on
                 Algorithms for Approximation, held at Royal Military
                 College of Science, Shrivenham, July 1988}",
  title =        "{Algorithms for approximation II: based on the
                 proceedings of the Second International Conference on
                 Algorithms for Approximation, held at Royal Military
                 College of Science, Shrivenham, July 1988}",
  publisher =    pub-CHAPMAN-HALL,
  address =      pub-CHAPMAN-HALL:adr,
  pages =        "514",
  year =         "1990",
  ISBN =         "0-412-34580-3",
  ISBN-13 =      "978-0-412-34580-7",
  LCCN =         "QA221 .I54 1988",
  bibdate =      "Thu Sep 01 23:55:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Algorithms for
                 Approximation (2nd: 1988: Royal Military College of
                 Science, Shrivenham, England)",
  subject =      "Approximation theory; Data processing; Congresses",
  tableofcontents = "Part One: Development of Algorithms / 1 \\
                 1. Spline Approximation / 3 \\
                 E. Arge, M. Dcehlen, T. Lyche and K. Morken /
                 Constrained spline approximation of functions and data
                 based on constrained knot removal / 4 \\
                 G. T. Anthony and M. G. Cox / Near real-time spline
                 fitting of long sequences of uniformly-spaced data / 21
                 \\
                 M. Bozzini and F. de Tisi / An algorithm for knot
                 location in bivariate least squares spline
                 approximation / 30 \\
                 M. G. Cox, P. M. Harris and H. M. Jones / A knot
                 placement strategy for least squares spline fitting
                 based on the use of local polynomial approximations /
                 37 \\
                 G. Opfer / An algorithm for nonlinear splines with
                 non-negativity constraints / 46 \\
                 C. Potier and C. Vercken / Spline curve fitting of
                 digitized contours / 54 \\
                 C. Rabut / A B-spline approximation algorithm for
                 quasi-interpolation or filtering / 62 \\
                 P. W. Smith / On knots and nodes for spline
                 interpolation / 72 \\
                 2. Polynomial and Piecewise Polynomial Approximation /
                 79 \\
                 W. Dahmen / A basis for certain spaces of multivariate
                 polynomials and exponentials / 80 \\
                 F. N. Fritschi / Monotone piecewise cubic data fitting
                 / 99 \\
                 M. Heilmann and M. W. M{\"u}ller / Direct and converse
                 results on simultaneous approximation by the method of
                 Bernstein--Durrmeyer operators / 107 \\
                 A. Iserles, P. E. Koch, S. P. N{\o}rsett and J. M.
                 Sanz-Serna / Orthogonality and approximation in a
                 Sobolev space / 117 \\
                 M. A. Lachance / Piecewise polynomial approximation of
                 polynomial curves / 125 \\
                 E. Quak and L. L. Schumaker / Calculation of the energy
                 of a piecewise polynomial surface / 134 \\
                 3. Interpolation / 145 \\
                 M. D. Buhmann and M. J. D. Powell / Radial basis
                 function interpolation on an infinite regular grid /
                 146 \\
                 L. Brutman / The Fourier operator of even order and its
                 application to an extremum problem in interpolation /
                 170 \\
                 N. Dyn and A. Ron / On multivariate polynomial
                 interpolation / 177 \\
                 N. Dyn, D. Levin and S. Rippen / Algorithms for the
                 construction of data dependent triangulations / 185 \\
                 C. Rademacher and K. Scherer / Algorithms for computing
                 best parametric cubic interpolation / 193 \\
                 4. Smoothing and Constraint Methods / 209 \\
                 M. Von Golitschek and L. L. Schumaker / Data fitting by
                 penalized least squares / 210 \\
                 K. W. Bosworth / A semiinfinite programming algorithm
                 for constrained best approximation / 228 \\
                 M. Bozzini and L. Lenarduzzi / Inference region for a
                 method of local approximation by using the residuals /
                 236 \\
                 5. Complex Approximation / 245 \\
                 G. A. Watson / Numerical methods for Chebyshev
                 approximation of complex-valued functions / 246 \\
                 P. T. P. Tang / A fast algorithm for linear complex
                 Chebyshev approximation / 265 \\
                 Part Two: Applications / 275 \\
                 6. Computer Aided Design and Geometric Modelling / 277
                 \\
                 N. Dyn, J. A. Gregory and D. Levin / Uniform
                 subdivision algorithms for curves and surfaces / 278
                 \\
                 T. B. Boffey, M. G. Cox, L. M. Delves and C. J.
                 Pursglove / Approximation by spheres / 296 \\
                 T. A. Foley / Interpolation of scattered data on a
                 spherical domain / 303 \\
                 A. B. Forbes / Least squares best fit geometric
                 elements / 311 \\
