%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%% author = "Nelson H. F. Beebe",
%%% version = "1.65",
%%% date = "19 September 2023",
%%% time = "11:15:29 MDT",
%%% filename = "parlett-beresford-n.bib",
%%% address = "University of Utah
%%% Department of Mathematics, 110 LCB
%%% 155 S 1400 E RM 233
%%% Salt Lake City, UT 84112-0090
%%% USA",
%%% telephone = "+1 801 581 5254",
%%% FAX = "+1 801 581 4148",
%%% URL = "https://www.math.utah.edu/~beebe",
%%% checksum = "43225 7907 35211 361152",
%%% email = "beebe at math.utah.edu, beebe at acm.org,
%%% beebe at computer.org (Internet)",
%%% codetable = "ISO/ASCII",
%%% keywords = "BibTeX; bibliography",
%%% license = "public domain",
%%% supported = "yes",
%%% docstring = "This is a bibliography of publications of
%%% Beresford Neill Parlett, B.A. (Oxford, 1955),
%%% Ph.D. (Stanford, 1962), Professor Emeritus of
%%% Computer Science, and Professor Emeritus of
%%% Mathematics, University of California,
%%% Berkeley. The companion LaTeX file
%%% parlett-beresford-n.ltx can be used to
%%% typeset this bibliography.
%%%
%%% Part 1 covers his publications, and Part 2
%%% covers publications about him by others.
%%%
%%% Beresford N. Parlett's personal Web site is
%%%
%%% http://math.berkeley.edu/~parlett/
%%%
%%% This bibliography contains a few additional
%%% entries that refer to the work of Beresford
%%% N. Parlett in their titles.
%%%
%%% At version 1.65, the year coverage looked
%%% like this:
%%%
%%% 1962 ( 1) 1983 ( 7) 2004 ( 4)
%%% 1963 ( 0) 1984 ( 7) 2005 ( 6)
%%% 1964 ( 4) 1985 ( 8) 2006 ( 4)
%%% 1965 ( 2) 1986 ( 4) 2007 ( 4)
%%% 1966 ( 7) 1987 ( 8) 2008 ( 4)
%%% 1967 ( 6) 1988 ( 7) 2009 ( 7)
%%% 1968 ( 1) 1989 ( 2) 2010 ( 2)
%%% 1969 ( 4) 1990 ( 9) 2011 ( 3)
%%% 1970 ( 2) 1991 ( 6) 2012 ( 1)
%%% 1971 ( 3) 1992 ( 10) 2013 ( 0)
%%% 1972 ( 3) 1993 ( 7) 2014 ( 1)
%%% 1973 ( 3) 1994 ( 9) 2015 ( 0)
%%% 1974 ( 5) 1995 ( 9) 2016 ( 1)
%%% 1975 ( 3) 1996 ( 8) 2017 ( 1)
%%% 1976 ( 5) 1997 ( 6) 2018 ( 0)
%%% 1977 ( 9) 1998 ( 2) 2019 ( 0)
%%% 1978 ( 5) 1999 ( 0) 2020 ( 2)
%%% 1979 ( 4) 2000 ( 7) 2021 ( 0)
%%% 1980 ( 7) 2001 ( 0) 2022 ( 1)
%%% 1981 ( 10) 2002 ( 5)
%%% 1982 ( 9) 2003 ( 5)
%%%
%%% Article: 138
%%% Book: 8
%%% InCollection: 1
%%% InProceedings: 27
%%% Misc: 2
%%% PhdThesis: 1
%%% Proceedings: 25
%%% TechReport: 58
%%%
%%% Total entries: 260
%%%
%%% Data for this bibliography have been
%%% collected from the University of Utah
%%% Mathematics Department bibliography archives,
%%% the TeX User Group bibliography archives, the
%%% Karlsruhe Computer Science bibliography
%%% archives, from the European Mathematical
%%% Society Zentralblatt fuer Mathematik
%%% database, from the American Mathematical
%%% Society MathSciNet database, from the
%%% publication list at Beresford N. Parlett's
%%% personal Web site, and from several online
%%% library catalogs, including those of the
%%% British Library, the Karlsruhe Virtual
%%% Library catalog, the Oxford University
%%% Library, and the US Library of Congress.
%%%
%%% This file is available as part of the BibNet
%%% Project. The master copy is available for
%%% public access on ftp.math.utah.edu in the
%%% directory tree /pub/bibnet/authors. It is
%%% mirrored to netlib.bell-labs.com in the directory
%%% tree /netlib/bibnet/authors, from which it is
%%% available via anonymous ftp and the Netlib
%%% service.
%%%
%%% The checksum field above contains a CRC-16
%%% checksum as the first value, followed by the
%%% equivalent of the standard UNIX wc (word
%%% count) utility output of lines, words, and
%%% characters. This is produced by Robert
%%% Solovay's checksum utility.",
%%% }
%%% ====================================================================
@Preamble{
"\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi" #
"\ifx \undefined \operatorname \def \operatorname #1{{\rm #1}}\fi"
}
%%% ====================================================================
%%% Institutions and their addresses:
@String{inst-CPAM-UCB = "Center for Pure and Applied Mathematics,
University of California, Berkeley"}
@String{inst-CPAM-UCB:adr = "Berkeley, CA, USA"}
@String{inst-ERL-CE-UCB = "Electronics Research Laboratory,
College of Engineering, University of
California, Berkeley"}
@String{inst-ERL-CE-UCB:adr = "Berkeley, CA, USA"}
@String{inst-UCB-EECS = "Department of Electrical Engineering
and Computer Science, University of
California, Berkeley"}
@String{inst-UCB-EECS:adr = "Berkeley, CA, USA"}
@String{inst-UTK-CS = "Department of Computer Science, University
of Tennessee, Knoxville"}
@String{inst-UTK-CS:adr = "Knoxville, TN 37996, USA"}
%%% ====================================================================
%%% Journal abbreviations:
@String{j-ACTA-NUMERICA = "Acta Numerica"}
@String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"}
@String{j-BIT = "BIT (Nordisk tidskrift for
informationsbehandling)"}
@String{j-BIT-NUM-MATH = "BIT Numerical Mathematics"}
@String{j-BULL-AMS-N-S = "Bulletin of the American Mathematical Society (new series)"}
@String{j-CACM = "Communications of the ACM"}
@String{j-COMM-PURE-APPL-MATH = "Communications on Pure and Applied
Mathematics (New York)"}
@String{j-COMP-J = "The Computer Journal"}
@String{j-COMP-PHYS-COMM = "Computer Physics Communications"}
@String{j-COMP-STRUCTURES = "Computers and Structures"}
@String{j-COMPUT-SCI-ENG = "Computing in Science and Engineering"}
@String{j-FOUND-COMPUT-MATH = "Foundations of Computational Mathematics.
The Journal of the Society for the Foundations
of Computational Mathematics"}
@String{j-IEEE-TRANS-VIS-COMPUT-GRAPH = "IEEE Transactions on Visualization
and Computer Graphics"}
@String{j-IMA-J-NUMER-ANAL = "IMA Journal of Numerical Analysis"}
@String{j-INT-J-HIGH-SPEED-COMPUTING = "International Journal of High Speed
Computing (IJHSC)"}
@String{j-INT-J-NUMER-METHODS-ENG = "International Journal for Numerical
Methods in Engineering"}
@String{j-J-ACM = "Journal of the ACM"}
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Mathematics"}
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@String{j-J-MATH-PHYS = "Journal of Mathematical Physics"}
@String{j-J-NUM-LIN-ALG-APPL = "Journal of Numerical linear algebra with
applications"}
@String{j-LINEAR-ALGEBRA-APPL = "Linear Algebra and its Applications"}
@String{j-MATH-COMPUT = "Mathematics of Computation"}
@String{j-NUM-LIN-ALG-APPL = "Numerical Linear Algebra with Applications"}
@String{j-NUM-MATH = "Numerische Mathematik"}
@String{j-PARALLEL-ALGORITHMS-APPL = "Parallel Algorithms and Applications"}
@String{j-PARALLEL-COMPUTING = "Parallel Computing"}
@String{j-SIAM-J-ALG-DISC-METH = "SIAM Journal on Algebraic and Discrete
Methods"}
@String{j-SIAM-J-APPL-MATH = "SIAM Journal on Applied Mathematics"}
@String{j-SIAM-J-MAT-ANA-APPL = "SIAM Journal on Matrix Analysis and
Applications"}
@String{j-SIAM-J-NUMER-ANAL = "SIAM Journal on Numerical Analysis"}
@String{j-SIAM-J-SCI-COMP = "SIAM Journal on Scientific Computing"}
@String{j-SIAM-J-SCI-STAT-COMP = "SIAM Journal on Scientific and Statistical
Computing"}
@String{j-SIAM-REVIEW = "SIAM Review"}
@String{j-SIGNUM = "ACM SIGNUM Newsletter"}
@String{j-THEOR-POPUL-BIOL = "Theoretical Population Biology"}
@String{j-TOMS = "ACM Transactions on Mathematical Software"}
@String{j-Z-ANGE-MATH-MECH = "Zeitschrift f{\"u}r Angewandte Mathematik
und Mechanik"}
%%% ====================================================================
%%% Publisher abbreviations:
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@String{pub-ACADEMIC:adr = "New York, NY, USA"}
@String{pub-ACM = "ACM Press"}
@String{pub-ACM:adr = "New York, NY 10036, USA"}
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@String{pub-CAMBRIDGE:adr = "Cambridge, UK"}
@String{pub-DUNOD = "Dunod"}
@String{pub-DUNOD:adr = "Paris, France"}
@String{pub-EDITORIAL-MIR = "Editorial Mir"}
@String{pub-EDITORIAL-MIR:adr = "Moscow, USSR"}
@String{pub-ELSEVIER = "Elsevier"}
@String{pub-ELSEVIER:adr = "Amsterdam, The Netherlands"}
@String{pub-ELSEVIER-SCIENCE = "Elsevier Science, Inc."}
@String{pub-ELSEVIER-SCIENCE:adr = "Amsterdam, The Netherlands"}
@String{pub-GRUYTER = "Walter de Gruyter"}
@String{pub-GRUYTER:adr = "Berlin, Germany"}
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@String{pub-IEEE:adr = "1109 Spring Street, Suite 300,
Silver Spring, MD 20910, USA"}
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@String{pub-PH = "Pren{\-}tice-Hall"}
@String{pub-PH:adr = "Upper Saddle River, NJ 07458, USA"}
@String{pub-PLENUM = "Plenum Press"}
@String{pub-PLENUM:adr = "New York, NY, USA; London, UK"}
@String{pub-SIAM = "Society for Industrial and Applied
Mathematics"}
@String{pub-SIAM:adr = "Philadelphia, PA, USA"}
@String{pub-SV = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr = "Berlin, Germany~/ Heidelberg,
Germany~/ London, UK~/ etc."}
@String{pub-WILEY = "Wiley"}
@String{pub-WILEY:adr = "New York, NY, USA; London, UK; Sydney, Australia"}
%%% ====================================================================
%%%
%%% Part 1 (of 2): publications by Beresford N. Parlett
%%%
%%% Bibliography entries, sorted by year, and then by citation label
%%% (with ``bibsort -byyear''):
@PhdThesis{Parlett:1962:BML,
author = "Beresford Neill Parlett",
title = "{I}. Bundles of matrices and the linear independence
of their minors; {II}. Applications of {Laguerre}'s
method to the matrix eigenvalue problem",
type = "{Ph.D.} dissertation",
school = "Department of Mathematics, Stanford University",
address = "Stanford, CA, USA",
pages = "v + 118",
year = "1962",
bibdate = "Fri Nov 11 05:07:47 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://www.genealogy.math.ndsu.nodak.edu/html/id.phtml?id=32898;
http://wwwlib.umi.com/dxweb/details?doc_no=5023767",
acknowledgement = ack-nhfb,
advisor = "George E. Forsythe",
}
@Article{Forsythe:1964:TPA,
author = "George E. Forsythe",
title = "Tests of {Parlett}'s {ALGOL} Eigenvalue Procedure {$ E
i g 3 $} (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "18",
number = "87",
pages = "486--487",
month = jul,
year = "1964",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2003771",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.40",
MRnumber = "0165669",
MRreviewer = "James H. Wilkinson",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
JSTOR database",
URL = "https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Parlett:1964:DUM,
author = "Beresford Parlett",
title = "The Development and Use of Methods of {$ L R $} Type",
journal = j-SIAM-REVIEW,
volume = "6",
number = "3",
pages = "275--295",
month = jul,
year = "1964",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1006066",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65.35",
MRnumber = "MR0172450 (30 \#2669)",
MRreviewer = "James H. Wilkinson",
bibdate = "Thu Mar 27 09:05:15 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/6/3;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
ZMnumber = "0242.65039",
acknowledgement = ack-nhfb,
classmath = "65F15 Eigenvalues (numerical linear algebra)",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "July 1964",
}
@Article{Parlett:1964:LMA,
author = "Beresford N. Parlett",
title = "{Laguerre}'s Method Applied to the Matrix Eigenvalue
Problem",
journal = j-MATH-COMPUT,
volume = "18",
number = "87",
pages = "464--485",
month = jul,
year = "1964",
CODEN = "MCMPAF",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.40",
MRnumber = "MR0165668 (29 \#2948)",
MRreviewer = "James H. Wilkinson",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
JSTOR database; Theory/Matrix.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib",
ZMnumber = "0124.33004",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "numerical analysis",
kwds = "nla, eig, Laguerre's method, polynomial",
}
@Article{Parlett:1964:NBA,
author = "Beresford Parlett",
title = "A Note on {La Budde}'s Algorithm (in {Technical Notes
and Short Papers})",
journal = j-MATH-COMPUT,
volume = "18",
number = "87",
pages = "505--506",
month = jul,
year = "1964",
CODEN = "MCMPAF",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.35",
MRnumber = "MR0165671 (29 \#2951)",
MRreviewer = "A. S. Householder",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
JSTOR database",
URL = "https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib",
ZMnumber = "0208.39902",
acknowledgement = ack-nhfb,
classmath = "*65F99 Numerical linear algebra",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Parlett:1965:CA,
author = "Beresford Parlett",
title = "Convergence of the {$ Q R $} algorithm",
journal = j-NUM-MATH,
volume = "7",
pages = "187--193",
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.40",
MRnumber = "MR0176600 (31 \#872)",
MRreviewer = "E. R. Hansen",
bibdate = "Sun Oct 17 19:01:15 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "See correction \cite{Parlett:1967:CCA}.",
URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
ZMnumber = "0132.36301",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "numerical analysis",
}
@Article{Parlett:1965:MEP,
author = "Beresford Parlett",
title = "Matrix Eigenvalue Problems",
journal = j-AMER-MATH-MONTHLY,
volume = "72",
number = "2, part II",
pages = "59--66",
year = "1965",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "65.40",
MRnumber = "MR0172452 (30 \#2671)",
MRreviewer = "P. J. Davis",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
ZMnumber = "0123.11302",
acknowledgement = ack-nhfb,
fjournal = "The American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
keywords = "numerical analysis",
}
@Article{Parlett:1966:BRB,
author = "B. N. Parlett",
title = "Book Review: {{\booktitle{The Algebraic Eigenvalue
Problem}} (J. H. Wilkinson)}",
journal = j-SIAM-REVIEW,
volume = "8",
number = "4",
pages = "543--545",
month = "????",
year = "1966",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1008125",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:05:39 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/8/4;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "October 1966",
}
@Article{Buchanan:1966:UCM,
author = "M. L. Buchanan and B. N. Parlett",
title = "The uniform convergence of matrix powers",
journal = j-NUM-MATH,
volume = "9",
pages = "51--54",
year = "1966",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.40",
MRnumber = "MR0205434 (34 \#5262)",
MRreviewer = "H.-O. Kreiss",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/nummath.bib",
ZMnumber = "0143.05104",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "linear algebra, forms",
}
@Article{Parlett:1966:ADD,
author = "Beresford Parlett",
title = "Accuracy and dissipation in difference schemes",
journal = j-COMM-PURE-APPL-MATH,
volume = "19",
number = "1",
pages = "111--123",
year = "1966",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640 (print), 1097-0312 (electronic)",
ISSN-L = "0010-3640",
MRclass = "65.65",
MRnumber = "MR0196957 (33 \#5141)",
MRreviewer = "H.-O. Kreiss",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "0173.44703",
acknowledgement = ack-nhfb,
fjournal = "Communications on Pure and Applied Mathematics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
keywords = "numerical analysis",
}
@Article{Parlett:1966:CQR,
author = "Beresford Parlett",
title = "Convergence of the {Q-R} algorithm for {Hessenberg}
matrices",
journal = j-CACM,
volume = "9",
number = "7",
pages = "475--475",
month = jul,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:07 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Parlett:1966:SIM,
author = "Beresford N. Parlett",
title = "Singular and Invariant Matrices Under the {$ {QR} $}
Transformation (in {Technical Notes and Short
Papers})",
journal = j-MATH-COMPUT,
volume = "20",
number = "96",
pages = "611--615",
month = oct,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.35",
MRnumber = "MR0213005 (35 \#3870)",
MRreviewer = "N. Gastinel",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
JSTOR database; Theory/Matrix.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib",
ZMnumber = "0238.65018",
acknowledgement = ack-nhfb,
classmath = "*65F30 Other matrix algorithms",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
kwds = "nla, eig, QR algorithm",
}
@Article{Rust:1966:SAC,
author = "B. Rust and W. R. Burrus and C. Schneeberger",
title = "A simple algorithm for computing the generalized
inverse of a matrix",
journal = j-CACM,
volume = "9",
number = "5",
pages = "381--385, 387",
month = may,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.35",
MRnumber = "33\#3448",
bibdate = "Tue May 28 07:33:09 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib",
abstract = "The generalized inverse of a matrix is important in
analysis because it provides an extension of the
concept of an inverse which applies to all matrices. It
also has many applications in numerical analysis, but
it is not widely used because the existing algorithms
are fairly complicated and require considerable storage
space. A simple extension has been found to the
conventional orthogonalization method for inverting
non-singular matrices, which gives the generalized
inverse with little extra effort and with no additional
storage requirements. The algorithm gives the
generalized inverse for any $m$ by n matrix {$A$},
including the special case when $ m + n $ and {$A$} is
non-singular and the case when $ m > n $ and {$ \mbox
{rank}(A) = n $}. In the first case the algorithm gives
the ordinary inverse of {$A$}. In the second case the
algorithm yields the ordinary least squares
transformation matrix {$ \mbox {INV}(A'A)A' $} and has
the advantage of avoiding the loss of significance
which results in forming the product {$ A'A $}
explicitly.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
kwds = "nla, ginv",
reviewer = "B. N. Parlett",
}
@Article{Varah:1966:CPA,
author = "J. M. Varah",
title = "Certification of {Parlett}'s {ALGOL} Eigenvalue
Procedure {$ \operatorname {Eig} $} 3 (in {Technical
Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "20",
number = "95",
pages = "437--438",
month = jul,
year = "1966",
CODEN = "MCMPAF",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
JSTOR database",
URL = "https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InProceedings{Parlett:1967:A,
author = "B. N. Parlett",
title = "The {$ L U $} and {$ Q R $} algorithms",
crossref = "Ralston:1967:MMD",
pages = "116--130",
year = "1967",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
acknowledgement = ack-nhfb,
}
@Article{Parlett:1967:CCA,
author = "Beresford Parlett",
title = "Correction to: ``{Convergence of the $ Q R $
algorithm}''",
journal = j-NUM-MATH,
volume = "10",
pages = "163--164",
year = "1967",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.35",
MRnumber = "MR0214278 (35 \#5129)",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "See \cite{Parlett:1965:CA}.",
URL = "https://www.math.utah.edu/pub/tex/bib/nummath.bib",
ZMnumber = "0171.36004",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "numerical analysis",
}
@Article{Parlett:1967:CDH,
author = "Beresford Parlett",
title = "Canonical Decomposition of {Hessenberg} Matrices (in
{Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "21",
number = "98",
pages = "223--227",
month = apr,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "15.30 (65.00)",
MRnumber = "MR0228519 (37 \#4099)",
MRreviewer = "A. S. Householder",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
JSTOR database",
URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib",
ZMnumber = "0159.20501",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "numerical analysis",
}
@Article{Parlett:1967:EA,
author = "B. N. Parlett",
title = "Eigenvalues, anyone?",
journal = j-SIGNUM,
volume = "1",
number = "3",
pages = "7--8",
month = feb,
year = "1967",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Mon Mar 5 17:26:25 MST 2007",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690",
}
@Article{Parlett:1967:LEF,
author = "Beresford Parlett",
title = "Letter to the Editor: On finding the eigenvalues of
real symmetric tridiagonal matrices",
journal = j-COMP-J,
volume = "9",
number = "4",
pages = "344--345",
month = feb,
year = "1967",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Thu Aug 25 09:00:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://comjnl.oxfordjournals.org/content/9/4/344.full.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Parlett:1968:GCB,
author = "Beresford N. Parlett",
title = "Global Convergence of the Basic {QR} Algorithm on
{Hessenberg} Matrices",
journal = j-MATH-COMPUT,
volume = "22",
number = "104",
pages = "803--817",
month = oct,
year = "1968",
CODEN = "MCMPAF",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.35",
MRnumber = "MR0247759 (40 \#1020)",
MRreviewer = "J. Vandergraft",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
JSTOR database; Theory/Matrix.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib",
ZMnumber = "0184.37602",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "numerical analysis",
kwds = "nla, eig, QR algorithm, Hessenberg matrix",
}
@Article{Parlett:1969:BMC,
author = "B. N. Parlett and C. Reinsch",
title = "Balancing a matrix for calculation of eigenvalues and
eigenvectors",
journal = j-NUM-MATH,
volume = "13",
pages = "293--304",
year = "1969",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
Theory/Matrix.bib",
note = "Also in \cite[pp. 315--326]{Wilkinson:1971:LA}.",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
ZMnumber = "0184.37703",
acknowledgement = ack-nhfb,
author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "eig; nla; numerical analysis; scaling; software",
xxpages = "292--304",
}
@InProceedings{Parlett:1969:CPA,
author = "B. N. Parlett and W. Kahan",
title = "On the convergence of a practical {$ Q R $} algorithm.