                 W. Freeden and J. C. Mason / Uniform piecewise
                 approximation on the sphere / 320 \\
                 7. Applications in Numerical Analysis / 335 \\
                 L. N. Trefethen / Approximation theory and numerical
                 linear algebra / 336 \\
                 M. Frontini, G. Rodriguez and S. Seatzu / An algorithm
                 for computing minimum norm solutions of the finite
                 moment problem / 361 \\
                 R. H. J. Gmelig Meyling / Numerical solution of the
                 biharmonic equation using different types of bivariate
                 spline functions / 369 \\
                 G. O. Olaofe / Quadrature solution of integral
                 equations: a uniform treatment of Fredholm and Volterra
                 equations / 377 \\
                 G. Walz / Increasing the convergence modulus of an
                 asymptotic expansion: an algorithm for numerical
                 differentiation / 387 \\
                 J. Williams / Approximation and parameter estimation in
                 ordinary differential equations / 395 \\
                 8. Applications in Other Disciplines / 405 \\
                 C. Zala and I. Barrodale / Applications of discrete
                 $L_1$ methods in science and engineering / 406 \\
                 J. C. Mason, A. E. Trefethen and S. J. Wilde /
                 Constrained complex approximation algorithms in
                 communication engineering / 424 \\
                 R. W. Allen and J. G. Metcalfe / Integration of
                 absolute amplitude from a decibel B-spline fit / 449
                 \\
                 M. G. Cox and H. M. Jones / A nonlinear least squares
                 data fitting problem arising in microwave measurement /
                 458 \\
                 J. C. Mason and S. J. Wilde / A complex minimax
                 algorithm for phase-only adaptation in antenna arrays /
                 466 \\
                 Part Three: Catalogue of Algorithms / 477 \\
                 E. Grosse / A catalogue of algorithms for approximation
                 / 479",
}


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filename: elefunt.bib
label: Ullrich:1990:CCA
editor: Christian Ullrich
volume: 7
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pages: 526
year: 1990
LCCN: QA76.9.C62 C664 1990
bibdate: Sat Nov 29 08:36:57 2003
bibtimestamp: 2003.11.29 08:36:57 ???
series: IMACS annals on computing and applied mathematics
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booktitle:
Contributions to Computer Arithmetic and Self-Validating Numerical Methods. (Proceedings of SCAN 89, held in Basel, Oct. 2--6, 1989)

title:
Contributions to Computer Arithmetic and Self-Validating Numerical Methods. (Proceedings of SCAN 89, held in Basel, Oct. 2--6, 1989)

bibsource:
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label: Anonymous:1991:PIS
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booktitle: Proceedings of the International Symposium on Supercomputing: Fukuoka, Japan, November 6--8, 1991
title: Proceedings of the International Symposium on Supercomputing: Fukuoka, Japan, November 6--8, 1991
publisher: Kyushu University Press
address: Fukuoka, Japan
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year: 1991
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bibdate: Sat Jan 11 10:14:06 MST 1997
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acknowledgement: ack-nhfb
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label: Bowers:1991:CCI
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bibdate: Wed May 9 08:56:08 MDT 2007
bibtimestamp: 2007.05.09 08:56:08 MDT
series: Progress in systems and control theory
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acknowledgement: ack-nhfb
raweditor: K. L. (Kenneth L.) Bowers and J. (John) Lund
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Computation and control II: proceedings of the second Bozeman conference, Bozeman, Montana, August 1--7, 1990

title:
Computation and control II: proceedings of the second Bozeman conference, Bozeman, Montana, August 1--7, 1990

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager

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                 1990}",
  title =        "{Computation and control II: proceedings of the second
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bibtype: proceedings
filename: elefunt.bib
label: IEEE:1991:PSA
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booktitle: Proceedings, Supercomputing '91: Albuquerque, New Mexico, November 18--22, 1991
title: Proceedings, Supercomputing '91: Albuquerque, New Mexico, November 18--22, 1991
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xxiii + 917
year: 1991
LCCN: QA76.5 .S894 1991
bibdate: Fri Aug 30 08:01:51 MDT 1996
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rawtitle: Proceedings, Supercomputing '91: Albuquerque, New Mexico, November 18--22, 1991
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ACM order number 415913. IEEE Computer Society Press order number 2158. IEEE catalog number 91CH3058-5.

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ACM order number 415913. IEEE Computer Society Press order number 2158. IEEE catalog number 91CH3058-5.