({With} discussion)",
crossref = "Morrell:1969:IPP",
volume = "1",
pages = "114--118",
year = "1969",
MRclass = "65.40",
MRnumber = "MR0255035 (40 \#8242)",
bibdate = "Mon Apr 25 18:24:02 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "0195.45002",
acknowledgement = ack-nhfb,
keywords = "numerical analysis",
}
@Article{Parlett:1969:NNM,
author = "B. N. Parlett",
title = "Notes on the number of multiplications required to
form the product of two {$ N \times N $} matrices",
journal = j-SIGNUM,
volume = "4",
number = "2",
pages = "9--12",
month = jun,
year = "1969",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Mon Mar 5 17:26:28 MST 2007",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690",
}
@Article{Parlett:1970:EPP,
author = "Beresford Parlett",
title = "Ergodic properties of populations. {I}. {The} one sex
model",
journal = j-THEOR-POPUL-BIOL,
volume = "1",
number = "??",
pages = "191--207",
year = "1970",
CODEN = "TLPBAQ",
DOI = "https://doi.org/10.1016/0040-5809(70)90034-1",
ISSN = "0040-5809 (print), 1096-0325 (electronic)",
ISSN-L = "0040-5809",
MRclass = "92A15",
MRnumber = "MR0325180 (48 \#3529)",
MRreviewer = "N. Keyfitz",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "0239.92007",
acknowledgement = ack-nhfb,
classmath = "*92D25 Population dynamics",
fjournal = "Theoretical Population Biology. An International
Journal",
journal-URL = "http://www.sciencedirect.com/science/journal/00405809",
}
@Article{Parlett:1970:SSL,
author = "B. Parlett and J. K. Reid",
title = "On the Solution of a System of Linear Equations whose
Matrix is Symmetric but not Definite",
journal = j-BIT,
volume = "10",
number = "3",
pages = "386--397",
year = "1970",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Sat Nov 14 09:14:57 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Bunch:1971:DMS,
author = "James R. Bunch and Beresford N. Parlett",
title = "Direct Methods for Solving Symmetric Indefinite
Systems of Linear Equations",
journal = j-SIAM-J-NUMER-ANAL,
volume = "8",
number = "4",
pages = "639--655",
month = dec,
year = "1971",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F05",
MRnumber = "MR0305564 (46 \#4694)",
MRreviewer = "John Todd",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
JSTOR database",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib",
ZMnumber = "0199.49802",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "numerical analysis",
remark = "Zentralblatt MATH database records this as number 3,
1970.",
}
@Article{Parlett:1971:AAR,
author = "Beresford N. Parlett",
title = "Analysis of Algorithms for Reflections in Bisectors",
journal = j-SIAM-REVIEW,
volume = "13",
number = "2",
pages = "197--208",
month = "????",
year = "1971",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1013037",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65.80",
MRnumber = "MR0290608 (44 \#7788)",
MRreviewer = "G. Fairweather",
bibdate = "Thu Mar 27 09:06:28 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/13/2;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
ZMnumber = "0217.52606",
acknowledgement = ack-nhfb,
classmath = "65F99 Numerical linear algebra 65G99 Error analysis
65Y20 Complexity and performance of numerical
algorithms",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "April 1971",
}
@Article{Partlett:1972:BRB,
author = "B. Partlett",
title = "Book Review: {{\booktitle{Handbook for Automatic
Computation, Vol. II, Linear Algebra}} (J. H. Wilkinson
and C. Reinsch)}",
journal = j-SIAM-REVIEW,
volume = "14",
number = "4",
pages = "658--661",
month = "????",
year = "1972",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1014116",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:06:44 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/14/4;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "October 1972",
subject-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022);
James H. Wilkinson (27 September 1919--5 October
1986)",
}
@InProceedings{Parlett:1972:CTM,
author = "B. Parlett",
title = "Can there be a marriage function?",
crossref = "Greville:1972:PDP",
pages = "107--135",
year = "1972",
MRclass = "92A15",
MRnumber = "MR0446591 (56 \#4916)",
MRreviewer = "R. Fischler",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Parlett:1973:GTP,
author = "B. N. Parlett and W. G. {Poole, Jr.}",
title = "A Geometric Theory for the {$ {QR} $}, {$ {LU} $} and
Power Iterations",
journal = j-SIAM-J-NUMER-ANAL,
volume = "10",
number = "2",
pages = "389--412",
month = apr,
year = "1973",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F15",
MRnumber = "MR0336979 (49 \#1752)",
MRreviewer = "J. Vandergraft",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
JSTOR database",
note = "Collection of articles dedicated to the memory of
George E. Forsythe",
URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib",
ZMnumber = "0227.65027; 0253.65018",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Parlett:1973:NHM,
author = "Beresford Parlett",
title = "Normal {Hessenberg} and moment matrices",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "6",
number = "??",
pages = "37--43",
month = "????",
year = "1973",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15",
MRnumber = "MR0324887 (48 \#3236)",
MRreviewer = "James H. Wilkinson",
bibdate = "Tue Feb 16 18:54:52 MST 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/linala1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0024379573900050",
ZMnumber = "0251.15022",
acknowledgement = ack-nhfb,
classmath = "*15A57 Other types of matrices 65F30 Other matrix
algorithms",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@Article{Parlett:1973:PGM,
author = "B. N. Parlett",
title = "Pr{\'e}sentation g{\'e}om{\'e}trique des m{\'e}thodes
de calcul des valeurs propres. ({French}) [{Geometric}
presentation of methods for calculation of
eigenvalues]",
journal = j-NUM-MATH,
volume = "21",
number = "3",
pages = "223--233",
year = "1973",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F15",
MRnumber = "MR0329229 (48 \#7571)",
MRreviewer = "A. S. Householder",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/nummath.bib",
ZMnumber = "0255.65020",
acknowledgement = ack-nhfb,
classification = "B0290H (Linear algebra); C4140 (Linear algebra)",
classmath = "*65F15 Eigenvalues (numerical linear algebra)",
corpsource = "Univ. California, Berkeley, CA, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "calculation; convergence; convergence of numerical
methods; eigenvalues; eigenvalues and eigenfunctions;
eigenvectors; geometric presentation; matrices; matrix
algebra; methods",
language = "French",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Kahan:1974:ALA,
author = "W. Kahan and B. N. Parlett",
title = "An Analysis of {Lanczos} Algorithms for Symmetric
Matrices",
number = "ERL-M467",
institution = inst-ERL-CE-UCB,
address = inst-ERL-CE-UCB:adr,
year = "1974",
bibdate = "Mon Apr 25 18:24:02 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
URL = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
}
@Article{Parlett:1974:BRB,
author = "B. N. Parlett",
title = "Book Review: {{\booktitle{Large Sparse Sets of Linear
Equations (J. K. Reid, ed.); Sparse Matrices and Their
Applications}} (Donald J. Rose and Ralph A. Willoughby,
ed.)}",
journal = j-SIAM-REVIEW,
volume = "16",
number = "3",
pages = "396--398",
month = "????",
year = "1974",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1016066",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:07:02 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/16/3;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "July 1974",
}
@Article{Parlett:1974:BRH,
author = "Beresford N. Parlett",
title = "Book Review: {H. R. Schwarz, H. Rutishauser \& E.
Stiefel, translated by P. Hertelendy,
\booktitle{Numerical Analysis of Symmetric Matrices},
Prentice-Hall, Inc., Englewood Cliffs, N. J., 1973, xi
+ 276 pp., 24 cm.}",
journal = j-MATH-COMPUT,
volume = "28",
number = "125",
pages = "328--328",
month = jan,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Wed Aug 26 06:30:00 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib",
URL = "https://www.jstor.org/stable/2005845",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@TechReport{Parlett:1974:CFT,
author = "Beresford N. Parlett",
title = "Computation of Functions of Triangular Matrices",
type = "Memorandum",
number = "ERL-M481",
institution = inst-ERL-CE-UCB,
address = inst-ERL-CE-UCB:adr,
pages = "18",
month = nov,
year = "1974",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
}
@Article{Parlett:1974:RQI,
author = "B. N. Parlett",
title = "The {Rayleigh} Quotient Iteration and Some
Generalizations for Nonnormal Matrices",
journal = j-MATH-COMPUT,
volume = "28",
number = "127",
pages = "679--693",
month = jul,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F15",
MRnumber = "MR0405823 (53 \#9615)",
MRreviewer = "James H. Wilkinson",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
JSTOR database; Theory/Matrix.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib",
ZMnumber = "0293.65023",
acknowledgement = ack-nhfb,
classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)",
classmath = "*65F15 Eigenvalues (numerical linear algebra) 15A18
Eigenvalues of matrices, etc",
corpsource = "Univ. California, Berkeley, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "eigenvector; generalizations; iterative methods; local
convergence; matrices; matrix algebra; nonnormal;
Rayleigh Quotient Iteration",
kwds = "nla, eig, Rayleigh quotient, nonnormal matrix",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Chan:1975:PCC,
author = "Sai-Pak Chan and R. Feldman and Beresford N. Parlett",
title = "A program to compute the condition numbers of matrix
eigenvalues without computing eigenvectors",
type = "Memorandum",
number = "ERL-M517",
institution = inst-ERL-CE-UCB,
address = inst-ERL-CE-UCB:adr,
pages = "44",
year = "1975",
bibdate = "Fri Nov 11 05:22:23 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Parlett:1975:ICC,
author = "B. N. Parlett and Y. Wang",
title = "The Influence of the Compiler on the Cost of
Mathematical Software{}\emdash in Particular on the
Cost of Triangular Factorization",
journal = j-TOMS,
volume = "1",
number = "1",
pages = "35--46",
month = mar,
year = "1975",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355626.355633",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
ZMnumber = "0312.68017",
acknowledgement = ack-nhfb,
classmath = "*68N01 General",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
keywords = "cs; lud; nla; software",
}
@TechReport{Parlett:1975:PCR,
author = "Beresford N. Parlett and R. Feldman",
title = "A program to compute the real {Schur} Form of a real
square matrix",
type = "Memorandum",
number = "ERL-M526",
institution = inst-ERL-CE-UCB,
address = inst-ERL-CE-UCB:adr,
pages = "28",
year = "1975",
bibdate = "Fri Nov 11 05:21:27 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Bunch:1976:DSM,
author = "James R. Bunch and Linda Kaufman and Beresford N.
Parlett",
title = "Decomposition of a Symmetric Matrix",
journal = j-NUM-MATH,
volume = "27",
number = "1",
pages = "95--109",
year = "1976",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01399088",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
Theory/Matrix.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
ZMnumber = "0342.65026",
acknowledgement = ack-nhfb,
classification = "B0290H (Linear algebra); C4140 (Linear algebra)",
classmath = "*65F35 Matrix norms, etc. (numerical linear algebra)
68W99 None of the above, but in this section",
corpsource = "Dept. of Math., Univ. of California, San Diego, CA,
USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "Cholesky; indefinite system; inertia; linear
equations; linear system; lud; matrix algebra; nla;
permutation matrix; symmetric matrix; triangular
factorisation",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Kahan:1976:HFS,
author = "W. Kahan and B. N. Parlett",
title = "How far should you go with the {Lanczos} process?",
crossref = "Bunch:1976:SMC",
pages = "131--144",
year = "1976",
MRclass = "65F15",
MRnumber = "MR0458836 (56 \#17036)",
MRreviewer = "Michael S. Martin",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
ZMnumber = "0345.65017",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 15A18
Eigenvalues of matrices, etc",
}
@Article{Parlett:1976:RAE,
author = "B. N. Parlett",
title = "A Recurrence Among the Elements of Functions of
Triangular Matrices",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "14",
number = "2",
pages = "117--121",
month = "????",
year = "1976",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(76)90018-5",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F30",
MRnumber = "MR0448846 (56 \#7151)",
MRreviewer = "C. G. Cullen",
bibdate = "Tue Feb 16 18:49:27 MST 2016",
bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/linala1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0024379576900185",
ZMnumber = "0353.65027",
acknowledgement = ack-nhfb,
classmath = "*65F99 Numerical linear algebra 15A15 Special matrix
functions",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
keywords = "nla, matrix function, triangular matrix",
}
@TechReport{Parlett:1976:RES,
author = "Beresford N. Parlett",
title = "Roundoff error in the solution of finite element
systems",
type = "Report",
number = "????",
institution = inst-ERL-CE-UCB,
address = inst-ERL-CE-UCB:adr,
pages = "21",
year = "1976",
bibdate = "Fri Nov 11 05:48:59 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Chan:1977:APC,
author = "S. P. Chan and R. Feldman and B. N. Parlett",
title = "{Algorithm 517}: {A} Program for Computing the
Condition Numbers of Matrix Eigenvalues Without
Computing Eigenvectors [{F2}]",
journal = j-TOMS,
volume = "3",
number = "2",
pages = "186--203",
month = jun,
year = "1977",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355732.355741",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Aug 27 22:34:22 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
ZMnumber = "0353.65026",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F35
Matrix norms, etc. (numerical linear algebra)",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
keywords = "condition estimation; eig; nla; nonsymmetric matrix;
pert; software",
}
@TechReport{Hoffman:1977:NPG,
author = "W. Hoffman and Beresford N. Parlett",
title = "A new proof of global convergence for the tridiagonal
{QL} algorithm",
type = "Memorandum",
number = "UCB/ERL M77/48",
institution = inst-ERL-CE-UCB,
address = inst-ERL-CE-UCB:adr,
pages = "18",
day = "7",
month = jul,
year = "1977",
bibdate = "Fri Nov 11 05:18:34 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Kahan:1977:CYC,
author = "W. M. Kahan and B. N. Parlett",
title = "Can You Count on Your Calculator?",
type = "Memorandum",
number = "UCB/ERL M77/21",
institution = inst-ERL-CE-UCB,
address = inst-ERL-CE-UCB:adr,
pages = "ii + 28",
day = "6",
month = apr,
year = "1977",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
note = "German Transl. Published In: Jahrbuch {\"U}berblicke
Mathematik 1978, Ed. by B. Fuchssteiner and others,
Bibliographisches Institut, Mannheim-Wien-Z{\"u}rich,
199--216, 1978",
URL = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
acknowledgement = ack-jr,
}
@Article{Parlett:1977:ICC,
author = "B. N. Parlett and Y. Wang",
title = "The influence of the compiler on the cost of
mathematical software---in particular on the cost of
triangular factorization",
journal = j-TOMS,
volume = "1",
pages = "35--46",
year = "1977",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
}
@TechReport{Parlett:1977:LAI,
author = "B. N. Parlett and D. S. Scott",
title = "The {Lanczos} algorithm with implicit deflation",
type = "Memorandum",
number = "UCB/ERL M77/70",
institution = inst-ERL-CE-UCB,
address = inst-ERL-CE-UCB:adr,
pages = "29",
day = "2",
month = dec,
year = "1977",
bibdate = "Fri Nov 11 05:16:39 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Parlett:1977:PNA,
author = "Beresford N. Parlett",
title = "Progress in numerical analysis",
type = "Memorandum",
number = "UCB/ERL M77/26",
institution = inst-ERL-CE-UCB,
address = inst-ERL-CE-UCB:adr,
pages = "30",
day = "13",
month = apr,
year = "1977",
bibdate = "Fri Nov 11 05:19:27 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Parlett:1977:PSD,
author = "Beresford N. Parlett",
title = "A program to swap diagonal blocks",
type = "Memorandum",
number = "UCB/ERL M77/66",
institution = inst-ERL-CE-UCB,
address = inst-ERL-CE-UCB:adr,
pages = "30",
day = "3",
month = nov,
year = "1977",
bibdate = "Fri Nov 11 05:17:40 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Parlett:1977:RES,
author = "Beresford Parlett",
title = "Roundoff error in the solution of finite element
systems",
crossref = "Bathe:1977:FCA",
pages = "632--654",
year = "1977",
MRclass = "65G05 (65N30)",
MRnumber = "MR0488692 (58 \#8211)",
MRreviewer = "Peter Lancaster",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Hoffmann:1978:NPG,
author = "W. Hoffmann and B. N. Parlett",
title = "A new proof of global convergence for the tridiagonal
{QL} algorithm",
journal = j-SIAM-J-NUMER-ANAL,
volume = "15",
number = "5",
pages = "929--937",
month = oct,
year = "1978",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0715060",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F15",
MRnumber = "MR507555 (80a:65075)",
MRreviewer = "S. F. McCormick",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
JSTOR database",
URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib",
ZMnumber = "0402.65019",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "Eigenpairs of Matrices; Global Convergence; Ql
Algorithm; Wilkinson'S Shift",
}
@TechReport{Kahan:1978:HFS,
author = "W. Kahan and B. N. Parlett",
title = "How far should you go with the {Lanczos} process?",
type = "Memorandum",
number = "UCB/ERL M78/48",
institution = inst-ERL-CE-UCB,
address = inst-ERL-CE-UCB:adr,
pages = "16",
year = "1978",
bibdate = "Fri Nov 11 05:15:08 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Kahan:1978:KSI,
author = "W. Kahan and B. N. Parlett",
title = "{K{\"o}nnen Sie sich auf Ihren Rechner verlassen?}
({German}) [Can you count on your calculator?]",
journal = "{Jahrbuch {\"U}berblicke Mathematik}",
volume = "??",
pages = "199--216",
year = "1978",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "0397.65081",
acknowledgement = ack-nhfb,
classmath = "*65Y99 Computer aspects of numerical algorithms 65D20
Computation of special functions 00A99 Miscellaneous
topics in general mathematics",
keywords = "Automated Algorithms; Error of Computation; Pocket
Calculator",
language = "German",
}
@Article{Parlett:1978:NPG,
author = "B. N. Parlett and W. Hoffman",
title = "New Proof of Global Convergence for Tridiagonal {$ Q L
$} Algorithm",
journal = j-SIAM-REVIEW,
volume = "20",
number = "3",
pages = "632--632",
month = "????",
year = "1978",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Parlett:1978:PNA,
author = "Beresford N. Parlett",
title = "Progress in Numerical Analysis",
journal = j-SIAM-REVIEW,
volume = "20",
number = "3",
pages = "443--456",
year = "1978",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1020066",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65-02",
MRnumber = "MR0494816 (58 \#13601)",
bibdate = "Sat Mar 29 09:52:53 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/20/3;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
ZMnumber = "0408.65002",
acknowledgement = ack-nhfb,
classmath = "*65-02 Research monographs (numerical analysis) 68Nxx
Software 00A06 Mathematics for non-mathematicians",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "Iterative Methods for Linear Equations; Library
Functions; Matrix Computations; Minimization; Numerical
Methods; Ordinary Differential Equations; Packages;
Program Libraries; Programming Languages; Progress in
Numerical Analysis; Quadrature; Small Matrix
Computations; Stored Matrices; Theoretical Treatment",
onlinedate = "July 1978",
}
@Article{Gear:1979:NCR,
author = "C. W. Gear and J. M. Ortega and B. Parlett and J. R.