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The proceedings of the second and third annual workshops for the ACM Special Interest Group on Forth: SIGForth '90, February 16--18, 1990, Dallas, Texas ldots SIGForth '91, March 7--9, 1991, San Antonio, Texas

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The proceedings of the second and third annual workshops for the ACM Special Interest Group on Forth: SIGForth '90, February 16--18, 1990, Dallas, Texas ldots SIGForth '91, March 7--9, 1991, San Antonio, Texas

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bibtype: proceedings
filename: elefunt.bib
label: Kornerup:1991:PIS
editor: Peter Kornerup and David W. Matula
booktitle: Proceedings: 10th IEEE Symposium on Computer Arithmetic: June 26--28, 1991, Grenoble, France
title: Proceedings: 10th IEEE Symposium on Computer Arithmetic: June 26--28, 1991, Grenoble, France
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xiii + 282
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LCCN: QA76.9.C62 S95 1991
bibdate: Thu Sep 01 23:18:52 1994
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  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 282",
  year =         "1991",
  ISBN =         "0-8186-9151-4 (case), 0-8186-6151-8 (microfiche),
                 0-7803-0187-0 (library binding)",
  ISBN-13 =      "978-0-8186-9151-5 (case), 978-0-8186-6151-8
                 (microfiche), 978-0-7803-0187-0 (library binding)",
  LCCN =         "QA76.9.C62 S95 1991",
  bibdate =      "Thu Sep 01 23:18:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Lewin:1991:SPP
editor: Leonard Lewin
booktitle: Structural Properties of Polylogarithms
title: Structural Properties of Polylogarithms
volume: 37
publisher: pub-AMS
address: pub-AMS:adr
pages: xviii + 412
year: 1991
ISBN: 0-8218-1634-9, 1-4704-1264-0 (e-book) OR 0821816349, 1470412640 (ebook)
ISBN13: 978-0-8218-1634-9, 978-1-4704-1264-7 (e-book) OR 9780821816349, 9781470412647 (ebook)
ISSN: 0076-5376 OR 00765376
MRclass: 33E20, 00B15, 11-02, 11F67, 11R70, 11R42, 19F27, 33-02, 33-06, 33B99
bibdate: Fri Jun 16 14:03:50 MDT 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2023.06.16 14:03:50 MDT
series: Mathematical surveys and monographs
acknowledgement: ack-nhfb
rawbooktitle: Structural Properties of Polylogarithms
raweditor: Leonard Lewin
rawtitle: Structural Properties of Polylogarithms
subject:
Logarithmic functions; Fonctions logarithmes; Mathematics; Algebra; Intermediate; Logarithmic functions; Fonctions logarithmes

TOC:
Preface / xiii Acknowledgments / xv List of Contributors / xvii 1: The Evolution of the Ladder Concept / L. Lewin / 1 1.1 Early History / 1 1.2 Functional Equations / 2 1.3 More Recent Numerical Results / 4 1.4 Current Developments / 6 1.5 Base on the Unit Circle and Clausen Function Ladders / 8 References / 9 2: Dilogarithmic Ladders / L. Lewin / 11 2.1 Derivation from Kummer's Functional Equation / 11 2.2 Relation to Clausen's Function / 15 2.3 A Three-Variable Dilogarithmic Functional Equation / 17 2.4 Functional Equations in the Complex Plane / 18 2.5 Cyclotomic Equations and Rogers' Function / 20 2.6 Accessible and Analytic Ladders / 21 2.7 Inaccessible Ladders / 23 References / 25 3: Polylogarithmic Ladders / M. Abouzahra and L. Lewin / 27 3.1 Kummer's Function and its Relation to the Polylogarithm / 27 3.2 Functional Equations for the Polylogarithm / 28 3.3 A Generalization of Rogers' Function to the $n$th Order / 31 3.4 Ladder Order-Independence on Reduction of Order / 33 3.5 Generic Ladders for the Base Equation $u^p + u^q = 1$ / 34 3.6 Examples of Ladders for $n < 3$ / 40 3.7 Examples of Ladders for $n < 4$ / 44 3.8 Examples of Ladders for $n < 5$ / 45 3.9 Polynomial Relations for Ladders / 46 References / 47 4: Ladders in the Trans-Kummer Region / M. Abouzahra and L. Lewin / 49 4.1 Ladder Results to $n = 9$ for the Base p / 49 4.2 Ladder Results to $n = 9$ for the Base co / 53 4.3 Ladder Results to $n = 6$ for the Base 6 / 62 4.4 The Nonexistence of Functional Equations at $n = 6$ with Arguments Limited to $pm z^m (1 - z)^r (1 + z)^s$ / 65 References / 67 5: Supemumary Ladders / M. Abouzahra and L. Lewin / 69 