Rice and M. Schultz and L. F. Shampine and P. Wolfe",
title = "Numerical Computation: {A} Report on Past, Present,
and Future Research",
journal = j-SIGNUM,
volume = "14",
number = "si-1",
pages = "1--48",
month = feb,
year = "1979",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1057517.1057518",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Sat Dec 29 14:38:45 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/signum.bib",
note = "Also published in \cite{Gear:1980:NCR}.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690",
}
@Article{Parlett:1979:BRH,
author = "Beresford N. Parlett",
title = "Book Review: {Herman H. Goldstine, {\em A history of
numerical analysis from the 16th through the 19th
century}. Studies in the History of Mathematics and
Physical Sciences 2, Springer-Verlag, New York,
Heidelberg, Berlin, 1977, xiv + 348 pp., \$24.80}",
journal = j-BULL-AMS-N-S,
volume = "1",
number = "2",
pages = "388--390",
month = "????",
year = "1979",
CODEN = "BAMOAD",
ISSN = "0273-0979 (print), 1088-9485 (electronic)",
ISSN-L = "0273-0979",
bibdate = "Wed Jun 08 12:29:41 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://projecteuclid.org/euclid.bams/1183544086",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society (new series)",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
}
@Article{Parlett:1979:LAS,
author = "B. N. Parlett and D. S. Scott",
title = "The {L{\'a}nczos} Algorithm with Selective
Orthogonalization",
journal = j-MATH-COMPUT,
volume = "33",
number = "145",
pages = "217--238",
month = jan,
year = "1979",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2006037",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F15",
MRnumber = "MR514820 (80c:65090)",
MRreviewer = "Colette Lebaud",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
JSTOR database; Theory/Matrix.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib",
ZMnumber = "0405.65015",
acknowledgement = ack-nhfb,
classcodes = "C4140 (Linear algebra)",
classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F25
Orthogonalization (numerical linear algebra)",
corpsource = "Univ. California, Berkeley, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "eigenvalues; eigenvalues and eigenfunctions;
eigenvectors; Eigenvectors; extreme; Extreme
Eigenvalues of a Large Symmetric Matrix; independence;
Lanczos algorithm; Lanczos Process; large symmetric
matrix; linear; Modification; selective
orthogonalization; Selective Orthogonalization",
kwds = "nla, eig, Lanczos Algorithm, orthogonalization",
treatment = "T Theoretical or Mathematical",
}
@Article{Rice:1979:NCN,
author = "J. R. Rice and C. W. Gear and J. Ortega and B. Parlett
and M. Schultz and L. F. Shampine and P. Wolfe and J.
F. Traub",
title = "Numerical computation: its nature and research
directions",
journal = j-SIGNUM,
volume = "14",
number = "3S (Special issue)",
pages = "1--48",
month = feb,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:06 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/signum.bib",
acknowledgement = ack-nhfb,
classcodes = "C1180 (Optimisation techniques); C4140 (Linear
algebra); C4170 (Differential equations)",
corpsource = "Purdue Univ., Lafayette, IN, USA",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690",
keywords = "curves; graphics; linear algebra; mathematical
software; nonlinear equations; numerical computation;
optimisation; optimization; ordinary differential
equations; partial differential equations; surfaces",
treatment = "G General Review",
}
@InCollection{Gear:1980:NCR,
author = "C. W. Gear and J. M. Ortega and B. Parlett and J. R.
Rice and M. Schultz and L. F. Shampine and P. Wolfe",
title = "Numerical Computation: {A} Report on Past, Present,
and Future Research",
crossref = "Arden:1980:WCA",
pages = "51--136",
year = "1980",
bibdate = "Sat Dec 29 14:40:07 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/signum.bib",
note = "Also published in \cite{Gear:1979:NCR}.",
acknowledgement = ack-nhfb,
}
@TechReport{Nour-Omid:1980:LVS,
author = "Bahram Nour-Omid and Beresford N. Parlett and Robert
L. Taylor",
title = "{Lanczos} versus subspace iteration for solution of
eigenvalue problems",
type = "Report",
number = "UC SESM 80-8",
institution = "Structural Engineering Laboratory, University of
California, Berkeley",
address = "Berkeley, CA, USA",
pages = "16",
year = "1980",
bibdate = "Fri Nov 11 05:12:33 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Parlett:1980:HSK,
author = "B. N. Parlett",
title = "How to solve {$ (K - \lambda M)z = 0 $} for large
{$K$} and {$M$}",
crossref = "Absi:1980:NME",
volume = "1",
pages = "97--106",
year = "1980",
MRclass = "65F15",
MRnumber = "MR660669 (83g:65044)",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "0455.65027",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra)",
keywords = "comparison; Lanczos algorithm; large eigenvalue
problems; numerical example; subspace iteration
method",
}
@Article{Parlett:1980:NLL,
author = "B. N. Parlett",
title = "A new look at the {Lanczos} algorithm for solving
symmetric systems of linear equations",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "29",
pages = "323--346",
year = "1980",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(80)90248-7",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F10",
MRnumber = "MR562767 (83e:65064)",
bibdate = "Wed Jan 22 17:57:24 MST 1997",
bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/linala1980.bib",
ZMnumber = "0431.65016",
acknowledgement = ack-nhfb,
classmath = "*65F10 Iterative methods for linear systems 65-04
Machine computation, programs (numerical analysis)
65F15 Eigenvalues (numerical linear algebra)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "conjugate gradient algorithm; implementation; Lanczos
algorithm; large sparse symmetric matrix; linear
system; selective orthogonalization;
tridiagonalization",
}
@Book{Parlett:1980:SEP,
author = "Beresford N. Parlett",
title = "The Symmetric Eigenvalue Problem",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xix + 348",
year = "1980",
ISBN = "0-13-880047-2",
ISBN-13 = "978-0-13-880047-5",
LCCN = "QA188 .P3",
MRclass = "65F15 (15A18)",
MRnumber = "MR570116 (81j:65063)",
MRreviewer = "Robert Todd Gregory",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/all_brec.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Prentice-Hall Series in Computational Mathematics",
series = "Series in Computational Mathematics",
ZMnumber = "0431.65017",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 15A18
Eigenvalues of matrices, etc. 15A57 Other types of
matrices 15-02 Research monographs (linear algebra)
65-02 Research monographs (numerical analysis) 15A23
Factorization of matrices 65F25 Orthogonalization
(numerical linear algebra)",
keywords = "bandmatrices; bounds for eigenvalues; eigenvalues;
generalized eigenvalue problem; Krylov sequences;
localization of eigenvalues; orthogonal
transformations; tridiagonal matrices; vector
iteration",
tableofcontents = "Notation: Inside Front Cover \\
Preface / xii \\
Introduction / xv \\
1: Basic Facts about Self-Adjoint Matrices / 1 \\
2: Tasks, Obstacles, and Aids / 17 \\
3: Counting Eigenvalues / 38 \\
4: Simple Vector Iterations / 58 \\
5: Deflation / 81 \\
6: Useful Orthogonal Matrices (Tools of the Trade) / 87
\\
7: Tridiagonal Form / 111 \\
8: The $QL$ and $QR$ Algorithms / 139 \\
9: Jacobi Methods / 174 \\
10: Eigenvalue Bounds / 185 \\
11: Approximations from a Subspace / 209 \\
12: Krylov Subspaces / 235 \\
13: Lanczos Algorithms / 257 \\
14: Subspace Iteration / 288 \\
15: The General Linear Eigenvalue Problem / 302 \\
A Appendix: Rank One and Elementary Matrices / 329 \\
B: Appendix: Chebyshev Polynomials / 331 \\
References / 334 \\
Annotated Bibliography / 341 \\
Author and Subject Index / 345",
tableofcontents = "Notation: Inside Front Cover \\
Preface / xii \\
Introduction / xv \\
1: Basic Facts about Self-Adjoint Matrices / 1 \\
1-1 Introduction / 1 \\
1-2 Euclidean Space / 1 \\
1-3 Eigenvalues / 5 \\
l-4 Self-Adjoint Matrices / 6 \\
1-5 Quadratic Forms / 10 \\
1-6 Matrix Norms / 13 \\
1-7 The Generalized Eigenvalue Problem / 16 \\
2: Tasks, Obstacles, and Aids / 17 \\
2-1 What is Small? What is Large? / 17 \\
2-2 Tasks / 19 \\
2-3 Conflicting Requirements / 20 \\
2-4 Finite Precision Arithmetic / 23 \\
2-5 Cancellation / 25 \\
2-6 Inner Product Analysis / 29 \\
2-7 Can Small Eigenvalues Be Found with Low Relative
Error? / 33 \\
2-8 Available Programs / 34 \\
2-9 Representative Timings / 36 \\
2-10 Alternative Computer Architecture / 37 \\
3: Counting Eigenvalues / 38 \\
3-1 Triangular Factorization / 38 \\
3-2 Error Analysis of Triangular Factorization / 43 \\
3-3 Slicing the Spectrum / 46 \\
3-4 Relation to Sturm Sequences / 52 \\
3-5 Bisection and Secant Methods / 53 \\
3-6 Hidden Eigenvalues / 55 \\
3-7 The Characteristic Polynomial / 57 \\
4: Simple Vector Iterations / 58 \\
4-1 Eigenvectors of Rank One Matrices / 58 \\
4-2 Direct and Inverse Iteration / 59 \\
4-3 Advantages of an Ill Conditioned System / 65 \\
4-4 Convergence and Orthogonality / 68 \\
4-5 Simple Error Bounds / 69 \\
4-6 The Rayleigh Quotient Iteration / 70 \\
4-7 Local Convergence / 72 \\
4-8 Monotonic Residuals / 75 \\
*4-9 Global Convergence / 76 \\
5: Deflation / 81 \\
5-1 Deflation by Subtraction / 81 \\
5-2 Deflation by Restriction / 84 \\
5-3 Deflation by Similarity Transformations / 85 \\
6: Useful Orthogonal Matrices (Tools of the Trade) / 87
\\
6-1 Orthogonals are Important / 87 \\
6-2 Permutations / 88 \\
6-3 Reflections (or Symmetries) / 90 \\
6-4 Plane Rotations / 92 \\
6-5 Error Propagation in a Sequence of Orthogonal
Congruences / 94 \\
6-6 Backward Error Analysis / 97 \\
6-7 The $QR$ Factorization and Gram--Schmidt / 98 \\
*6-8 Fast Scaled Rotations / 100 \\
*6-9 Orthogonalization in the Face of Roundoff / 105
\\
7: Tridiagonal Form / 111 \\
7-1 Introduction / 111 \\
7-2 Uniqueness of Reduction / 112 \\
7-3 Minimizing Characteristics / 114 \\
7-4 Explicit Reduction of a Full Matrix / 117 \\
7-5 Reduction of a Banded Matrix / 120 \\
7-6 Irrelevant Instability / 122 \\
7-7 Eigenvalues are Simple / 124 \\
7-8 Orthogonal Polynomials / 125 \\
7-9 Eigenvectors of T / 127 \\
7-10 Sturm Sequences / 131 \\
7-11 When to Neglect an Off-Diagonal Element / 133 \\
7-12 Inverse Eigenvalue Problems / 136 \\
8: The $QL$ and $QR$ Algorithms / 139 \\
8-1 Introduction / 139 \\
8-2 The $QL$ Transformation / 140 \\
8-3 Preservation of Bandwidth / 141 \\
8-4 Relation between $QL$ and $QR$ / 142 \\
8-5 $QL$, the Power Method, and Inverse Iteration / 144
\\
8-6 Convergence of the Basic $QL$ Algorithm / 145 \\
8-7 The Rayleigh Quotient Shift / 146 \\
8-8 The Off-Diagonal Elements / 148 \\
8-9 Residual Bounds Using Wilkinson's Shift / 149 \\
8-10 Tridiagonal $QL$ Always Converges / 151 \\
8-11 Asymptotic Convergence Rates / 154 \\
8-12 Tridiagonal $QL$ with Explicit Shift / 157 \\
8-13 Chasing the Bulge / 159 \\
8-14 Shifts for all Seasons / 162 \\
8-15 Casting Out Square Roots / 164 \\
8-16 $QL$ for Banded Matrices / 170 \\
9: Jacobi Methods / 174 \\
9-1 Rotation in the Plane / 174 \\
9-2 Jacobi Rotations / 176 \\
9-3 Convergence / 178 \\
9-4 Various Strategies / 180 \\
9-5 Ultimate Quadratic Convergence / 181 \\
9-6 Assessment of Jacobi Methods / 183 \\
10: Eigenvalue Bounds / 185 \\
10-1 Cauchy's Interlace Theorem / 186 \\
10-2 The Minimax Characterization / 188 \\
10-3 The Monotonicity Theorem / 191 \\
10-4 The Residual Interlace Theorem / 194 \\
10-5 Lehmann's Optimal Intervals / 198 \\
10-6 Use of Bounds on the Missing Submatrix / 203 \\
10-7 Use of Gaps in A's Spectrum / 206 \\
11: Approximations from a Subspace / 209 \\
11-1 Subspaces and Their Representation / 209 \\
11-2 Invariant Subspaces / 211 \\
11-3 The Rayleigh--Ritz Procedure / 213 \\
11-4 Optimality / 215 \\
11-5 Residual Bounds on Clustered Ritz Values / 218 \\
11-6 No Residual Bounds on Ritz Vectors / 221 \\
11-7 Gaps in the Spectrum / 221 \\
11-8 Condensing the Residual / 225 \\
*11-9 A Priori Bounds for Interior Ritz Approximations
/ 226 \\
*11-10 Nonorthogonal Bases / 229 \\
*11-11 An Extension Theorem / 231 \\
12: Krylov Subspaces / 235 \\
12-1 Introduction / 235 \\
12-2 Basic Properties / 237 \\
12-3 Representation by Polynomials / 239 \\
12-4 The Error Bounds of Kaniel and Saad / 242 \\
12-5 Comparison with the Power Method / 250 \\
12-6 Partial Reduction to Tridiagonal Form / 252 \\
13: Lanczos Algorithms / 257 \\
13-1 Krylov + Rayleigh--Ritz = Lanczos / 257 \\
13-2 Assessing Accuracy / 260 \\
13-3 The Effects of Finite Precision Arithmetic / 262
\\
13-4 Paige's Theorem / 264 \\
13-5 An Alternative Formula for 13 1 / 268 \\
13-6 Convergence=> Loss of Orthogonality / 270 \\
13-7 Maintaining Orthogonality / 272 \\
*13-8 Selective Orthogonalization / 275 \\
13-9 Analysis of Selective Orthogonalization / 279 \\
*13-10 Band (or Block) Lanczos / 284 \\
14: Subspace Iteration / 288 \\
14-1 Introduction / 288 \\
14-2 Implementations / 289 \\
14-3 Improvements / 293 \\
*14-4 Convergence / 296 \\
14-5 Sectioning / 299 \\
15: The General Linear Eigenvalue Problem / 302 \\
15-1 Introduction / 302 \\
15-2 Symmetry is Not Enough / 303 \\
15-3 Simultaneous Diagonalization of Two Quadratic
Forms / 306 \\
15-4 Explicit Reduction to Standard Form / 309 \\
*15-5 The Fix--Heiberger Reduction / 311 \\
15-6 The $QZ$ Algorithm / 314 \\
15-7 Jacobi Generalized / 315 \\
15-8 Implicit Reduction to Standard Form / 316 \\
15-9 Simple Vector Iterations / 317 \\
15-10 Rayleigh Ritz Approximations / 321 \\
15-11 Lanczos Algorithms / 323 \\
15-12 Subspace Iteration / 325 \\
15-13 Practical Considerations / 327 \\
A Appendix: Rank One and Elementary Matrices / 329 \\
B: Appendix: Chebyshev Polynomials / 331 \\
References / 334 \\
Annotated Bibliography / 341 \\
Author and Subject Index / 345",
}
@Article{Berman:1981:DSO,
author = "A. Berman and B. N. Parlett and R. J. Plemmons",
title = "Diagonal scaling to an orthogonal matrix",
journal = j-SIAM-J-ALG-DISC-METH,
volume = "2",
number = "1",
pages = "57--65",
month = mar,
year = "1981",
CODEN = "SJAMDU",
DOI = "https://doi.org/10.1137/0602008",
ISSN = "0196-5212 (print), 2168-345X (electronic)",
ISSN-L = "0196-5212",
MRclass = "65F35 (15A21)",
MRnumber = "MR604511 (82d:65040)",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/siamjalgdiscmeth.bib",
ZMnumber = "0498.65024",
acknowledgement = ack-nhfb,
classification = "C4140 (Linear algebra); C4170 (Differential
equations)",
classmath = "*65F35 Matrix norms, etc. (numerical linear algebra)
35L45 First order hyperbolic systems, initial value
problems",
corpsource = "Dept. of Math., Technion-Israel Inst. of Technol.,
Haifa, Israel",
fjournal = "Society for Industrial and Applied Mathematics.
Journal on Algebraic and Discrete Methods",
journal-URL = "http://epubs.siam.org/loi/sjamdu",
keywords = "algorithm; diagonal matrix; diagonal scaling; energy
conserving norm; Hadamard quotient; hyperbolic
equations; matrix algebra; orthogonal matrix; partial
differential equation; partial differential equations;
positive matrix; scaling factors",
treatment = "A Application; T Theoretical or Mathematical",
}
@TechReport{Parlett:1981:ACT,
author = "Beresford N. Parlett",
title = "Analytic complexity theory and the solution of {$ A X
= b $}",
type = "Technical Report",
number = "PAM-40",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = jun,
year = "1981",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@TechReport{Parlett:1981:FSF,
author = "Beresford N. Parlett and B. Nour-Omid and M. R. Li",
title = "A fast solver free of fill-in for finite element
problems",
type = "Technical Report",
number = "PAM-42",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = jun,
year = "1981",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@TechReport{Parlett:1981:HSK,
author = "Beresford N. Parlett",
title = "How to solve {$ (K - \lambda M)z = 0 $} for large
{$K$} and {$M$}",
type = "Technical Report",
number = "PAM-39",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = jun,
year = "1981",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@TechReport{Parlett:1981:LAL,
author = "Beresford N. Parlett and D. Taylor",
title = "A look-ahead {Lanczos} algorithm for unsymmetric
matrices",
type = "Technical Report",
number = "PAM-43",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = jun,
year = "1981",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Parlett:1981:BRBa,
author = "B. Parlett and R. Tolimieri",
title = "Book Review: {{\booktitle{A Matrix Eigenvalue
Problem}} (G. Efroymson, A. Steger and S. Steinberg)}",
journal = j-SIAM-REVIEW,
volume = "23",
number = "1",
pages = "105--105",
month = "????",
year = "1981",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1023014",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:53:16 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/23/1;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1981",
}
@Article{Parlett:1981:BRBb,
author = "B. N. Parlett",
title = "Book Review: {{\booktitle{{LINPACK} Users' Guide}} (J.
J. Dongarra, J. R. Bunch, C. B. Moler and G. W.
Stewart)}",
journal = j-SIAM-REVIEW,
volume = "23",
number = "1",
pages = "126--128",
month = "????",
year = "1981",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1023033",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:53:16 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/23/1;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1981",
}
@TechReport{Parlett:1981:MSD,
author = "Beresford N. Parlett and T. L. Landis",
title = "Methods for scaling to doubly stochastic form",
type = "Technical Report",
number = "PAM-44",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = jun,
year = "1981",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Parlett:1981:PNA,
author = "Beresford Parlett",
title = "Progress in numerical analysis",
journal = "Yingyong Shuxue yu Jisuan Shuxue",
volume = "3",
pages = "1--10",
year = "1981",
MRclass = "65-02",
MRnumber = "MR656304 (83d:65005)",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "Translated from the English by Wu Mu",
acknowledgement = ack-nhfb,
fjournal = "Yingyong Shuxue yu Jisuan Shuxue. Applied Mathematics
and Computational Mathematics",
}
@Article{Parlett:1981:TPL,
author = "B. N. Parlett and J. K. Reid",
title = "Tracking the Progress of the {Lanczos} Algorithm for
Large Symmetric Eigenproblems",
journal = j-IMA-J-NUMER-ANAL,
volume = "1",
number = "2",
pages = "135--155",
year = "1981",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/1.2.135",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65F15",
MRnumber = "MR616327 (82e:65039)",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
MathSciNet database",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib",
ZMnumber = "0474.65022",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 65Y99
Computer aspects of numerical algorithms",
fjournal = "IMA (Institute of Mathematics and its Applications).
Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "interpolation procedures; Lanczos algorithm; large
symmetric matrix",
}
@Article{Kahan:1982:RBA,
author = "W. Kahan and B. N. Parlett and E. Jiang",
title = "Residual Bounds on Approximate Eigensystems of
Nonnormal Matrices",
journal = j-SIAM-J-NUMER-ANAL,
volume = "19",
number = "3",
pages = "470--484",
month = jun,
year = "1982",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0719030",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F15 (65F35)",
MRnumber = "MR656463 (83h:65050)",
MRreviewer = "William W. Hager",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database",
URL = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Li:1982:FSF,
author = "M. R. Li and B. Nour-Omid and B. N. Parlett",
title = "A Fast Solver Free of Fill-in for Finite-element
Problems",
journal = j-SIAM-J-NUMER-ANAL,
volume = "19",
number = "6",
pages = "1233--1242",
month = dec,
year = "1982",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0719088",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F10 (65F05 65N30)",
MRnumber = "MR679662 (84b:65031)",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
JSTOR database",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@TechReport{Parlett:1982:AUE,
author = "Beresford N. Parlett and B. Nour-Omid",
title = "An algorithm to update eigenvalues of a growing
symmetric tridiagonal matrix",
type = "Technical Report",
number = "PAM-104",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = oct,
year = "1982",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@Article{Parlett:1982:ELE,
author = "B. N. Parlett and H. Simon and L. M. Stringer",
title = "On Estimating the Largest Eigenvalue with the
{L{\'a}nczos} Algorithm",
journal = j-MATH-COMPUT,
volume = "38",
number = "157",
pages = "153--165",
month = jan,
year = "1982",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2007471",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F15",
MRnumber = "MR637293 (82m:65033)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
JSTOR database; Theory/Matrix.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib",
acknowledgement = ack-nhfb,
classcodes = "B0210 (Algebra); B0290H (Linear algebra); C1110
(Algebra); C4140 (Linear algebra)",
corpsource = "Dept. of Math., Univ. of California, Berkeley, CA,
USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "definite matrix; eigenvalue; eigenvalues and
eigenfunctions; Lanczos algorithm; large matrices;
matrix algebra; methods; misconvergence; numerical;
positive",
kwds = "nla, eig, Lanczos algorithm",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Parlett:1982:EP,
author = "Beresford N. Parlett and B. Nour-Omid",
title = "Element preconditioning",
type = "Technical Report",
number = "PAM-103",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = oct,
year = "1982",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@Article{Parlett:1982:MSD,
author = "B. N. Parlett and T. L. Landis",
title = "Methods for Scaling to Doubly Stochastic Form",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "48",
number = "??",
pages = "53--79",
year = "1982",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(82)90099-4",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A12 (15A51 65F35)",
MRnumber = "MR683210 (84b:15007)",
MRreviewer = "Ray C. Shiflett",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/linala1980.bib",
ZMnumber = "0508.15003",
acknowledgement = ack-nhfb,
classmath = "*15A12 Conditioning of matrices 65F35 Matrix norms,
etc. (numerical linear algebra) 15A51 Stochastic
matrices",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "convergence theorem; doubly stochastic matrices; nla,
eig, nonnegative matrix, doubly stochastic matrix;
scaling",
xxtitle = "Methods for Scaling to Double Stochastic Form",
}
@InProceedings{Parlett:1982:TMS,
author = "B. N. Parlett",
title = "Two monitoring schemes for the {Lanczos} algorithm",
crossref = "Glowinski:1982:CMA",
year = "1982",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "0499.65017",
acknowledgement = ack-nhfb,
classmath = "*65F10 Iterative methods for linear systems 65F15
Eigenvalues (numerical linear algebra) 65F25
Orthogonalization (numerical linear algebra)",
keywords = "Lanczos algorithm; monitoring schemes; symmetric
matrices",
}
@Article{Parlett:1982:WFT,
author = "B. N. Parlett",
title = "{Winograd}'s {Fourier} transform via circulants",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "45",
number = "??",
pages = "137--155",
year = "1982",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(82)90217-8",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65T05 (68C25)",
MRnumber = "MR660985 (83f:65222)",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/linala1980.bib",
ZMnumber = "0515.65099",
acknowledgement = ack-nhfb,
classmath = "*65T40 Trigonometric approximation and interpolation
65F30 Other matrix algorithms 15A23 Factorization of
matrices 42A15 Trigonometric interpolation",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "associated circulant matrices; discrete Fourier
transform; eigenvalue-eigenvector decomposition; na,
nla, eig, fft, fast algorithm, circulant matrix; real
arithmetic; Winograd's algorithm",
}
@TechReport{McCurdy:1983:ACD,
author = "A. McCurdy and K. C. Ng and Beresford N. Parlett",
title = "Accurate computation of divided differences of the
exponential function",
type = "Technical Report",
number = "PAM-160",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = jun,
year = "1983",
bibdate = "Fri Nov 11 09:06:19 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Nour-Omid:1983:LVS,
author = "Bahram Nour-Omid and Beresford N. Parlett and Robert
L. Taylor",
title = "{Lanczos} versus subspace iteration for solution of
eigenvalue problems",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "19",
number = "6",
pages = "859--871",
year = "1983",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620190608",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "0521.65024",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 74S05
Finite element methods",
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
keywords = "comparison of methods; Lanczos algorithm; large eigen
problems; subspace iteration",
}
@Article{Nour-Omid:1983:NLM,
author = "Bahram Nour-Omid and Beresford N. Parlett and Robert
L. Taylor",
title = "A {Newton--Lanczos} method for solution of nonlinear
finite element equations",
journal = j-COMP-STRUCTURES,
volume = "16",
number = "1--4",
pages = "241--252",
year = "1983",
CODEN = "CMSTCJ",
DOI = "https://doi.org/10.1016/0045-7949(83)90164-5",
ISSN = "0045-7949 (print), 1879-2243 (electronic)",
ISSN-L = "0045-7949",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "0499.73058",
acknowledgement = ack-nhfb,
classmath = "*74S05 Finite element methods 65H10 Systems of
nonlinear equations (numerical methods)",
fjournal = "Computers and Structures",
journal-URL = "http://www.sciencedirect.com/science/journal/00457949",
keywords = "asymptotic cost estimates; initial-boundary value
problems; Lanczos algorithm; linearized set of
equations; local convergence characteristics; modified
Newton method; Newton's method; Newton--Lanczos method;
partial reorthogonalization; quasi-Newton; rate of
convergence; selective orthogonalization; varied from
superlinear to quadratic by controlling certain
tolerance",
}
@TechReport{Parlett:1983:EMS,
author = "Beresford N. Parlett and H. Wu and W. D. Wu",
title = "Eigenvector matrices of symmetric tridiagonals",
type = "Technical Report",
number = "PAM-174",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = aug,
year = "1983",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@Book{Parlett:1983:SPS,
author = "Beresford N. Parlett",
title = "Simmetrichnaya problema sobstvennykh znachenii.
Chislennye metody ({Russian}) [The symmetric eigenvalue
problem. Numerical methods]",
publisher = pub-EDITORIAL-MIR,
address = pub-EDITORIAL-MIR:adr,
pages = "384",
year = "1983",
MRclass = "65-02 (15A18 65F15)",
MRnumber = "MR702348 (85b:65003)",
MRreviewer = "K. Moszy{\'n}ski",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "Translated from the English by Kh. D. Ikranov and Yu.
A. Kuznetsov.",
ZMnumber = "0524.65023",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 15A18
Eigenvalues of matrices, etc. 15-02 Research monographs
(linear algebra) 65-02 Research monographs (numerical
analysis) 15A23 Factorization of matrices 15A57 Other
types of matrices 65F25 Orthogonalization (numerical
linear algebra)",
keywords = "bandmatrices; bounds for eigenvalues; eigenvalues;
generalized eigenvalue problem; Krylov sequences;
localization of eigenvalues; orthogonal
transformations; tridiagonal matrices; vector
iteration",
language = "Russian",
}
@TechReport{Parlett:1983:SSE,
author = "Beresford N. Parlett",
title = "The software scene in the extraction of eigenvalues
from sparse matrices",
type = "Technical Report",
number = "PAM-132",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = mar,
year = "1983",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@TechReport{Parlett:1983:URE,
author = "Beresford N. Parlett and B. Nour-Omid",
title = "The use of refined error bound when updating
eigenvalues of tridiagonals",
type = "Technical Report",
number = "PAM-175",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = sep,
year = "1983",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@Article{McCurdy:1984:ACD,
author = "A. McCurdy and K. C. Ng and B. N. Parlett",
title = "Accurate Computation of Divided Differences of the
Exponential Function",
journal = j-MATH-COMPUT,
volume = "43",
number = "168",
pages = "501--528",
month = oct,
year = "1984",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2008291",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D20 (33A10 65G05)",
MRnumber = "MR758198 (86e:65029)",
MRreviewer = "S. Conde",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
JSTOR database",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@TechReport{Nour-Omid:1984:HIS,
author = "N. Nour-Omid and B. N. Parlett",
title = "How to implement the spectral transformation",
type = "Technical Report",
number = "PAM-224",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
pages = "????",
year = "1984",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Parlett:1984:ECM,
author = "Beresford N. Parlett and B. Nour-Omid and J. Natvig",
title = "Effect of the {CYBER 205} on methods for computing
natural frequencies of structures",
type = "Technical Report",
number = "PAM-218",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = apr,
year = "1984",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@Article{Parlett:1984:EMS,
author = "B. N. Parlett and W. D. Wu",
title = "Eigenvector matrices of symmetric tridiagonals",
journal = j-NUM-MATH,
volume = "44",
number = "1",
pages = "103--110",
month = jun,
year = "1984",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01389758",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F15",
MRnumber = "MR745089 (85h:65083)",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
classification = "B0210 (Algebra); C1110 (Algebra)",
corpsource = "Maths. Dept., Univ. of California, Berkeley, CA, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "eigenvalues and eigenfunctions; eigenvector matrix;
matrix algebra; symmetric tridiagonals",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Parlett:1984:LAL,
author = "B. N. Parlett and D. R. Taylor and Z. S. Liu",
title = "The look ahead {L{\'a}nczos} algorithm for large
unsymmetric eigenproblems",
crossref = "Glowinski:1984:CMA",
pages = "87--96",
year = "1984",
MRclass = "65F15",
MRnumber = "MR806772 (86k:65028)",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "0564.65021",
abstract = "A modification of the Lanczos algorithm for solving
eigenproblems for large unsymmetric matrices is
proposed. The algorithm is based on the idea of the
pivoting strategy introduced in the paper of {\it J. R.
Bunch} and {\it B. N. Parlett} [SIAM J. Numer. Anal. 8,
639-655 (1971; Zbl 0199.498)], which reduces the
occurrence of breakdown of the algorithm. Some details
of the modified algorithm are discussed",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra)",
keywords = "breakdown; Lanczos algorithm; large unsymmetric
matrices; pivoting strategy",
reviewer = "T. Reginska",
}
@Article{Parlett:1984:SSE,
author = "B. N. Parlett",
title = "The Software Scene in the Extraction of Eigenvalues
from Sparse Matrices",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "5",
number = "3",
pages = "590--604",
month = sep,
year = "1984",
CODEN = "SIJCD4",
DOI = "https://doi.org/10.1137/0905042",
ISSN = "0196-5204",
ISSN-L = "0196-5204",
MRclass = "65F15 (65F50)",
MRnumber = "MR754487 (85i:65048)",
MRreviewer = "David R. Kincaid",
bibdate = "Mon Mar 31 09:59:24 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fortran2.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib",
ZMnumber = "0573.65025",
acknowledgement = ack-nhfb,
classification = "C4140 (Linear algebra); C7310 (Mathematics
computing)",
classmath = "*65F15 Eigenvalues (numerical linear algebra) 15-04
Machine computation, programs (linear algebra) 65F50
Sparse matrices 68N99 Software",
conflocation = "Fairfield Glade, TN, USA; 25-27 Oct. 1982",
conftitle = "Sparse Matrix Symposium",
corpsource = "Dept. of Math., California Univ., Berkeley, CA, USA",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
keywords = "dense matrices; efficiency; eigenvalue programs;
eigenvalues; eigenvalues and eigenfunctions; EISPACK;
FORTRAN subroutines; Lanczos; Lanczos algorithm; matrix
algebra; reliability; software; software packages;
sparse matrices; subspace iteration; survey on
available software; users",
reviewer = "F. M{\'o}ricz",
sponsororg = "Army Res. Office; Office of Naval Res.; Oak Ridge Nat.