5.1 The Concept of Supemumary Results / 69 5.2 Supemumary Results for $p = 4$ / 71 5.3 Supemumary Results for $p = 5$ / 76 5.4 Supemumary Results for $p = 6$ / 78 5.5 Supemumary Results for the Equation-family $u^6m + 1 u^6r - 1$ = 1 / 80 5.6 Supemumary Results for an Irreducible Quintic / 82 5.7 Supemumary Ladders from a 15-Term Functional Equation / 84 5.8 Supemumary Ladders on the Unit Circle / 90 References 6: Functional Equations and Ladders / L. Lewin / 97 6.1 New Categories of Functional Equations / 97 6.2 The $rho $-family of Equations / 100 6.3 The $omega $-family of Equations / 109 6.4 The $theta $-family of Equations / 115 Acknowledgements / 121 References / 121 7: Multivariable Polylogarithm Identities / G. A. Ray / 123 7.0 Introduction / 123 7.1 A General Identity for the Dilogarithm / 123 7.2 A General Identity for the Bloch-Wigner Function / 135 7.3 A General Identity for the Trilogarithm and $D_3(z)$ / 141 7.4 Linear Power Relations among Dilogarithms / 147 7.5 Cyclotomic Equations and Bases for Polylogarithm Relations / 154 7.6 Mahler's Measure and Salem/Pisot Numbers / 160 7.7 Recent Results for Supemumary Ladders / 165 References / 168 8: Functional Equations of Hyperlogarithms / G. Wechsung / 171 8.1 Hyperlogarithms / 171 8.2 Logarithmic Singularities / 172 8.3 The Linear Spaces LI$_n$ and PLI$_n$ / 176 8.4 Functional Equations of Hyperlogarithms / 177 8.5 A Reduction Problem / 181 References / 184 9: Kummer-Type Functional Equations of Polylogarithms / G. Wechsung / 185 9.1 Automorphic Functions / 185 9.2 Kummer-Type Functional Equations / 186 9.3 A Method to Construct Functional Equations / 191 9.4 The Nonexistence of a Kummer-Type Functional Equation for $Li _6$ / 197 References / 203 10: The Basic Structure of Polylogarithmic Equations / Z. Wojtkowiak / 205 10.1 Introduction / 205 10.2 Canonical Unipotent Connection on $P^1(mathbb C)a_1, ldots , a_n+1$ / 211 10.3 Horizontal Sections / 213 10.4 Easy Lemmas about Monodromy / 215 10.5 Functional Equations / 216 10.6 Functional Equations of Polylogarithms / 218 10.7 Functional Equations of Lower Degree Polylogarithms / 223 10.8 Generalized Bloch Groups / 228 Acknowledgements / 231 References / 231 11: $K$-Theory, Cyclotomic Equations and Clausen's Function / J. Browkin / 233 11.1 Algebraic Background / 233 11.2 Analytic Background / 238 11.3 $K$-theoretic Background / 248 11.4 Examples / 251 11.5 Problems and Conjectures / 270 References / 272 12: Function Theory of Polylogarithms / S. Bloch / 275 13: Partition Identities and the Dilogarithm / J. H. Loxton / 287 13.1 Introduction / 287 13.2 Cyclotomic Equations / 290 13.3 Accessible Relations / 291 13.4 Partition Identities / 292 13.5 Generalisations and Extensions / 297 References / 299 14: The Dilogarithm and Volumes of Hyperbolic Polytopes / R. Kellerhals / 301 14.0 Introduction / 301 14.1 A Particular Class of Hyperbolic Polytopes / 303 14.2 The Volume of a rf-Truncated Orthoscheme / 309 14.3 Applications / 321 14.4 Further Aspects / 328 References / 335 15: Introduction to Higher Logarithms / R. M. Hain and R. MacPherson / 337 15.1 The Problem of Generalizing the Logarithm and the Dilogarithm / 337 15.2 The Quest for Higher Logarithms / 340 15.3 Higher Logarithms / 341 15.4 The Higher Logarithm Bicomplex / 343 15.5 Multivalued Deligne Cohomology / 346 15.6 Higher Logarithms as Deligne Cohomology Classes / 350 Acknowledgements 3 / 51 References / 352 16: Some Miscellaneous Results / L. Lewin / 355 16.1 Clausen's Function and the Di-Gamma Function for Rational Arguments / 355 16.2 An Infinite Integral of a Product of Two Polylogarithms / 359 16.3 Cyclotomic and Polylogarithmic Equations for a Salem Number / 364 16.4 New Functional Equations / 373 References / 374 Appendix A. Special Values and Functional Equations of Polylogarithms / D. Zagier / 377 0. Introduction / 377 1. The Basic Algebraic Relation and the Definition of $mathcal A_m(F)$ / 378 2. Examples of Dilogarithm Relations / 383 3. Examples for Higher Order Polylogarithms / 385 4. Examples: Ladders / 387 5. Existence of Relations among Polylogarithm Values of Arbitrarily High Order / 390 6. A Conjecture on Linear Independence / 391 7. Functional Equations / 392 References / 399 Appendix B. Summary of the Informal Polylogarithm Workshop, November 17--18, 1990, MIT, Cambridge, Massachusetts / 401 R. MacPherson and H. Sah / List of Participants / 401 Abbreviated Summary / 402 Bibliography / 405 Index / 409