Lab",
treatment = "P Practical",
}
@Book{Cullum:1985:LAL,
author = "Jane K. Cullum and Ralph A. Willoughby",
title = "{Lanczos} Algorithms for Large Symmetric Eigenvalue
Computations, Volume {I} Theory",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "xiv + 273",
year = "1985",
ISBN = "0-8176-3058-9",
ISBN-13 = "978-0-8176-3058-4",
bibdate = "Mon Mar 6 15:34:09 GMT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
acknowledgement = ack-nhfb,
mynote = "Only skimmed. Tiny typeface. Emphasizes `local
orthogonality is enough' approach, as opposed to
Parlett \cite{Parlett:1980:SEP}'s `global orthogonality
is crucial'. They summarize Paige's error analysis but
don't (?) given any of their own.",
}
@Article{Nour-Omid:1985:EPU,
author = "B. Nour-Omid and B. N. Parlett",
title = "Element preconditioning using splitting techniques",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "6",
number = "3",
pages = "761--770",
month = jul,
year = "1985",
CODEN = "SIJCD4",
DOI = "https://doi.org/10.1137/0906051",
ISSN = "0196-5204",
ISSN-L = "0196-5204",
MRclass = "65F10 (49D07 65N20)",
MRnumber = "MR791197 (86h:65046)",
MRreviewer = "Beny Neta",
bibdate = "Mon Mar 31 09:59:33 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib;
Parallel/mgnet.bib; Parallel/Multi.grid.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib",
ZMnumber = "0582.65019",
abstract = "For large sparse linear systems {$ A x = b $} arising
in the solution of partial differential equations via
the finite element method, preconditioning of the
conjugate gradient method is considered. Splitting
techniques are used for the preconditioning. The
resulting method is examined and it's behaviour tested
on a model problem.",
acknowledgement = ack-nhfb,
classification = "B0290P (Differential equations); C4170 (Differential
equations)",
classmath = "*65F10 Iterative methods for linear systems 65N30
Finite numerical methods (BVP of PDE) 65F35 Matrix
norms, etc. (numerical linear algebra) 35J25 Second
order elliptic equations, boundary value problems",
corpsource = "Center for Pure and Appl. Math., California Univ.,
Berkeley, CA, USA",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
keywords = "assembly process; boundary-value problems; code;
conjugate gradient algorithm; conjugate gradient
method; element preconditioning; elliptic boundary
value problems; finite element analysis; finite element
method; large sparse linear systems; large symmetric
systems; numerical example; preconditioning; Splitting;
splitting techniques",
onlinedate = "July 1985",
reviewer = "V. Mehrmann",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Parlett:1985:CSI,
author = "Beresford N. Parlett and Y. Saad",
title = "Complex shift and invert strategies for real
matrices",
type = "Research report",
number = "RR-424",
institution = "Department of Computer Science, Yale University",
address = "New Haven, CT, USA",
pages = "17",
year = "1985",
bibdate = "Fri Nov 11 05:42:25 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Parlett:1985:DAA,
author = "Beresford N. Parlett and K. C. Ng",
title = "Development of an accurate algorithm for {$ \exp (B t)
$}",
type = "Technical Report",
number = "PAM-294",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = aug,
year = "1985",
bibdate = "Fri Nov 11 09:06:19 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Parlett:1985:ILA,
author = "B. Parlett and B. Nour-Omid and J. Jatvig",
title = "Implementation of {Lanczos} Algorithms on Vector
Computers",
crossref = "Numrich:1985:SA",
pages = "1--18",
year = "1985",
bibdate = "Thu Nov 10 18:36:35 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/ovr.bib",
acknowledgement = ack-nhfb,
}
@Article{Parlett:1985:LAL,
author = "Beresford N. Parlett and Derek R. Taylor and Zhishun
A. Liu",
title = "A look-ahead {L{\'a}nczos} algorithm for unsymmetric
matrices",
journal = j-MATH-COMPUT,
volume = "44",
number = "169",
pages = "105--124",
month = jan,
year = "1985",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2007796",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F15",
MRnumber = "MR771034 (86f:65072)",
MRreviewer = "Youcef Saad",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
JSTOR database; Parallel/par.lin.alg.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib",
ZMnumber = "0564.65022",
abstract = "The Lanczos algorithm for nonsymmetric matrices is
studied. It is shown how breakdown caused by a pair of
corresponding basis vectors being orthogonal can be
remedied by computing further vectors in the Krylov
sequences. This corresponds to performing $ 2 \times 2
$ pivots when factorizing the moment matrix, which may
be indefinite for nonsymmetric eigenproblems. It is
stated that when $ 2 \times 2 $ pivots are insufficient
to continue the process, all eigenvalues have
converged. Results of a few numerical tests are
reported.",
acknowledgement = ack-nhfb,
classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)",
classmath = "*65F15 Eigenvalues (numerical linear algebra)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "eigenvalues and eigenfunctions; instability; Krylov
sequences; Lanczos algorithm; look-ahead Lanczos
algorithm; matrix; matrix algebra; moment; nonsymmetric
eigenproblems; numerical tests; plasma; triangular
factorization; tridiagonal matrix; unsymmetric
matrices",
reviewer = "A. Ruhe",
treatment = "T Theoretical or Mathematical",
}
@Article{Parlett:1985:URE,
author = "B. N. Parlett and B. Nour-Omid",
title = "The Use of a Refined Error Bound When Updating
Eigenvalues of Tridiagonals",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "68",
number = "??",
pages = "179--219",
year = "1985",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(85)90213-7",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (65-04)",
MRnumber = "MR794821 (86j:65046)",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/linala1980.bib",
ZMnumber = "0629.65037",
abstract = "For computing some eigenvalues of a given symmetric
matrix {$A$} the Lanczos algorithm is used. It provides
a nested sequence of tridiagonal matrices {$ T \sb j
$}, whose eigenvalues approximate those of A. The
eigenvalues of {$ T \sb j $} tend to stagnate quite
early (as functions of j). An algorithm (ANALYZE T) is
described, which is a part of the inner loops of the
Lanczos algorithm, and which monitors the convergence
behaviour of the Ritz values. It helps, e.g., to avoid
the so-called misconvergence.",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 15-04
Machine computation, programs (linear algebra)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "convergence; eigenvalues; Lanczos algorithm;
misconvergence; nested sequence of tridiagonal
matrices; nla, eig, pert, tridiagonal matrix; Ritz
values",
reviewer = "L. Elsner",
xxpages = "179--220",
}
@Article{Natvig:1986:ECC,
author = "J. Natvig and B. Nour-Omid and B. N. Parlett",
title = "Effect of the {CYBER 205} on the choice of method for
solving the eigenvalue problem {$ (A - \lambda M) x = 0
$}",
journal = j-J-COMPUT-APPL-MATH,
volume = "15",
number = "2",
pages = "137--159",
month = jun,
year = "1986",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(86)90023-3",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:56 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042786900233",
ZMnumber = "0635.65032",
abstract = "For the eigenvalue problem {$ A x = \lambda M x $},
{$A$}, {$B$} large, sparse, symmetric matrices, two
methods, subspace iteration and Lanczos method, are
compared when running on typical examples from
structural dynamic analysis (order of {$A$}, {$B$} up
to 8000) on a Cyber 205. A fixed number of eigenpairs
is calculated. As on serial computers it turns out on
this vector computer that the Lanczos algorithm is
considerably faster. However, on problems with
substantial overhead in reading\slash writing, a block
Lanczos method is preferable.",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F50
Sparse matrices",
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "comparison of methods; eigenvalue problem; Lanczos
method; large, sparse, symmetric matrices; subspace
iteration; vector computer; vectorization",
reviewer = "L. Elsner",
}
@InProceedings{Parlett:1986:ACM,
author = "B. N. Parlett and K. C. Ng",
title = "Accurate computation of the matrix exponential",
crossref = "Glowinski:1986:CMA",
pages = "107--116",
year = "1986",
MRclass = "65F30",
MRnumber = "MR905289 (89f:65048)",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "0677.65040",
abstract = "This document describes a program to compute the
exponential of a given $ n \times n $ matrix B
multiplied by a scalar $ \tau $ that is to be thought
of as representing time. Our primary goal has been to
achieve as much accuracy as working precision permits
without resorting to simulated higher precision. The
final product is more complicated than we anticipated
at the outset. How these complications came to be
accepted is the theme of this story. The cases we
consider may be of interest to those who wish to use
the matrix exponential in their work. We hasten to add
that the code acts simply on simple cases.",
acknowledgement = ack-nhfb,
classmath = "*65F30 Other matrix algorithms 15-04 Machine
computation, programs (linear algebra) 15A60 Appl. of
functional analysis to matrix theory",
keywords = "accuracy; accurate computation; matrix exponential;
program; working precision",
}
@InProceedings{Schreiber:1986:BRC,
author = "Robert S. Schreiber and Beresford N. Parlett",
title = "Block reflectors: Computation and applications",
crossref = "Glowinski:1982:CMA",
pages = "71--79",
year = "1986",
MRclass = "65F30 (65W05)",
MRnumber = "MR905287 (88h:65090)",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "0677.65039",
abstract = "A block reflector is an orthogonal, symmetric matrix
that reverses a subspace whose dimension may be greater
than one. We shall develop the properties of block
reflectors and give an algorithm for computing a block
reflector that introduces a block of zero into a
matrix. We consider the compact representation of block
reflectors, some applications, and their use in
parallel computers.",
acknowledgement = ack-nhfb,
classmath = "*65F30 Other matrix algorithms 65Y05 Parallel
computation (numerical methods)",
keywords = "algorithm; block reflector; orthogonal, symmetric
matrix; parallel computers",
}
@Article{Nour-Omid:1987:HIS,
author = "Bahram Nour-Omid and Beresford N. Parlett and Thomas
Ericsson and Paul S. Jensen",
title = "How to Implement the Spectral Transformation",
journal = j-MATH-COMPUT,
volume = "48",
number = "178",
pages = "663--673",
month = apr,
year = "1987",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2007835",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F15",
MRnumber = "MR878698 (88f:65062)",
MRreviewer = "William W. Hager",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
JSTOR database",
URL = "https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib",
ZMnumber = "0638.65026",
acknowledgement = ack-nhfb,
classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)",
classmath = "*65F15 Eigenvalues (numerical linear algebra)",
corpsource = "Lockheed Palo Alto, Res. Lab., CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "algebra; Cholesky factor; eigenpairs; eigenvalue;
eigenvalue equations; eigenvalues and eigenfunctions;
factorization; inverse; iteration; iterative methods;
Lanczos algorithm; linear; matrix; numerical methods;
reductions; Ritz vectors; spectral transformation;
symmetric matrices; transformation step",
reviewer = "L. Boubel{\'\i}kov{\'a}",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Parlett:1987:BRT,
author = "Beresford N. Parlett and Robert Schreiber",
title = "Block reflectors: theory and computation",
type = "Technical Report",
number = "PAM-378",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = may,
year = "1987",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@TechReport{Parlett:1987:CJH,
author = "Beresford N. Parlett",
title = "A contribution of {J. H. Wilkinson} to numerical
analysis",
type = "Technical Report",
number = "PAM-372",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = apr,
year = "1987",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@TechReport{Parlett:1987:CLC,
author = "Beresford N. Parlett and B. Nour-Omid and A. Raefsky",
title = "Comparison of {Lanczos} with conjugate gradient using
element preconditioning",
type = "Technical Report",
number = "PAM-363",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = feb,
year = "1987",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@Article{Parlett:1987:CSI,
author = "Beresford N. Parlett and Youcef Saad",
title = "Complex Shift and Invert Strategies for Real
Matrices",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "88/89",
number = "??",
pages = "575--595",
year = "1987",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(87)90126-1",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F05",
MRnumber = "MR882464 (88d:65056)",
MRreviewer = "H. R. Schwarz",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib",
URL = "https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
https://www.math.utah.edu/pub/tex/bib/linala1980.bib",
ZMnumber = "0623.65045",
abstract = "Algorithms for the nonsymmetric eigenvalue problem {$
(F - \lambda M)X = 0 $} with real matrices are studied.
It is shown that the symmetry around the real axis can
be exploited in algorithms based on inverse iteration.
Algorithm are developed which use either the real or
the imaginary part of {$ (F - \lambda M) \sp {-1}M $},
obtained by a complex banded Gaussian elimination.
Numerical results are given for an example arising from
a brusselator model of a tubular chemical reactor.",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 80A32
Chemically reacting flows",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "Algorithm; banded Gaussian elimination; inverse
iteration; nonsymmetric eigenvalue problem; Numerical
results; tubular chemical reactor",
reviewer = "A. Ruhe",
}
@TechReport{Parlett:1987:MLA,
author = "Beresford N. Parlett",
title = "Misconvergence in the {Lanczos} algorithm",
type = "Technical Report",
number = "PAM-404",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = dec,
year = "1987",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Parlett:1987:PSD,
author = "Beresford N. Parlett and K. C. Ng",
title = "Programs to swap diagonal blocks",
type = "Technical Report",
number = "PAM-381",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = jun,
year = "1987",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@TechReport{Parlett:1987:SAE,
author = "Beresford N. Parlett",
title = "The state-of-the-art in extracting eigenvalues and
eigenvectors in structural mechanics",
type = "Technical Report",
number = "PAM-373",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = apr,
year = "1987",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@TechReport{Gao:1988:CCS,
author = "F. Gao and Beresford N. Parlett",
title = "Communication cost of sparse {Cholesky} factorization
on a hypercube",
type = "Technical Report",
number = "PAM-436",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = dec,
year = "1988",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Le:1988:FIT,
author = "J. Le and Beresford N. Parlett",
title = "On the forward instability of the {$ Q R $}
transformation",
type = "Technical Report",
number = "PAM-419",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = jul,
year = "1988",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Nour-Omid:1988:CLC,
author = "B. Nour-Omid and B. Parlett and A. Raefsky",
title = "Comparison of {Lanczos} with Conjugate Gradient Using
Element Preconditioning",
crossref = "Glowinski:1988:FIS",
pages = "250--260",
year = "1988",
bibdate = "Thu Nov 10 18:35:12 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/ovr.bib",
ZMnumber = "0658.65034",
acknowledgement = ack-nhfb,
classmath = "*65F10 Iterative methods for linear systems 65F35
Matrix norms, etc. (numerical linear algebra) 65N30
Finite numerical methods (BVP of PDE) 35J25 Second
order elliptic equations, boundary value problems",
keywords = "conjugate gradients; finite elements; Lanczos method;
preconditioning",
reviewer = "H. R. Schwarz",
}
@TechReport{Parlett:1988:HMS,
author = "Beresford N. Parlett and B. Nour-Omid and Zhishun A.
Liu",
title = "How to maintain semi-orthogonality among {Lanczos}
vectors",
type = "Technical Report",
number = "PAM-420",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = jul,
year = "1988",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Parlett:1988:UII,
author = "Beresford N. Parlett and H. C. Chen",
title = "Use of an indefinite inner product for computing
damped natural modes",
type = "Technical Report",
number = "PAM-435",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = nov,
year = "1988",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Schreiber:1988:BRT,
author = "Robert S. Schreiber and Beresford N. Parlett",
title = "Block Reflectors: {Theory} and Computation",
journal = j-SIAM-J-NUMER-ANAL,
volume = "25",
number = "1",
pages = "189--205",
month = feb,
year = "1988",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0725014",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F05 (65F20)",
MRnumber = "MR923934 (89c:65040)",
MRreviewer = "David R. Hill",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
JSTOR database; Theory/Matrix.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/ovr.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib",
ZMnumber = "0637.65017",
abstract = "Block reflectors are the generalization of the
Householder transformation to block elimination
(instead of single element). A complete theory is
presented. Some stable algorithms are introduced. Block
reflectors are advantageous on parallel computers.",
acknowledgement = ack-nhfb,
classmath = "*65F05 Direct methods for linear systems 65F20
Overdetermined systems (numerical linear algebra) 65Y05
Parallel computation (numerical methods)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "block elimination; Block reflectors; Householder
transformation; parallel computers; QR-factorization;
stable algorithms",
kwds = "math, la, nla, Householder transformation, qrd, prll",
reviewer = "W. Sch{\"o}nauer",
}
@TechReport{Parlett:1989:SBI,
author = "Beresford N. Parlett",
title = "Some basic information on information-based complexity
theory",
type = "Technical Report",
number = "PAM-460",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = jul,
year = "1989",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@Article{Parlett:1989:TBB,
author = "Beresford N. Parlett and Bahram Nour-Omid",
title = "Towards a black box {Lanczos} program",
journal = j-COMP-PHYS-COMM,
volume = "53",
number = "1--3",
pages = "169--179",
month = may,
year = "1989",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(89)90158-6",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:26 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.sciencedirect.com/science/article/pii/0010465589901586",
ZMnumber = "0798.65054",
abstract = "The Lanczos algorithm may be used to find a few
eigenvalues and eigenvectors of a large matrix. We
describe some of the difficulties encountered in trying
to make a black box program requiring no judgements
from the user.",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra)",
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
keywords = "black box program; eigenvalues; eigenvectors; Lanczos
algorithm; large matrix",
}
@Article{Gao:1990:NCA,
author = "Feng Gao and Beresford N. Parlett",
title = "A note on communication analysis of parallel sparse
{Cholesky} factorization on a hypercube",
journal = j-PARALLEL-COMPUTING,
volume = "16",
number = "1",
pages = "59--60",
month = nov,
year = "1990",
CODEN = "PACOEJ",
DOI = "https://doi.org/10.1016/0167-8191(90)90158-6",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
MRclass = "65Y05",
MRnumber = "MR1089846 (92a:65361)",
bibdate = "Mon Apr 14 12:07:40 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib",
acknowledgement = ack-nhfb,
classification = "B0290H (Linear algebra); C4140 (Linear algebra);
C4240 (Programming and algorithm theory)",
corpsource = "Dept. of Comput. Sci. British Columbia Univ.,
Vancouver, BC, Canada",
fjournal = "Parallel Computing. Theory and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191",
keywords = "communication analysis; factorization; hypercube;
linear algebra; nested-dissection method; parallel
algorithms; parallel sparse Cholesky",
treatment = "P Practical; T Theoretical or Mathematical",
}
@InProceedings{Parlett:1990:CJH,
author = "Beresford N. Parlett",
title = "The Contribution of {J. H. Wilkinson} to Numerical
Analysis",
crossref = "Nash:1990:HSC",
pages = "17--30",
year = "1990",
MRclass = "01A70 (65-03)",
MRnumber = "MR1203099",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
acknowledgement = ack-nhfb,
mycrossref = "Nash:1990:HSC",
}
@InProceedings{Parlett:1990:LAI,
author = "B. N. Parlett and H. C. Chen",
title = "The {Lanczos} algorithm with indefinite inner
product",
crossref = "Kaashoek:1990:PIS",
volume = "5",
pages = "393--400",
year = "1990",
MRclass = "65F15 (15A18 70J10 73K12)",
MRnumber = "MR1115469 (92g:65043)",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
series = "Progr. Systems Control Theory",
ZMnumber = "0719.65026",
abstract = "A quadratic eigenvalue problem with symmetric positive
definite coefficient matrices may be reduced to linear
form while retaining symmetry in the new coefficients
but neither of them will be positive definite. Formally
the symmetric Lanczos algorithm and subspace iteration
may be used to compute some eigenpairs of the linear
problem. The trouble is that the basis vectors are
orthogonal with respect to an indefinite inner product
so there is no assurance that they will be linearly
independent. Nevertheless this is an attractive way to
solve the original problem and we discuss how to
implement it and how it relates to the unsymmetric
Lanczos procedures. We discuss complex origin shifts,
the Look-Ahead version, reorthogonalization, and error
bounds.",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra)",
keywords = "complex origin shifts; eigenpairs; error bounds;
indefinite inner product; Look-Ahead version; quadratic
eigenvalue problem; reorthogonalization; subspace
iteration; symmetric Lanczos algorithm",
}
@InProceedings{Parlett:1990:MLA,
author = "Beresford N. Parlett",
title = "Misconvergence in the {Lanczos} Algorithm",
crossref = "Cox:1990:RNC",
pages = "7--24",
year = "1990",
MRclass = "65F15",
MRnumber = "MR1098315 (91m:65110)",
bibdate = "Tue Nov 2 19:30:33 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
ZMnumber = "0726.65032",
abstract = "Theoretical and computational tools are developed in
this paper that help to understand and predict the
apparent misconvergence in Lanczos' method for matrices
with clustered eigenvalues. A computable ``point of
discovery'' is given that aids with discovering
eigenvalues hidden by the misconvergence of the Ritz
values in Lanczos' algorithm. The solution hinges on
``Ritz intervals'' and their ``effective spread'',
rather than the Ritz values themselves.",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F35
Matrix norms, etc. (numerical linear algebra) 15A42
Inequalities involving eigenvalues and eigenvectors",
keywords = "convergence; Lanczos' method; matrices with clustered
eigenvalues; misconvergence; point of discovery; Ritz
intervals; Ritz values",
reviewer = "F. Uhlig (Auburn)",
}
@TechReport{Parlett:1990:RTF,
author = "Beresford N. Parlett",
title = "Reduction to tridiagonal form and minimal
realizations",
type = "Technical Report",
number = "PAM-486",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = jan,
year = "1990",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@Article{Parlett:1990:UIP,
author = "B. N. Parlett and H. C. Chen",
title = "Use of indefinite pencils for computing damped natural
modes",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "140",
number = "??",
pages = "53--88",
year = "1990",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(90)90222-X",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (15A18)",
MRnumber = "MR1075543 (92b:65030)",
MRreviewer = "M. Tismenetsky",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/linala1990.bib",
ZMnumber = "0725.65055",
abstract = "A quadratic eigenvalue problem {$ (\lambda \sp 2 \sb i
\cdot M + \lambda \sb i C + K) \omega \sb i = 0, $} $ i
= 1, ..., 2 n $ is solved where {$M$}, {$C$}, {$K$} are
real symmetric and positive definite $ n \times n $
matrices. This problem may be reduced to linear
symmetric but not positive definite form. The new
problem is {$ (A - 1 / \lambda B)z = 0, $} where {$A$},
{$B$} are symmetric but indefinite matrices.\par
The problems are solved by means of the Lanczos
algorithm. When {$K$} is singular, then the shifted
problem is solved. Real or complex origin shifts,
reorthogonalization, and error bounds are discussed.
Several methods for solving the reduced problem are
mentioned. Some dangers are described, and examples are
given comparing the Lanczos algorithm with subspace
iteration.",
acknowledgement = ack-nhfb,
classmath = "*65H17 Eigenvalue and bifurcation problems of
nonlinear algebraic equations 65F15 Eigenvalues
(numerical linear algebra)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "comparison of methods; error bounds; indefinite
pencils; Lanczos algorithm; quadratic eigenvalue
problem; reorthogonalization; subspace iteration;
symmetric positive definite matrices",
reviewer = "L. Boubel{\'\i}kov{\'a} (Praha)",
}
@Article{Golub:1991:DJW,
author = "G. Golub and B. Parlett",
title = "Dedication to {J. Wallace Givens}",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "12",
number = "1",
pages = "U1--U1",
month = jan,
year = "1991",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@TechReport{Hill:1991:RIP,
author = "R. O. Hill and Beresford N. Parlett",
title = "Refined interlacing properties",
type = "Technical Report",
number = "PAM-517",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = jan,
year = "1991",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Parlett:1991:IMR,
author = "Beresford N. Parlett and Wee-Liang Heng",
title = "Implementation of minimal representation in {$2$D}
{Ising} model calculations",
type = "Technical Report",
number = "PAM-550",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = may,
year = "1991",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "Longer version (60 pages)(to be published) of \#549",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@InProceedings{Parlett:1991:QFI,
author = "Beresford N. Parlett and Jian Le",
title = "{QR}; its forward instability and failure to
converge",
crossref = "Albrecht:1991:NTE",
pages = "177--189",
year = "1991",
MRclass = "65F10 (65F35)",
MRnumber = "MR1109104",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
series = "Internat. Ser. Numer. Math.",
ZMnumber = "0724.65036",
abstract = "The QR factorization of a rectangular matrix {$B$} is
known to be backward stable; however, forward
instability may occur, i.e., the computed orthogonal
transformations are far from the exact ones. On the
other hand, if the rank of {$B$} happens to be smaller
than the number of columns, then the QR factorization
is not unique. The paper shows precisely that forward
instability occurs if and only if {$B$} is close to a
matrix whose QR factorization is not unique. The
analysis is focussed on tridiagonal matrices and upper
Hessenberg ones; the implementation of the QR algorithm
is the usual one consisting in a shift followed by
premultiplication by plane rotation matrices. Several
illustrative examples are also discussed.",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F25
Orthogonalization (numerical linear algebra)",
keywords = "convergence; forward instability; Hessenberg matrices;
QR algorithm; QR factorization; rectangular matrix;
tridiagonal matrices",
reviewer = "J. P. Milaszewicz (Buenos Aires)",
}
@Article{Parlett:1991:SMP,
author = "Beresford N. Parlett",
title = "Symmetric matrix pencils",
journal = j-J-COMPUT-APPL-MATH,
volume = "38",
number = "1--3",
pages = "373--385",
day = "23",
month = dec,
year = "1991",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(91)90183-K",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "15A22 (65F15)",
MRnumber = "MR1146990 (92m:15011)",
MRreviewer = "F. Szidarovszky",
bibdate = "Sat Feb 25 13:02:23 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
note = "Proceedings of the International Symposium on
Computational Mathematics (Matsuyama, 1990).",
URL = "http://www.sciencedirect.com/science/article/pii/037704279190183K",
ZMnumber = "0772.15005",
abstract = "Typical matrix eigenvalue problems, quadratic or
linear, are best formulated as pencils {$ (A, M) $} in
which both {$A$} and {$M$} are real and symmetric. This
fact is emphasized in the paper through a set of
physical examples. Then, the canonical forms are used
to explain the role of the sign characteristic attached
to real eigenvalues.\par
The Rayleigh quotient is analyzed to describe real
eigenvalues and it seems plausible that the class of
definite Hermitian pencils is the broadest extension of
the class of Hermitian matrices that retains the
classical properties. This sheds new light on the class
of definite pencils and the stability of their
eigenvalues under perturbations. The reduction of
indefinite pencils to useful sparse forms is also
mentioned.",
acknowledgement = ack-nhfb,
classmath = "*15A22 Matrix pencils 15A18 Eigenvalues of matrices,
etc",
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "canonical forms; congruence; definite pencils;
equivalence; Hermitian pencils; indefinite pencils;
matrix eigenvalue problems; matrix pencils; Rayleigh
quotient; rotation transformation; stability; symmetric
matrix pencils",
reviewer = "M. de la Sen (Bilbao)",
}
@TechReport{Fernando:1992:ASVa,
author = "K. Vince Fernando and Beresford N. Parlett",
title = "Accurate Singular Values and Differential qd
Algorithms",
type = "Technical Report",
number = "TR2/92",
institution = "NAG Ltd.",
address = "Oxford, UK",
pages = "????",
month = jul,
year = "1992",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "To appear in Numer. Math.",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Fernando:1992:ASVb,
author = "K. Vince Fernando and Beresford N. Parlett",
title = "Accurate singular values and differential qd
algorithms",
type = "Technical Report",
number = "PAM-554",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = jul,
year = "1992",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Fernando:1993:ASVc,
author = "K. Vince Fernando and Beresford N. Parlett",
title = "Accurate singular values and differential qd
algorithms",
crossref = "Moonen:1993:LAL",
pages = "371--374",
year = "1993",
bibdate = "Thu May 29 18:42:39 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Hill:1992:RIP,
author = "R. O. {Hill, Jr.} and B. N. Parlett",
title = "Refined Interlacing Properties",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "1",
pages = "239--247",
month = jan,
year = "1992",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A18 (15A42)",
MRnumber = "MR1146664 (92m:15007)",
MRreviewer = "Lajos L{\'a}szl{\'o}",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
ZMnumber = "0747.15004",
abstract = "Interlacing results and theorems for eigenvalues due
to Cauchy, Golub, and Kahan are extended and related to
the last component of eigenvectors.",
acknowledgement = ack-nhfb,
classmath = "*15A42 Inequalities involving eigenvalues and
eigenvectors 15A18 Eigenvalues of matrices, etc. 65F15
Eigenvalues (numerical linear algebra)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
keywords = "Cauchy's interlace theorem; crowded interlacing;
eigenvalues; eigenvectors",
reviewer = "B. Ruffer-Beedgen (Ladenburg)",
}
@Article{Hirsch:1992:ERS,
author = "Morris W. Hirsch and Richard S. Palais",
title = "{Editors}' remarks: {``Some basic information on
information-based complexity theory'' [Bull. Amer.
Math. Soc. (N.S.) {\bf 26} (1992), no. 1, 3--27;
MR1102755 (94e:68077a)] by B. N. Parlett and
``Perspectives on information-based complexity'' [Bull.
Amer. Math. Soc. (N.S.) {\bf 26} (1992), no. 1, 29--52;
MR1102756 (94e:68077b)] by J. F. Traub and H.
Wo{\'z}niakowski}",
journal = j-BULL-AMS-N-S,
volume = "26",
number = "1",
pages = "1--2",
year = "1992",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/S0273-0979-1992-00238-0",
ISSN = "0273-0979 (print), 1088-9485 (electronic)",
MRclass = "68Q30 (00A30 65Y20)",
MRnumber = "MR1141473 (94e:68076)",
MRreviewer = "Arthur G. Werschulz",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Society. Bulletin. New Series",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
}
@TechReport{Parlett:1992:MES,
author = "Beresford N. Parlett and Tzon-Tzer Lu",
title = "Minimum eigenvalue separation",
type = "Technical Report",
number = "PAM-560",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = jul,
year = "1992",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@TechReport{Parlett:1992:MMR,
author = "Beresford N. Parlett and Wee-Liang Heng",
title = "The method of minimal representations in {$2$D}
{Ising} model calculations",
type = "Technical Report",
number = "PAM-549",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = may,
year = "1992",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "Abbreviated version (14 pages) of \#550",
acknowledgement = ack-nhfb,
}
@Article{Parlett:1992:RMS,
author = "Beresford N. Parlett",
title = "The rewards for maintaining semi-orthogonality among
{Lanczos} vectors",
journal = j-J-NUM-LIN-ALG-APPL,
volume = "1",
number = "2",
pages = "243--267",
year = "1992",
CODEN = "NLAAEM",
ISSN = "0129-3281",
MRclass = "65F15",
MRnumber = "MR1182241 (93g:65054)",
bibdate = "Thu Jan 23 19:03:25 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/numlinaa.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Numerical Linear Algebra with
Applications",
}
@Article{Parlett:1992:RTF,
author = "Beresford N. Parlett",
title = "Reduction to Tridiagonal Form and Minimal
Realizations",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "2",
pages = "567--593",
month = apr,
year = "1992",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/0613036",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F30 (15A57 65F50 93B20)",
MRnumber = "MR1152769 (93c:65059)",
MRreviewer = "Valeriu Prepeli{\c{t}}{\u{a}}",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
ZMnumber = "0754.65040",
acknowledgement = ack-nhfb,
classmath = "*65F30 Other matrix algorithms 65F15 Eigenvalues
(numerical linear algebra) 65K10 Optimization
techniques (numerical methods) 15A21 Canonical forms,
etc. 93B10 Canonical structure of systems",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
keywords = "condition number; Gram--Schmidt process; Krylow
sequences; Lanczos algorithm; minimal realizations;
orthogonal polynomials; reduction to tridiagonal form;
three-term recurrence relations; time-invariant;
time-invariant linear dynamical systems; tridiagonal
matrix",
reviewer = "A. Roose (Tallinn)",
}
@Article{Parlett:1992:SBI,
author = "Beresford N. Parlett",
title = "Some Basic Information on Information-Based Complexity
Theory",
journal = j-BULL-AMS-N-S,
volume = "26",
number = "1",
pages = "3--27",
year = "1992",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/S0273-0979-1992-00239-2",
ISSN = "0273-0979 (print), 1088-9485 (electronic)",
MRclass = "68Q30 (65Y20)",
MRnumber = "MR1102755 (94e:68077a)",
MRreviewer = "Arthur G. Werschulz",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
ZMnumber = "0765.65042",
abstract = "Numerical analysts might be expected to pay close
attention to a branch of complexity theory called
information-based complexity theory (IBCT), which
produces an abundance of impressive results about the
quest for approximate solutions to mathematical
problems. Why then do most numerical analysts turn a
cold shoulder to IBCT? Close analysis of two
representative papers reveals a mixture of nice new
observations, error bounds repackaged in new language,
misdirected examples, and misleading theorems.\par
Some elements in the framework of IBCT, erected to
support a rigorous yet flexible theory, make it
difficult to judge whether a model is off-target or
reasonably realistic. For instance, a sharp distinction
is made between information and algorithms restricted
to this information. Yet the information itself usually
comes from an algorithm, so the distinction clouds the
issues and can lead to true but misleading inferences.
Another troublesome aspect of IBCT is a free parameter
{$F$}, the class of admissible problem instances. By
overlooking {$F$}'s membership fee, the theory
sometimes distorts the economics of problem solving in
a way reminiscent of agricultural subsidies.\par
The current theory's surprising results only pertain to
unnatural situations, and its genuinely new insights
might serve us better if expressed in the conventional
modes of error analysis and approximation theory.",
acknowledgement = ack-nhfb,
classmath = "*65F10 Iterative methods for linear systems 68Q25
Analysis of algorithms and problem complexity 65Y20
Complexity and performance of numerical algorithms
65F15 Eigenvalues (numerical linear algebra) 65F20
Overdetermined systems (numerical linear algebra)",
fjournal = "American Mathematical Society. Bulletin. New Series",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
keywords = "approximate solutions to mathematical problems; error
analysis; information-based complexity; optimal
solution of large eigenpair problems; optimal solution
of large linear systems",
}
@Article{Traub:1992:PIB,
author = "J. F. Traub and H. Wo{\'z}niakowski",
title = "Perspectives on Information-Based Complexity",
journal = j-BULL-AMS-N-S,
volume = "26",
number = "1",
pages = "29--52",
year = "1992",
CODEN = "BAMOAD",
ISSN = "0273-0979 (print), 1088-9485 (electronic)",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "Reply to \cite{Parlett:1992:SBI}",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
acknowledgement = ack-nhfb,
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
}
@InProceedings{Fernando:1993:DA,
author = "K. Vince Fernando and Beresford N. Parlett",
title = "Differential qd algorithms",
crossref = "Reichel:1993:NLA",
pages = "75--100",
year = "1993",
MRclass = "65F05",
MRnumber = "MR1244154 (94j:65038)",
MRreviewer = "I. P{\u{a}}v{\u{a}}loiu",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "0794.65023",
abstract = "We have discovered a new implementation of the qd
algorithm that has a far wider domain of stability than
Rutishauser's version. Our algorithm was developed from
the examination of the LR-Cholesky transformation and
can be adapted to parallel computation in stark
contrast to traditional qd. Our algorithm also
yields useful a posteriori upper and lower bounds on
the smallest singular value of a bidiagonal
matrix.\par
The zero-shift bidiagonal QR of {\it J. Demmel} and
{\it W. Kahan} [SIAM J. Sci. Stat. Comput. 11, No. 5,
873--912 (1990; Zbl 0705.65027)] computes the smallest
singular values to maximal relative accuracy and the
others to maximal absolute accuracy with little or no
degradation in efficiency when compared with the
LINPACK code. Our algorithm obtains maximal relative
accuracy for all the singular values and runs at least
four times faster than the LINPACK code.",
acknowledgement = ack-nhfb,
classmath = "*65F05 Direct methods for linear systems 65Y05
Parallel computation (numerical methods) 65F15
Eigenvalues (numerical linear algebra) 65B05
Extrapolation to the limit",
keywords = "$qd$ algorithm; bidiagonal matrix; LR-Cholesky
transformation; parallel computation;
quotient-difference algorithm; singular value
decomposition",
}
@TechReport{Fernando:1993:ICA,
author = "K. Vince Fernando and Beresford N. Parlett",
title = "Implicit {Cholesky} algorithms for singular values and
vectors",
type = "Technical Report",
number = "PAM-587",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = aug,
year = "1993",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Paige:1993:ASEa,
author = "C. C. Paige and B. N. Parlett and H. A. {Van der
Vorst}",
title = "Approximate solutions and eigenvalue bounds from
{Krylov} subspaces",
number = "PAM-579",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = feb,
year = "1993",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib",
URL = "https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib",
acknowledgement = ack-nhfb,
notes = "Published in \cite{Paige:1995:ASE}.",
}
@Article{Parlett:1993:FIT,
author = "Beresford N. Parlett and Jian Le",
title = "Forward Instability of Tridiagonal {$ Q R $}",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "14",
number = "1",
pages = "279--316",
month = jan,
year = "1993",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/0614022",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15",
MRnumber = "MR1199561 (93k:65033)",
MRreviewer = "James Weldon Demmel",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
ZMnumber = "0767.65031",
abstract = "In computing eigenvalues only backward stability is
required, however, the {$ Q R $} transformation has
other uses and then forward stability is needed. This
paper gives examples, analyzes the forward instability,
and shows that it occurs only when the shift causes
``premature deflation''.\par
It is also shown that forward stability is governed by
the size of the last entry in normalized eigenvectors
of leading principal submatrices, and the extreme
values of the derivative of each entry of the
transformed matrix as a function of the shift is
determined.",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
keywords = "$QR$ transformation; eigenvalues; eigenvectors;
forward instability; premature deflation; sensitivity
analysis; tridiagonal matrices",
reviewer = "F. Szidarovszky (Tucson)",
}
@Article{Berry:1994:CES,
author = "M. W. Berry and B. N. Parlett and A. H. Sameh",
title = "Computing Extremal Singular Triplets of Sparse
Matrices on a Shared-Memory Multiprocessor",
journal = j-INT-J-HIGH-SPEED-COMPUTING,
volume = "6",
number = "2",
pages = "239--276",
year = "1994",
CODEN = "IHSCEZ",
DOI = "https://doi.org/10.1142/S0129053394000123",
ISSN = "0129-0533",
ISSN-L = "0129-0533",
bibdate = "Mon Feb 25 11:19:25 MST 2002",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/ijhsc.bib; OCLC
Article1st database",
URL = "http://www.worldscientific.com/doi/abs/10.1142/S0129053394000123",
acknowledgement = ack-nhfb,
fjournal = "International Journal of High Speed Computing
(IJHSC)",
journal-URL = "http://www.worldscientific.com/worldscinet/ijhsc",
}
@Article{Fernando:1994:ASV,
author = "K. Vince Fernando and Beresford N. Parlett",
title = "Accurate singular values and differential qd
algorithms",
journal = j-NUM-MATH,
volume = "67",
number = "2",
pages = "191--229",
month = mar,
year = "1994",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s002110050024",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F15",
MRnumber = "MR1262781 (95a:65071)",
MRreviewer = "Roland W. Freund",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://link.springer.de/link/service/journals/00211/bibs/4067002/40670191.htm;
http://science.springer.de/nmee/bibs/4067002/40670191.htm;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
ZMnumber = "0814.65036",
abstract = "An algorithm to compute the singular values of a
bidiagonal matrix based on the quotient difference
algorithm by {\it H. Rutishauser} [Z. Angew. Math.
Phys. 5, 233-251 (1954; Zbl 0055.347)] is studied. It
is implemented using neither square roots nor
subtractions and gives high relative accuracy for small
singular values, is very fast and can be implemented in
parallel. Comparisons are made to the recent algorithm
by {\it J. Demmel} and {\it W. Kahan} [SIAM J. Sci.