rawTOC:
Preface / xiii \\ Acknowledgments / xv \\ List of Contributors / xvii \\ \\ 1: The Evolution of the Ladder Concept / L. Lewin / 1 \\ 1.1 Early History / 1 \\ 1.2 Functional Equations / 2 \\ 1.3 More Recent Numerical Results / 4 \\ 1.4 Current Developments / 6 \\ 1.5 Base on the Unit Circle and Clausen Function Ladders / 8 \\ References / 9 \\ \\ 2: Dilogarithmic Ladders / L. Lewin / 11 \\ 2.1 Derivation from Kummer's Functional Equation / 11 \\ 2.2 Relation to Clausen's Function / 15 \\ 2.3 A Three-Variable Dilogarithmic Functional Equation / 17 \\ 2.4 Functional Equations in the Complex Plane / 18 \\ 2.5 Cyclotomic Equations and Rogers' Function / 20 \\ 2.6 Accessible and Analytic Ladders / 21 \\ 2.7 Inaccessible Ladders / 23 \\ References / 25 \\ \\ 3: Polylogarithmic Ladders / M. Abouzahra and L. Lewin / 27 \\ 3.1 Kummer's Function and its Relation to the Polylogarithm / 27 \\ 3.2 Functional Equations for the Polylogarithm / 28 \\ 3.3 A Generalization of Rogers' Function to the $n$th Order / 31 \\ 3.4 Ladder Order-Independence on Reduction of Order / 33 \\ 3.5 Generic Ladders for the Base Equation $u^p + u^q = 1$ / 34 \\ 3.6 Examples of Ladders for $n < 3$ / 40 \\ 3.7 Examples of Ladders for $n < 4$ / 44 \\ 3.8 Examples of Ladders for $n < 5$ / 45 \\ 3.9 Polynomial Relations for Ladders / 46 \\ References / 47 \\ \\ 4: Ladders in the Trans-Kummer Region / M. Abouzahra and L. Lewin / 49 \\ 4.1 Ladder Results to $n = 9$ for the Base p / 49 \\ 4.2 Ladder Results to $n = 9$ for the Base co / 53 \\ 4.3 Ladder Results to $n = 6$ for the Base 6 / 62 \\ 4.4 The Nonexistence of Functional Equations at $n = 6$ with Arguments Limited to $\pm z^m (1 - z)^r (1 + z)^s$ / 65 \\ References / 67 \\ \\ 5: Supemumary Ladders / M. Abouzahra and L. Lewin / 69 \\ 5.1 The Concept of Supemumary Results / 69 \\ 5.2 Supemumary Results for $p = 4$ / 71 \\ 5.3 Supemumary Results for $p = 5$ / 76 \\ 5.4 Supemumary Results for $p = 6$ / 78 \\ 5.5 Supemumary Results for the Equation-family $u^{6m + 1} u^{6r - 1}$ = 1 / 80 \\ 5.6 Supemumary Results for an Irreducible Quintic / 82 \\ 5.7 Supemumary Ladders from a 15-Term Functional Equation / 84 \\ 5.8 Supemumary Ladders on the Unit Circle / 90 \\ References \\ 6: Functional Equations and Ladders / L. Lewin / 97 \\ 6.1 New Categories of Functional Equations / 97 \\ 6.2 The $\rho$-family of Equations / 100 \\ 6.3 The $\omega$-family of Equations / 109 \\ 6.4 The $\theta$-family of Equations / 115 \\ Acknowledgements / 121 \\ References / 121 \\ \\ 7: Multivariable Polylogarithm Identities / G. A. Ray / 123 \\ 7.0 Introduction / 123 \\ 7.1 A General Identity for the Dilogarithm / 123 \\ 7.2 A General Identity for the Bloch-Wigner Function / 135 \\ 7.3 A General Identity for the Trilogarithm and $D_3(z)$ / 141 \\ 7.4 Linear Power Relations among Dilogarithms / 147 \\ 7.5 Cyclotomic Equations and Bases for Polylogarithm Relations / 154 \\ 7.6 Mahler's Measure and Salem/Pisot Numbers / 160 \\ 7.7 Recent Results for Supemumary Ladders / 165 \\ References / 168 \\ \\ 8: Functional Equations of Hyperlogarithms / G. Wechsung / 171 \\ 8.1 Hyperlogarithms / 171 \\ 8.2 Logarithmic Singularities / 172 \\ 8.3 The Linear Spaces LI$_n$ and PLI$_n$ / 176 \\ 8.4 Functional Equations of Hyperlogarithms / 177 \\ 8.5 A Reduction Problem / 181 \\ References / 184 \\ \\ 9: Kummer-Type Functional Equations of Polylogarithms / G. Wechsung / 185 \\ 9.1 Automorphic Functions / 185 \\ 9.2 Kummer-Type Functional Equations / 186 \\ 9.3 A Method to Construct Functional Equations / 191 \\ 9.4 The Nonexistence of a Kummer-Type Functional Equation for $\Li_6$ / 197 \\ References / 203 \\ \\ 10: The Basic Structure of Polylogarithmic Equations / Z. Wojtkowiak / 205 \\ 10.1 Introduction / 205 \\ 10.2 Canonical Unipotent Connection on $P^1(\mathbb{C})\{a_1, \ldots{}, a_{n+1}\}$ / 211 \\ 10.3 Horizontal Sections / 213 \\ 10.4 Easy Lemmas about Monodromy / 215 \\ 10.5 Functional Equations / 216 \\ 10.6 Functional Equations of Polylogarithms / 218 \\ 10.7 Functional Equations of Lower Degree Polylogarithms / 223 \\ 10.8 Generalized Bloch Groups / 228 \\ Acknowledgements / 231 \\ References / 231 \\ \\ 11: $K$-Theory, Cyclotomic Equations and Clausen's Function / J. Browkin / 233 \\ 11.1 Algebraic Background / 233 \\ 11.2 Analytic Background / 238 \\ 11.3 $K$-theoretic Background / 248 \\ 11.4 Examples / 251 \\ 11.5 Problems and Conjectures / 270 \\ References / 272 \\ \\ 12: Function Theory of Polylogarithms / S. Bloch / 275 \\ \\ 13: Partition Identities and the Dilogarithm / J. H. Loxton / 287 \\ 13.1 Introduction / 287 \\ 13.2 Cyclotomic Equations / 290 \\ 13.3 Accessible Relations / 291 \\ 13.4 Partition Identities / 292 \\ 13.5 Generalisations and Extensions / 297 \\ References / 299 \\ \\ 14: The Dilogarithm and Volumes of Hyperbolic Polytopes / R. Kellerhals / 301 \\ 14.0 Introduction / 301 \\ 14.1 A Particular Class of Hyperbolic Polytopes / 303 \\ 14.2 The Volume of a rf-Truncated Orthoscheme / 309 \\ 14.3 Applications / 321 \\ 14.4 Further Aspects / 328 \\ References / 335 \\ \\ 15: Introduction to Higher Logarithms / R. M. Hain and R. MacPherson / 337 \\ 15.1 The Problem of Generalizing the Logarithm and the Dilogarithm / 337 \\ 15.2 The Quest for Higher Logarithms / 340 \\ 15.3 Higher Logarithms / 341 \\ 15.4 The Higher Logarithm Bicomplex / 343 \\ 15.5 Multivalued Deligne Cohomology / 346 \\ 15.6 Higher Logarithms as Deligne Cohomology Classes / 350 \\ Acknowledgements 3 / 51 \\ References / 352 \\ \\ 16: Some Miscellaneous Results / L. Lewin / 355 \\ 16.1 Clausen's Function and the Di-Gamma Function for Rational Arguments / 355 \\ 16.2 An Infinite Integral of a Product of Two Polylogarithms / 359 \\ 16.3 Cyclotomic and Polylogarithmic Equations for a Salem Number / 364 \\ 16.4 New Functional Equations / 373 \\ References / 374 \\ \\ Appendix A. Special Values and Functional Equations of Polylogarithms / D. Zagier / 377 \\ 0. Introduction / 377 \\ 1. The Basic Algebraic Relation and the Definition of $\mathcal{A}_m(F)$ / 378 \\ 2. Examples of Dilogarithm Relations / 383 \\ 3. Examples for Higher Order Polylogarithms / 385 \\ 4. Examples: Ladders / 387 \\ 5. Existence of Relations among Polylogarithm Values of Arbitrarily High Order / 390 \\ 6. A Conjecture on Linear Independence / 391 \\ 7. Functional Equations / 392 \\ References / 399 \\ \\ Appendix B. Summary of the Informal Polylogarithm Workshop, November 17--18, 1990, MIT, Cambridge, Massachusetts / 401 \\ R. MacPherson and H. Sah / List of Participants / 401 \\ Abbreviated Summary / 402 \\ Bibliography / 405 \\ Index / 409

entry:
@Book{Lewin:1991:SPP,
  editor =       "Leonard Lewin",
  booktitle =    "Structural Properties of Polylogarithms",
  title =        "Structural Properties of Polylogarithms",
  volume =       "37",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "xviii + 412",
  year =         "1991",
  ISBN =         "0-8218-1634-9, 1-4704-1264-0 (e-book)",
  ISBN-13 =      "978-0-8218-1634-9, 978-1-4704-1264-7 (e-book)",
  ISSN =         "0076-5376",
  MRclass =      "33E20, 00B15, 11-02, 11F67, 11R70, 11R42, 19F27,
                 33-02, 33-06, 33B99",
  bibdate =      "Fri Jun 16 14:03:50 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Mathematical surveys and monographs",
  acknowledgement = ack-nhfb,
  editor-dates = "22-Jul-1919--13-Aug-2007",
  editor-url =   "https://en.wikipedia.org/wiki/Leonard_Lewin_(telecommunications_engineer)",
  subject =      "Logarithmic functions; Fonctions logarithmes;
                 Mathematics; Algebra; Intermediate; Logarithmic
                 functions; Fonctions logarithmes",
  tableofcontents = "Preface / xiii \\
                 Acknowledgments / xv \\
                 List of Contributors / xvii \\
                 \\
                 1: The Evolution of the Ladder Concept / L. Lewin / 1
                 \\
                 1.1 Early History / 1 \\
                 1.2 Functional Equations / 2 \\
                 1.3 More Recent Numerical Results / 4 \\
                 1.4 Current Developments / 6 \\