Stat. Comput. 11, No. 5, 873-912 (1990; Zbl
0705.65027)].",
acknowledgement = ack-nhfb,
classification = "B0290H (Linear algebra); B0290P (Differential
equations); C4140 (Linear algebra); C4170 (Differential
equations); C7310 (Mathematics)",
classmath = "*65F15 Eigenvalues (numerical linear algebra) 65Y05
Parallel computation (numerical methods)",
corpsource = "NAG Ltd., Oxford, UK",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "a posteriori upper bounds; algorithm; bidiagonal
matrix; Cholesky LR transformation; convergence of
numerical methods; differential $qd$ algorithms;
differential equations; LINPACK code; lower bounds;
mathematics computing; matrix algebra; parallel
computation; quotient difference algorithm; singular
values; stability; zero-shift bidiagonal QR",
reviewer = "A. Ruhe (G{\"o}teborg)",
treatment = "P Practical; T Theoretical or Mathematical",
}
@InProceedings{Parlett:1994:DWF,
author = "Beresford N. Parlett",
title = "Do We Fully Understand the Symmetric {Lanczos}
Algorithm Yet?",
crossref = "Brown:1994:PCL",
pages = "93--107",
year = "1994",
MRclass = "65Y20 (65F15)",
MRnumber = "MR1298225 (95f:65238)",
bibdate = "Sat Mar 4 14:38:48 GMT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
acknowledgement = ack-nhfb,
}
@Article{Parlett:1994:MMR,
author = "Beresford N. Parlett and Wee-Liang Heng",
title = "The method of minimal representations in {$2$D}
{Ising} model calculations",
journal = j-J-COMPUT-PHYS,
volume = "114",
number = "2",
pages = "257--264",
month = oct,
year = "1994",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1006/jcph.1994.1164",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
MRclass = "82B20 (82B80)",
MRnumber = "MR1294929",
bibdate = "Mon Jan 2 07:54:57 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999184711648",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@InProceedings{Parlett:1994:PDQ,
author = "Beresford N. Parlett and K. Vince Fernando",
title = "Parallel differential qd for singular vectors",
crossref = "Natori:1994:MAP",
pages = "242--250",
year = "1994",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "0807.65035",
abstract = "Two qd algorithms (stationary and progressive) to
compute singular vectors when accurate singular values
are given, are established. The differential forms of
these algorithms permit the calculation of accurate and
mutually orthogonal singular vectors in an
embarrassingly concurrent procedure.",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 65Y05
Parallel computation (numerical methods)",
keywords = "$qd$ algorithms; parallel differential; singular
values; singular vectors",
reviewer = "W. Heinrichs (D{\"u}sseldorf)",
}
@InProceedings{Parlett:1994:SVD,
author = "Beresford N. Parlett and K. Vince Fernando",
title = "Singular vectors via differential qd",
crossref = "Lewis:1994:ALA",
pages = "161--165",
year = "1994",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "0819.65050",
abstract = "We describe how to use two qd algorithms
(stationary and progressive) to compute singular
vectors when accurate singular values are given. The
differential forms of these algorithms permit the
calculation of accurate and mutually orthogonal
singular vectors in an embarrassingly concurrent
procedure.",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra)",
keywords = "$qd$ algorithms; differential $qd$; singular values;
singular vectors",
}
@Article{Edelman:1995:PMN,
author = "Alan Edelman and Walter F. Mascarenhas",
title = "On {Parlett}'s matrix norm inequality for the
{Cholesky} decomposition",
journal = j-NUM-LIN-ALG-APPL,
volume = "2",
number = "3",
pages = "243--250",
year = "1995",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.1680020306",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
MRclass = "65F05 (65F35)",
MRnumber = "96e:65018",
MRreviewer = "J. Segethov{\'a}",
bibdate = "Thu Jan 23 18:22:28 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/numlinaa.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
}
@Article{Fernando:1995:ICA,
author = "K. Vince Fernando and Beresford N. Parlett",
title = "Implicit {Cholesky} algorithms for singular values and
vectors of triangular matrices",
journal = j-NUM-LIN-ALG-APPL,
volume = "2",
number = "6",
pages = "507--531",
year = "1995",
CODEN = "NLAAEM",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
MRclass = "65F15",
MRnumber = "MR1367058 (96h:65057)",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/numlinaa.bib",
ZMnumber = "0841.65022",
abstract = "The equivalence of the implicit Cholesky algorithm and
a special version of the LP algorithm is proved.
Intermediate quantities in the transformation furnish
several attractive approximations to the smallest
singular value. Shifting combined with the method
improves accuracy.",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F05
Direct methods for linear systems",
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
keywords = "eigenvalues; factorizations; implicit Cholesky
algorithm; Jacobi methods; LP algorithm; noise spaces;
null spaces; QR algorithm; singular value; triangular
matrices",
reviewer = "F. Szidarovszky (Tucson)",
}
@TechReport{Fernando:1995:WFM,
author = "K. Vince Fernando and Beresford N. Parlett and
Inderjit Dhillon",
title = "A way to find the most redundant equation in a
tridiagonal system",
type = "Technical Report",
number = "PAM-635",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = may,
year = "1995",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Paige:1995:ASE,
author = "Chris C. Paige and Beresford N. Parlett and Henk A.
{van der Vorst}",
title = "Approximate solutions and eigenvalue bounds from
{Krylov} subspaces",
journal = j-NUM-LIN-ALG-APPL,
volume = "2",
number = "2",
pages = "115--133",
year = "1995",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.1680020205",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
MRclass = "65F15",
MRnumber = "MR1323816 (96a:65054)",
MRreviewer = "Colette Lebaud",
bibdate = "Thu Jan 23 18:22:28 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/numlinaa.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
}
@Article{Parlett:1995:NA,
author = "Beresford N. Parlett",
title = "The new {qd} algorithms",
journal = j-ACTA-NUMERICA,
volume = "4",
pages = "459--491",
year = "1995",
CODEN = "ANUMFU",
DOI = "https://doi.org/10.1017/S0962492900002580",
ISBN = "0-521-48255-0",
ISBN-13 = "978-0-521-48255-4",
ISSN = "0962-4929 (print), 1474-0508 (electronic)",
ISSN-L = "0962-4929",
MRclass = "65F15",
MRnumber = "MR1352476 (96g:65041)",
MRreviewer = "Hongyuan Zha",
bibdate = "Sat Sep 24 10:23:33 MDT 2011",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/UIA.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/actanumerica.bib",
ZMnumber = "0835.65059",
acknowledgement = ack-nhfb,
ajournal = "Acta Numer.",
classmath = "*65F15 Eigenvalues (numerical linear algebra) 65Y05
Parallel computation (numerical methods)",
fjournal = "Acta Numerica",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU",
keywords = "$qd$-algorithms; CFR; eigenvalues; eigenvectors;
Gram--Schmidt orthogonalization; LR-algorithms;
parallel computation; quotient-difference algorithm;
singular values; tridiagonal matrices",
onlinedate = "07 November 2008",
reviewer = "H. Matthies (Hamburg)",
}
@InProceedings{Parlett:1995:SVD,
author = "Beresford N. Parlett and K. Vince Fernando",
title = "Singular vectors via differential qd",
crossref = "Bailey:1995:PSS",
pages = "564--568",
year = "1995",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "0836.65059",
abstract = "We describe how to use two qd algorithms
(stationary and progressive) to compute singular
vectors when accurate singular values are given. The
differential forms of these algorithms permit the
calculation of accurate and mutually orthogonal
singular vectors in an embarrassingly concurrent
procedure.",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 65B05
Extrapolation to the limit",
keywords = "$qd$ algorithms; inverse iteration; singular values;
singular vectors",
}
@TechReport{Parlett:1996:COE,
author = "Beresford N. Parlett",
title = "The construction of orthogonal eigenvectors for tight
clusters by use of submatrices",
type = "Technical Report",
number = "PAM-664",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = jan,
year = "1996",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Parlett:1996:FRP,
author = "B. N. Parlett and J. He",
title = "Frequency response plots: New approaches",
journal = j-Z-ANGE-MATH-MECH,
volume = "76",
number = "Supplement 3",
pages = "78--80",
year = "1996",
CODEN = "ZAMMAX",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
MRclass = "93C80",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "0925.93610",
acknowledgement = ack-nhfb,
classmath = "*93C80 Frequency-response methods",
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
}
@Article{Parlett:1996:IST,
author = "B. N. Parlett",
title = "Invariant subspaces for tightly clustered eigenvalues
of tridiagonals",
journal = j-BIT-NUM-MATH,
volume = "36",
number = "3",
pages = "542--562",
month = sep,
year = "1996",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01731933",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
MRclass = "65F15",
MRnumber = "MR1410097 (97j:65065)",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "International Linear Algebra Year (Toulouse, 1995).",
URL = "http://www.mai.liu.se/BIT/contents/bit36.html;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
ZMnumber = "0856.15009",
abstract = "The invariant subspace of a real symmetric tridiagonal
matrix {$T$} associated with a tight cluster of $m$
eigenvalues has a special structure. This structure is
revealed by the defined envelope of the subspace having
$m$ high hills separated by $ m - 1 $ low valleys. This
paper describes a long technical report that shows the
existence of $m$ submatrices of {$T$} each one having a
single eigenvalue in the cluster interval whose
normalized eigenvector has small entries in the first
and last positions. These little eigenvectors determine
a distinguished basis for an approximating subspace
whose overlap matrix is tridiagonal and close to the
identity. The only communication needed among the
submatrices to make an orthogonal basis is between
nearest neighbors. A variety of examples illustrate the
theory.",
acknowledgement = ack-nhfb,
classmath = "*15A18 Eigenvalues of matrices, etc. 15A57 Other types
of matrices",
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "eigenvectors; invariant subspace; real symmetric
tridiagonal matrix; tightly clustered eigenvalues",
reviewer = "K. Burian (Hav{\'\i}rov)",
}
@InProceedings{Parlett:1996:OEG,
author = "B. N. Parlett",
title = "Orthogonal eigenvectors without {Gram--Schmidt}",
crossref = "Watson:1996:NA",
pages = "140--153",
year = "1996",
MRclass = "65F15",
MRnumber = "MR1405621 (97d:65019)",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Parlett:1996:WHM,
author = "Beresford N. Parlett",
title = "What {Hadamard} missed",
type = "Technical Report",
number = "PAM-671",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = mar,
year = "1996",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@InProceedings{Shub:1996:PDD,
author = "M. Shub and Alexandre Chorin and Arieh Iserles and
Beresford Parlett and Steve Smale and Shmuel Winograd",
title = "Panel discussion: {Does} numerical analysis need a
model of computation?",
crossref = "Renegar:1996:MNA",
volume = "32",
pages = "1--18",
year = "1996",
bibdate = "Tue Nov 2 18:47:44 MST 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
acknowledgement = ack-nhfb,
annote = "Described as proceedings",
keywords = "AMS; applied mathematics; numerical analysis; SIAM",
}
@Article{Bakkaloglu:1997:PPA,
author = "B. Bakkalo{\u{g}}lu and K. Erciye{\c{s}} and {\c{C}}.
K. Ko{\c{c}}",
title = "A parallelization of {Parlett}'s algorithm for
functions of triangular matrices",
journal = j-PARALLEL-ALGORITHMS-APPL,
volume = "11",
number = "1--2",
pages = "61--69",
month = may,
year = "1997",
CODEN = "PAAPEC",
DOI = "https://doi.org/10.1080/10637199708915587",
ISSN = "1063-7192",
ISSN-L = "1026-7689",
MRclass = "65Y05 (65F30)",
MRnumber = "MR1462307 (98c:65208)",
bibdate = "Tue Dec 23 19:03:42 MST 2003",
bibsource = "http://www.gbhap-us.com/journals/728/728-top.htm;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
MathSciNet database",
URL = "https://www.math.utah.edu/pub/tex/bib/parallelalgorithmsappl.bib",
acknowledgement = ack-nhfb,
fjournal = "Parallel Algorithms and Applications",
journal-URL = "http://www.tandfonline.com/loi/gpaa20",
remark = "Also cited as v12 n8 pp 61--69 1998.",
}
@Article{Kandic:1997:ECH,
author = "Dragan B. Kandi{\'c} and Beresford Parlett and
Branimir D. Reljin and Petar M. Vasi{\'c}",
title = "Explicit Construction of Hyperdominant Symmetric
Matrices With Assigned Spectrum",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "258",
number = "1--3",
pages = "41--51",
month = jun,
year = "1997",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/S0024-3795(96)00161-9",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A18; 15-XX",
MRnumber = "MR1444093 (97m:15011)",
MRreviewer = "F. Szidarovszky",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "http://www.elsevier.com/locate/laa;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/browse.cgi?year=1997&volume=258&issue=1-3&aid=9600161;
https://www.math.utah.edu/pub/tex/bib/linala1990.bib",
ZMnumber = "0878.15004",
abstract = "A matrix {$ A = (a_{ij}) $} is upper (lower)
Hessenberg if $ a_{ij} = 0 $ whenever $ i & g t; j + 1
$ $ (j & g t; i + 1) $. Orthogonal Hessenberg matrices
have a unique representation in the form {$ \prod_{i =
1}^n P_i $}, where the {$ P_i $} are plane rotators
(Lemma 2). A real matrix is called hyperdominant if it
has nonnegative diagonals and nonpositive off diagonals
and all row sums are nonnegative. It is shown (Theorem
2) that for any set of $ n & g t; 1 $ numbers $ 0 \leq
\lambda_1 \leq \lambda_2 \leq \dots \leq \lambda_n $
there exists a nontrivial hyperdominant matrix with
spectrum $ \{ \lambda_1, \dots, \lambda_n \} $",
acknowledgement = ack-nhfb,
classmath = "*15A18 Eigenvalues of matrices, etc. 15A57 Other types
of matrices",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "hyperdominant symmetric matrices; inverse eigenvalue
problem",
reviewer = "W. Wieslaw (Wroclaw)",
}
@Article{Parlett:1997:FSW,
author = "Beresford N. Parlett and Inderjit S. Dhillon",
title = "{Fernando}'s Solution to {Wilkinson}'s Problem: An
Application of Double Factorization",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "267",
number = "1--3",
pages = "247--279",
month = dec,
year = "1997",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/S0024-3795(97)80053-5",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A23",
MRnumber = "MR1479123 (99f:15018)",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "http://www.elsevier.com/locate/laa;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://www.cs.utexas.edu/users/inderjit/public_papers/pdonfer.pdf;
http://www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/browse.cgi?year=1997&volume=267&issue=1-3&aid=9700022;
https://www.math.utah.edu/pub/tex/bib/linala1990.bib",
ZMnumber = "0886.65033",
abstract = "An algorithm for the computation of eigenvectors to a
real symmetric tridiagonal matrix, when eigenvalues are
already computed, is studied. It is built up on a
recursion, used already by {\it W. Givens} (J. Assoc.
Comput. Mach. 4, 298--307 (1957); MR 19.10806).
Following a suggestion by {\it K. V. Fernando} [On
computing an eigenvector of a tridiagonal matrix. I:
Basic results, SIAM J. Matrix Anal. Appl. 18, No. 4,
1013--1034 (1997)], it is shown at which coordinate
this recursion should be started, in order to be stable
and yield orthogonal eigenvectors, also when the
eigenvalue approximations are multiple to the accuracy
used. These starting coordinates are found by running
Gaussian elimination both forwards and backwards.
Several numerical examples are included.",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "algorithm; double factorization; eigenvalues;
eigenvectors; Gaussian elimination; numerical examples;
symmetric tridiagonal matrix",
reviewer = "A. Ruhe (G{\"o}teborg)",
}
@InProceedings{Parlett:1997:NMR,
author = "Beresford N. Parlett and Jianxun He",
booktitle = "{Proceedings of the 36th IEEE Conference on Decision
and Control, 1997}",
title = "Nearly minimal reduced order systems",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "3867--3872",
year = "1997",
DOI = "https://doi.org/10.1109/CDC.1997.652465",
bibdate = "Tue Mar 5 09:03:06 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=652465",
acknowledgement = ack-nhfb,
journal-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5239",
}
@InProceedings{Parlett:1997:NVP,
author = "Beresford N. Parlett",
title = "New versions of qd for products of bidiagonals",
crossref = "Buhmann:1997:ATO",
pages = "183--200",
year = "1997",
MRclass = "65F15",
MRnumber = "MR1601711",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "1031.65044",
acknowledgement = ack-nhfb,
classmath = "*65F05 Direct methods for linear systems 65F50 Sparse
matrices",
keywords = "$qd$-algorithm; Gram--Schmidt process; LR algorithm;
product of two bidiagonal matrices; triangular
factorization; tridiagonal matrix",
}
@Book{Parlett:1998:SEP,
author = "Beresford N. Parlett",
title = "The Symmetric Eigenvalue Problem",
volume = "20",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xxiv + 398",
year = "1998",
DOI = "https://doi.org/10.1137/1.9781611971163",
ISBN = "0-89871-402-8 (paperback), 1-61197-116-0 (e-book)",
ISBN-13 = "978-0-89871-402-9 (paperback), 978-1-61197-116-3
(e-book)",
LCCN = "QA188 .P37 1998",
MRclass = "65F15 (15A18)",
MRnumber = "MR1490034 (99c:65072)",
MRreviewer = "F. Szidarovszky",
bibdate = "Fri Nov 21 06:49:56 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Corrected reprint \cite{Parlett:1980:SEP}.",
series = "Classics in Applied Mathematics",
URL = "http://www.loc.gov/catdir/enhancements/fy0708/97040623-d.html",
ZMnumber = "0885.65039",
abstract = "According to Parlett, ``Vibrations are everywhere, and
so too are the eigenvalues associated with them. As
mathematical models invade more and more disciplines,
we can anticipate a demand for eigenvalue calculations
in an ever richer variety of contexts''. Anyone who
performs these calculations will welcome the reprinting
of Parlett's book (originally published in 1980). In
this unabridged, amended version, Parlett covers
aspects of the problem that are not easily found
elsewhere. The chapter titles convey the scope of the
material succinctly. The aim of the book is to present
mathematical knowledge that is needed in order to
understand the art of computing eigenvalues of real
symmetric matrices, either all of them or only a few.