                 1.5 Base on the Unit Circle and Clausen Function
                 Ladders / 8 \\
                 References / 9 \\
                 \\
                 2: Dilogarithmic Ladders / L. Lewin / 11 \\
                 2.1 Derivation from Kummer's Functional Equation / 11
                 \\
                 2.2 Relation to Clausen's Function / 15 \\
                 2.3 A Three-Variable Dilogarithmic Functional Equation
                 / 17 \\
                 2.4 Functional Equations in the Complex Plane / 18 \\
                 2.5 Cyclotomic Equations and Rogers' Function / 20 \\
                 2.6 Accessible and Analytic Ladders / 21 \\
                 2.7 Inaccessible Ladders / 23 \\
                 References / 25 \\
                 \\
                 3: Polylogarithmic Ladders / M. Abouzahra and L. Lewin
                 / 27 \\
                 3.1 Kummer's Function and its Relation to the
                 Polylogarithm / 27 \\
                 3.2 Functional Equations for the Polylogarithm / 28 \\
                 3.3 A Generalization of Rogers' Function to the $n$th
                 Order / 31 \\
                 3.4 Ladder Order-Independence on Reduction of Order /
                 33 \\
                 3.5 Generic Ladders for the Base Equation $u^p + u^q =
                 1$ / 34 \\
                 3.6 Examples of Ladders for $n < 3$ / 40 \\
                 3.7 Examples of Ladders for $n < 4$ / 44 \\
                 3.8 Examples of Ladders for $n < 5$ / 45 \\
                 3.9 Polynomial Relations for Ladders / 46 \\
                 References / 47 \\
                 \\
                 4: Ladders in the Trans-Kummer Region / M. Abouzahra
                 and L. Lewin / 49 \\
                 4.1 Ladder Results to $n = 9$ for the Base p / 49 \\
                 4.2 Ladder Results to $n = 9$ for the Base co / 53 \\
                 4.3 Ladder Results to $n = 6$ for the Base 6 / 62 \\
                 4.4 The Nonexistence of Functional Equations at $n = 6$
                 with Arguments Limited to $\pm z^m (1 - z)^r (1 + z)^s$
                 / 65 \\
                 References / 67 \\
                 \\
                 5: Supemumary Ladders / M. Abouzahra and L. Lewin / 69
                 \\
                 5.1 The Concept of Supemumary Results / 69 \\
                 5.2 Supemumary Results for $p = 4$ / 71 \\
                 5.3 Supemumary Results for $p = 5$ / 76 \\
                 5.4 Supemumary Results for $p = 6$ / 78 \\
                 5.5 Supemumary Results for the Equation-family $u^{6m +
                 1} u^{6r - 1}$ = 1 / 80 \\
                 5.6 Supemumary Results for an Irreducible Quintic / 82
                 \\
                 5.7 Supemumary Ladders from a 15-Term Functional
                 Equation / 84 \\
                 5.8 Supemumary Ladders on the Unit Circle / 90 \\
                 References \\
                 6: Functional Equations and Ladders / L. Lewin / 97 \\
                 6.1 New Categories of Functional Equations / 97 \\
                 6.2 The $\rho$-family of Equations / 100 \\
                 6.3 The $\omega$-family of Equations / 109 \\
                 6.4 The $\theta$-family of Equations / 115 \\
                 Acknowledgements / 121 \\
                 References / 121 \\
                 \\
                 7: Multivariable Polylogarithm Identities / G. A. Ray /
                 123 \\
                 7.0 Introduction / 123 \\
                 7.1 A General Identity for the Dilogarithm / 123 \\
                 7.2 A General Identity for the Bloch-Wigner Function /
                 135 \\
                 7.3 A General Identity for the Trilogarithm and
                 $D_3(z)$ / 141 \\
                 7.4 Linear Power Relations among Dilogarithms / 147 \\
                 7.5 Cyclotomic Equations and Bases for Polylogarithm
                 Relations / 154 \\
                 7.6 Mahler's Measure and Salem/Pisot Numbers / 160 \\
                 7.7 Recent Results for Supemumary Ladders / 165 \\
                 References / 168 \\
                 \\
                 8: Functional Equations of Hyperlogarithms / G.
                 Wechsung / 171 \\
                 8.1 Hyperlogarithms / 171 \\
                 8.2 Logarithmic Singularities / 172 \\
                 8.3 The Linear Spaces LI$_n$ and PLI$_n$ / 176 \\
                 8.4 Functional Equations of Hyperlogarithms / 177 \\
                 8.5 A Reduction Problem / 181 \\
                 References / 184 \\
                 \\
                 9: Kummer-Type Functional Equations of Polylogarithms /
                 G. Wechsung / 185 \\
                 9.1 Automorphic Functions / 185 \\
                 9.2 Kummer-Type Functional Equations / 186 \\
                 9.3 A Method to Construct Functional Equations / 191
                 \\
                 9.4 The Nonexistence of a Kummer-Type Functional
                 Equation for $\Li_6$ / 197 \\
                 References / 203 \\
                 \\
                 10: The Basic Structure of Polylogarithmic Equations /
                 Z. Wojtkowiak / 205 \\
                 10.1 Introduction / 205 \\
                 10.2 Canonical Unipotent Connection on
                 $P^1(\mathbb{C})\{a_1, \ldots{}, a_{n+1}\}$ / 211 \\
                 10.3 Horizontal Sections / 213 \\
                 10.4 Easy Lemmas about Monodromy / 215 \\
                 10.5 Functional Equations / 216 \\
                 10.6 Functional Equations of Polylogarithms / 218 \\
                 10.7 Functional Equations of Lower Degree
                 Polylogarithms / 223 \\
                 10.8 Generalized Bloch Groups / 228 \\
                 Acknowledgements / 231 \\
                 References / 231 \\
                 \\
                 11: $K$-Theory, Cyclotomic Equations and Clausen's
                 Function / J. Browkin / 233 \\
                 11.1 Algebraic Background / 233 \\
                 11.2 Analytic Background / 238 \\
                 11.3 $K$-theoretic Background / 248 \\
                 11.4 Examples / 251 \\
                 11.5 Problems and Conjectures / 270 \\
                 References / 272 \\
                 \\
                 12: Function Theory of Polylogarithms / S. Bloch / 275
                 \\
                 \\
                 13: Partition Identities and the Dilogarithm / J. H.
                 Loxton / 287 \\
                 13.1 Introduction / 287 \\
                 13.2 Cyclotomic Equations / 290 \\
                 13.3 Accessible Relations / 291 \\
                 13.4 Partition Identities / 292 \\
                 13.5 Generalisations and Extensions / 297 \\
                 References / 299 \\
                 \\
                 14: The Dilogarithm and Volumes of Hyperbolic Polytopes
                 / R. Kellerhals / 301 \\
                 14.0 Introduction / 301 \\
                 14.1 A Particular Class of Hyperbolic Polytopes / 303
                 \\
                 14.2 The Volume of a rf-Truncated Orthoscheme / 309 \\
                 14.3 Applications / 321 \\
                 14.4 Further Aspects / 328 \\
                 References / 335 \\
                 \\
                 15: Introduction to Higher Logarithms / R. M. Hain and
                 R. MacPherson / 337 \\
                 15.1 The Problem of Generalizing the Logarithm and the
                 Dilogarithm / 337 \\
                 15.2 The Quest for Higher Logarithms / 340 \\
                 15.3 Higher Logarithms / 341 \\
                 15.4 The Higher Logarithm Bicomplex / 343 \\
                 15.5 Multivalued Deligne Cohomology / 346 \\
                 15.6 Higher Logarithms as Deligne Cohomology Classes /
                 350 \\
                 Acknowledgements 3 / 51 \\
                 References / 352 \\
                 \\
                 16: Some Miscellaneous Results / L. Lewin / 355 \\
                 16.1 Clausen's Function and the Di-Gamma Function for
                 Rational Arguments / 355 \\
                 16.2 An Infinite Integral of a Product of Two
                 Polylogarithms / 359 \\
                 16.3 Cyclotomic and Polylogarithmic Equations for a
                 Salem Number / 364 \\
                 16.4 New Functional Equations / 373 \\
                 References / 374 \\
                 \\
                 Appendix A. Special Values and Functional Equations of
                 Polylogarithms / D. Zagier / 377 \\
                 0. Introduction / 377 \\
                 1. The Basic Algebraic Relation and the Definition of
                 $\mathcal{A}_m(F)$ / 378 \\
                 2. Examples of Dilogarithm Relations / 383 \\
                 3. Examples for Higher Order Polylogarithms / 385 \\
                 4. Examples: Ladders / 387 \\
                 5. Existence of Relations among Polylogarithm Values of
                 Arbitrarily High Order / 390 \\
                 6. A Conjecture on Linear Independence / 391 \\
                 7. Functional Equations / 392 \\
                 References / 399 \\
                 \\
                 Appendix B. Summary of the Informal Polylogarithm
                 Workshop, November 17--18, 1990, MIT, Cambridge,
                 Massachusetts / 401 \\
                 R. MacPherson and H. Sah / List of Participants / 401
                 \\
                 Abbreviated Summary / 402 \\
                 Bibliography / 405 \\
                 Index / 409",
}