The author explains why the selected information really
matters and he is not shy about making judgments. The
commentary is lively but the proofs are terse. The
first nine chapters are based on a matrix on which it
is possible to make similarity transformations
explicitly. The only source of error is inexact
arithmetic. The last five chapters turn to large sparse
matrices and the task of making approximations and
judging them.",
acknowledgement = ack-nhfb,
acknowledgement = ack-njh # " and " # ack-nhfb # " and " # ack-rah,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 15A18
Eigenvalues of matrices, etc. 15A23 Factorization of
matrices 15A57 Other types of matrices 15-02 Research
monographs (linear algebra) 65-02 Research monographs
(numerical analysis) 65F25 Orthogonalization (numerical
linear algebra)",
keywords = "bandmatrices; bounds for eigenvalues; eigenvalues;
generalized eigenvalue problem; Krylov sequences;
localization of eigenvalues; orthogonal
transformations; tridiagonal matrices; vector
iteration",
libnote = "Not yet in my library.",
remark = "Unabridged, corrected republication of the original
edition (1980; Zbl 0431.65017)",
tableofcontents = "Convergence theory for the Rayleigh quotient
iteration \\
Eigenvectors of tridiagonals \\
Convergence theory, simpler than Wilkinson's, for
Wilkinson's shift strategy in $Q L$ and $Q R$ \\
New proofs and sharper results for error bounds \\
Optimal properties of Rayleigh--Ritz approximations \\
Approximation theory from Krylov subspaces, Paige's
theorem for noisy Lanczos algorithms, and
semiorthogonality among Lanczos vectors \\
Four flavors of subspace iteration",
}
@Article{Parlett:1998:SSP,
author = "Beresford N. Parlett",
title = "Spectral sensitivity of products of bidiagonals",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "275/276",
number = "1--3",
pages = "417--431",
day = "15",
month = may,
year = "1998",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (15A18)",
MRnumber = "MR1628402 (99e:65063)",
MRreviewer = "Yao Zhang",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "http://www.elsevier.com/locate/laa;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "Proceedings of the Sixth Conference of the
International Linear Algebra Society (Chemnitz,
1996).",
URL = "http://www.elsevier.com/cas/tree/store/laa/sub/1998/275-276/1-3/6055.pdf;
http://www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/browse.cgi?year=1998&volume=275-276&issue=1-3&aid=6055;
https://www.math.utah.edu/pub/tex/bib/linala1990.bib",
ZMnumber = "0933.15010",
abstract = "Simple formulae are derived for certain relative
condition numbers. Tridiagonal matrices may be
represented as products of bidiagonals in various ways
depending on properties such as symmetry and positive
definiteness. The condition numbers give the
amplification factor for relative changes in a nonzero
eigenvalue caused by relative changes in an entry of a
bidiagonal factor. The formulae show that in many, but
not all cases these condition numbers are of modest
size. Several examples illustrate the results and raise
new questions.",
acknowledgement = ack-nhfb,
classmath = "*15A12 Conditioning of matrices",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "condition numbers; eigenvalue; products of
bidiagonals; spectral sensitivity; tridiagonal
matrices",
}
@Article{Barlow:2000:ASE,
author = "J. L. Barlow and Beresford N. Parlett and
Kre{\v{s}}imir Veseli{\'c}",
title = "The accurate solution of eigenvalue problems",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "309",
number = "1--3",
pages = "1--2",
day = "15",
month = apr,
year = "2000",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/S0024-3795(00)00059-8",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Mon Oct 9 10:54:41 MDT 2000",
bibsource = "http://www.elsevier.com/locate/laa;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://www.elsevier.nl/gej-ng/10/30/19/126/25/25/abstract.html;
http://www.elsevier.nl/gej-ng/10/30/19/126/25/25/article.pdf;
https://www.math.utah.edu/pub/tex/bib/linala2000.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Parlett:2000:A,
author = "Beresford N. Parlett",
title = "The {$ Q R $} Algorithm",
journal = j-COMPUT-SCI-ENG,
volume = "2",
number = "1",
pages = "38--42",
month = jan # "\slash " # feb,
year = "2000",
CODEN = "CSENFA",
DOI = "https://doi.org/10.1109/5992.814656",
ISSN = "1521-9615 (print), 1558-366X (electronic)",
ISSN-L = "1521-9615",
bibdate = "Fri Oct 13 14:31:09 2000",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://dlib.computer.org/cs/books/cs2000/pdf/c1038.pdf;
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=814656;
http://www.computer.org/cse/cs1999/c1038abs.htm;
https://www.math.utah.edu/pub/tex/bib/computscieng.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing in Science and Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
}
@Article{Parlett:2000:IAP,
author = "Beresford N. Parlett and Osni A. Marques",
title = "An implementation of the $ d q d s $ algorithm
(positive case)",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "309",
number = "1--3",
pages = "217--259",
day = "15",
month = apr,
year = "2000",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/S0024-3795(00)00010-0",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15",
MRnumber = "MR1758369 (2001d:65048)",
bibdate = "Mon Oct 9 10:54:41 MDT 2000",
bibsource = "http://www.elsevier.com/locate/laa;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "See original LAPACK Working note in
\cite{Parlett:2002:IDA}.",
URL = "http://www.elsevier.nl/gej-ng/10/30/19/126/25/37/abstract.html;
http://www.elsevier.nl/gej-ng/10/30/19/126/25/37/article.pdf;
https://www.math.utah.edu/pub/tex/bib/lawn.bib;
https://www.math.utah.edu/pub/tex/bib/linala2000.bib",
ZMnumber = "0952.65031",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "differential quotient-difference algorithm with
shifts; dqds algorithm; IEEE arithmetic; shifting;
smallest eigenvalue; splitting",
remark = "Proceedings of the International Workshop on Accurate
Solution of Eigenvalue Problems (University Park, PA,
1998)",
reviewer = "F. Szidarovszky (Tucson)",
}
@Article{Parlett:2000:PSP,
author = "Beresford N. Parlett",
title = "Problems and Solutions: {Problems}: 10839",
journal = j-AMER-MATH-MONTHLY,
volume = "107",
number = "10",
pages = "950",
year = "2000",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "Contributed Item",
MRnumber = "MR1543775",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
fjournal = "The American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@Article{Parlett:2000:RRR,
author = "Beresford N. Parlett and Inderjit S. Dhillon",
title = "Relatively Robust Representations of Symmetric
Tridiagonals",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "309",
number = "1--3",
pages = "121--151",
day = "15",
month = apr,
year = "2000",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/S0024-3795(99)00262-1",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15",
MRnumber = "MR1758365 (2001e:65064)",
MRreviewer = "Raffaella Pavani",
bibdate = "Mon Oct 9 10:54:41 MDT 2000",
bibsource = "http://www.elsevier.com/locate/laa;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://www.elsevier.nl/gej-ng/10/30/19/126/25/33/abstract.html;
http://www.elsevier.nl/gej-ng/10/30/19/126/25/33/article.pdf;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/linala2000.bib",
ZMnumber = "0948.65026",
abstract = "The triangular factorization of an unreduced symmetric
tridiagonal matrix is considered with respect to
relative changes in the nontrivial entries of the lower
left matrix and the diagonal part. The effect of these
changes is modeled by diagonal scaling matrices.
Relative changes in the eigenvalues of the tridiagonal
matrix are studied in detail with respect to the inner
perturbations induced by the scaling matrix.
Furthermore, an algorithm for computing numerically
orthogonal eigenvectors is sketched. This algorithm
does not rely on the Gram--Schmidt process but requires
conditions on the locus of eigenvalues.",
acknowledgement = ack-nhfb,
classmath = "*65F05 Direct methods for linear systems 65F35 Matrix
norms, etc. (numerical linear algebra) 65F50 Sparse
matrices",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "algorithm; diagonal scaling matrices; eigenvalues;
error analysis; orthogonal eigenvectors; symmetric
tridiagonal matrix; triangular factorization",
remark = "Proceedings of the International Workshop on Accurate
Solution of Eigenvalue Problems (University Park, PA,
1998)",
reviewer = "Thomas Sonar (Braunschweig)",
}
@Article{Parlett:2000:TR,
author = "Beresford N. Parlett",
title = "For tridiagonals {$T$} replace {$T$} with {$ L D L^t
$}",
journal = j-J-COMPUT-APPL-MATH,
volume = "123",
number = "1--2",
pages = "117--130",
day = "1",
month = nov,
year = "2000",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/S0377-0427(00)00394-0",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65F10 (65F35)",
MRnumber = "MR1798522 (2001j:65055)",
bibdate = "Sat Feb 25 12:43:37 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
note = "Numerical analysis 2000, Vol. III. Linear algebra",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042700003940",
ZMnumber = "0970.65032",
abstract = "The author discusses two of the ideas needed to
compute eigenvectors that are orthogonal without making
use of the Gram--Schmidt procedure when some of the
eigenvalues are tightly clustered. In the first of the
new schemes, the radical new goal is to compute an
approximate eigenvector for a given approximate
eigenvalue with a relative residual property. In the
second scheme, due to the relative gaps in the spectrum
the origin is shifted and the triangular factorization
is used. In the development, the recently discovered
differential stationary QD algorithms are used.
Examples of both ideas, using four by four systems, are
given",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F05
Direct methods for linear systems",
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "clustered eigenvalues; eigenvalue; LDU factorization;
numerical examples; orthogonal eigenvectores; QD
algorithm; triangular factorization",
reviewer = "R. P. Tewarson (Stony Brook)",
}
@TechReport{Dhillon:2002:OER,
author = "Inderjit S. Dhillon and Beresford N. Parlett",
title = "Orthogonal Eigenvectors and Relative Gaps",
type = "LAPACK Working Note",
number = "154",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = aug,
year = "2002",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "UT-CS-02-474, August 2002 Published in
\cite{Dhillon:2004:OER}.",
URL = "https://www.math.utah.edu/pub/tex/bib/lawn.bib;
http://www.netlib.org/lapack/lawns/lawn154.ps;
http://www.netlib.org/lapack/lawnspdf/lawn154.pdf",
acknowledgement = ack-nhfb,
}
@TechReport{Parlett:2002:IDA,
author = "Beresford N. Parlett and Osni A. Marques",
title = "An implementation of the $ d q d s $ algorithm
positive case",
type = "LAPACK Working Note",
number = "155",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = aug,
year = "2002",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "LBNL-43726, UT-CS-02-475, August 2002. Published in
\cite{Parlett:2000:IDA}.",
URL = "https://www.math.utah.edu/pub/tex/bib/lawn.bib;
http://www.netlib.org/lapack/lawns/lawn155.ps;
http://www.netlib.org/lapack/lawnspdf/lawn155.pdf",
acknowledgement = ack-nhfb,
}
@Article{Parlett:2002:LEP,
author = "Beresford N. Parlett and Olaf Krafft and Martin
Schaefer",
title = "The Largest Eigenvalue of a Positive Definite
Symmetric Matrix: 10839",
journal = j-AMER-MATH-MONTHLY,
volume = "109",
number = "10",
pages = "922--923",
month = dec,
year = "2002",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jan 30 12:00:15 MST 2012",
bibsource = "http://www.jstor.org/journals/00029890.html;
http://www.jstor.org/stable/i355032;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib",
URL = "http://www.jstor.org/stable/3072468",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@Article{Parlett:2002:MDD,
author = "Beresford N. Parlett",
title = "The (matrix) discriminant as a determinant",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "355",
number = "1--3",
pages = "85--101",
day = "1",
month = nov,
year = "2002",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/S0024-3795(02)00335-X",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A15 (15A57)",
MRnumber = "MR1930139 (2003i:15008)",
MRreviewer = "Jorma Kaarlo Merikoski",
bibdate = "Mon Apr 28 07:27:18 MDT 2003",
bibsource = "http://www.elsevier.com/locate/laa;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://www.elsevier.nl/gej-ng/10/30/19/201/27/33/abstract.html;
https://www.math.utah.edu/pub/tex/bib/linala2000.bib",
ZMnumber = "1018.15006",
acknowledgement = ack-nhfb,
classmath = "*15A15 Special matrix functions 15A21 Canonical forms,
etc. 15A63 Bilinear forms, etc",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "inner product space; matrix determinant; matrix
discriminant; similarity transformations",
reviewer = "V{\'a}clav Burjan (Praha)",
}
@Misc{Parlett:2002:QA,
author = "Beresford N. Parlett",
title = "The {QR} Algorithm",
howpublished = "World-Wide Web document",
pages = "15",
day = "22",
month = apr,
year = "2002",
bibdate = "Mon Apr 25 18:25:57 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "Lecture notes for Math 128.",
URL = "http://www.cs.berkeley.edu/~wkahan/Math128/Parlett.pdf;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
acknowledgement = ack-nhfb,
}
@Book{Barlow:2003:SIA,
editor = "Jesse L. Barlow and Beresford N. Parlett",
title = "Special issue on accurate solution of eigenvalue
problems",
publisher = pub-ELSEVIER-SCIENCE,
address = pub-ELSEVIER-SCIENCE:adr,
pages = "iv + 425",
year = "2003",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
MRclass = "15-06 (65F15)",
MRnumber = "MR1903024",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "Including papers from the 3rd International Workshop
(IWASEP) held in Hagen, July 3--6, 2000, Linear Algebra
Appl. {\bf 358} (2003).",
acknowledgement = ack-nhfb,
}
@Article{Dhillon:2003:OER,
author = "Inderjit S. Dhillon and Beresford N. Parlett",
title = "Orthogonal Eigenvectors and Relative Gaps",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "25",
number = "3",
pages = "858--899",
month = jul,
year = "2003",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479800370111",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (15A18 15A23)",
MRnumber = "MR2081239 (2005k:65078)",
MRreviewer = "Daniel Kressner",
bibdate = "Sat Apr 16 10:32:32 MDT 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/25/3;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "See original LAPACK Working note in
\cite{Dhillon:2002:OER}.",
URL = "http://epubs.siam.org/sam-bin/dbq/article/37011;
https://www.math.utah.edu/pub/tex/bib/lawn.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Parlett:2003:PEF,
author = "Beresford N. Parlett",
title = "Perturbation of eigenpairs of factored symmetric
tridiagonal matrices",
journal = j-FOUND-COMPUT-MATH,
volume = "3",
number = "2",
pages = "207--223",
year = "2003",
DOI = "https://doi.org/10.1007/s10208-001-0051-5",
ISSN = "1615-3375 (print), 1615-3383 (electronic)",
ISSN-L = "1615-3375",
MRclass = "65F15",
MRnumber = "MR1966300 (2004f:65044)",
MRreviewer = "Mei-Qin Chen",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "1028.65027",
abstract = "The solution of the tridiagonal eigenproblem is
discussed for an indefinite symmetric matrix allowing a
triangular factorization {$ T = L D L^t $}, where {$D$}
is a diagonal matrix and {$L$} has $1$'s on the
diagonal and is lower bidiagonal, {$ L = I + \tilde {L}
$}. From the study of the behaviour of the eigenvalues
and eigenvectors under small changes in the nonzero
entries of {$D$} and {$ \tilde {L} $} the condition
numbers are obtained. For the element growth in the
factorization, it is shown that some eigenpairs are
robust and others are sensitive. A $ 4 \times 4 $
example with huge element growth for which the standard
multiplicative perturbation theory fails to predict
that the two very small eigenvalues are determined to
high relative accuracy is given. This example shows the
advantage of the new method.",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F50
Sparse matrices 65F35 Matrix norms, etc. (numerical
linear algebra)",
fjournal = "Foundations of Computational Mathematics. The Journal
of the Society for the Foundations of Computational
Mathematics",
journal-URL = "http://link.springer.com/journal/10208",
keywords = "condition number; eigenvalues; eigenvectors;
perturbation; triangular factorization; tridiagonal
eigenproblem",
reviewer = "V{\'a}clav Burjan (Praha)",
}
@Article{Parlett:2003:SDF,
author = "Beresford N. Parlett",
title = "The spectral diameter as a function of the diagonal
entries",
journal = j-NUM-LIN-ALG-APPL,
volume = "10",
number = "7",
pages = "595--602",
month = oct # "\slash " # nov,
year = "2003",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.338",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
MRclass = "15A42 (05C50 15A57)",
MRnumber = "MR2030625 (2004m:15028)",
MRreviewer = "Jorma Kaarlo Merikoski",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "http://www.interscience.wiley.com/jpages/1070-5325;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
http://www3.interscience.wiley.com/journalfinder.html",
note = "Dedicated to the 70th birthday of Ivo Marek",
URL = "https://www.math.utah.edu/pub/tex/bib/numlinaa.bib",
ZMnumber = "02206752",
abstract = "For certain specified real symmetric matrices {$A$}
the spectral diameter of {$ A - \operatorname {diag}(A)
$} is less than or equal to the spectral diameter of
{$A$}. Included are irreducible matrices whose
undirected graphs have no cycles.",
acknowledgement = ack-nhfb,
classmath = "*65F99 Numerical linear algebra 65F15 Eigenvalues
(numerical linear algebra)",
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
keywords = "acyclic; spectral diameter; tridiagonal matrices",
onlinedate = "8 Oct 2003",
}
@TechReport{Dhillon:2004:DIM,
author = "Inderjit S. Dhillon and Beresford N. Parlett and
Christof V{\"o}mel",
title = "The Design and Implementation of the {MRRR}
Algorithm",
type = "LAPACK Working Note",
number = "162",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = feb,
year = "2004",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "UT-CS-04-541, December, 2004.",
URL = "https://www.math.utah.edu/pub/tex/bib/lawn.bib;
http://www.netlib.org/lapack/lawns/lawn162.ps;
http://www.netlib.org/lapack/lawnspdf/lawn162.pdf",
acknowledgement = ack-nhfb,
}
@Article{Dhillon:2004:MRC,
author = "Inderjit S. Dhillon and Beresford N. Parlett",
title = "Multiple representations to compute orthogonal
eigenvectors of symmetric tridiagonal matrices",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "387",
number = "1",
pages = "1--28",
day = "1",
month = aug,
year = "2004",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2003.12.028",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (15A18)",
MRnumber = "MR2069265 (2005d:65055)",
MRreviewer = "Daniel Kressner",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
http://www.sciencedirect.com/science/journal/00243795",
URL = "https://www.math.utah.edu/pub/tex/bib/linala2000.bib",
ZMnumber = "1055.65048",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 15A18
Eigenvalues of matrices, etc. 15A23 Factorization of
matrices",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "clustered eigenvalues; eigenvectors; high relative
accuracy; orthogonality; relatively robust
representations; symmetric tridiagonal matrix",
reviewer = "Alan L.Andrew (Bundoora)",
}
@Article{Dhillon:2004:OER,
author = "Inderjit S. Dhillon and Beresford N. Parlett",
title = "Orthogonal Eigenvectors and Relative Gaps",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "25",
number = "3",
pages = "858--899",
month = jul,
year = "2004",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/25/3;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "See original LAPACK Working note in
\cite{Dhillon:2002:OER}.",
URL = "http://epubs.siam.org/sam-bin/dbq/article/37011",
ZMnumber = "1068.65046",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F25
Orthogonalization (numerical linear algebra) 15A23
Factorization of matrices",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
keywords = "$qd$-type algorithm; algorithm GETvec; bidiagonal
factorization; comparison of methods; eigenvectors;
inverse iteration; numerical examples; orthogonality;
symmetric tridiagonal matrix",
reviewer = "Juan Ramon Torregrosa Sanchez (Valencia)",
}
@TechReport{Parlett:2004:HMA,
author = "Beresford N. Parlett and Christof V{\"o}mel",
title = "How the {MRRR} Algorithm Can Fail on Tight Eigenvalue
Clusters",
type = "LAPACK Working Note",
number = "163",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
pages = "15",
month = dec,
year = "2004",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "UT-CS-04-542, December, 2004.",
URL = "http://www.eecs.berkeley.edu/Pubs/TechRpts/2004/CSD-04-1367.pdf;
https://www.math.utah.edu/pub/tex/bib/lawn.bib;
http://www.netlib.org/lapack/lawns/lawn163.ps;
http://www.netlib.org/lapack/lawnspdf/lawn163.pdf",
acknowledgement = ack-nhfb,
}
@Article{Bai:2005:GSO,
author = "Zhong-Zhi Bai and Beresford N. Parlett and Zeng-Qi
Wang",
title = "On generalized successive overrelaxation methods for
augmented linear systems",
journal = j-NUM-MATH,
volume = "102",
number = "1",
pages = "1--38",
month = nov,
year = "2005",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-005-0643-0",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F10",
MRnumber = "MR2206670 (2006j:65077)",
MRreviewer = "Heike Fa{\ss}bender",
bibdate = "Sat Nov 26 18:13:08 MST 2005",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=102&issue=1;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=102&issue=1&spage=1",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Dhillon:2005:GMM,
author = "Inderjit S. Dhillon and Beresford N. Parlett and
Christof V{\"o}mel",
title = "Glued Matrices and the {MRRR} Algorithm",
journal = j-SIAM-J-SCI-COMP,
volume = "27",
number = "2",
pages = "496--510",
month = mar,
year = "2005",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/040620746",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F15",
MRnumber = "MR2202231 (2006k:65098)",
MRreviewer = "Cristina Tablino Possio",
bibdate = "Mon Nov 21 14:52:52 MST 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/27/2;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/62074",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@TechReport{Marques:2005:SCM,
author = "Osni A. Marques and Beresford N. Parlett and Christof
V{\"o}mel",
title = "Subset Computations with the {MRRR} Algorithm",
type = "LAPACK Working Note",
number = "167",
institution = "Computer Science Division, University of California,
Berkeley",
address = "Berkeley, CA, USA",
pages = "9",
day = "26",
month = sep,
year = "2005",
bibdate = "Mon Mar 20 12:30:00 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "Also issued as Technical Report UCB//CSD-05-1392",
URL = "http://www.netlib.org/lapack/lawnspdf/lawn167.pdf",
abstract = "The main advantage of inverse iteration over the QR
algorithm and Divide \& Conquer for the symmetric
tridiagonal eigenproblem is that subsets of eigenpairs
can be computed at reduced cost.
The MRRR algorithm (MRRR = Multiple Relatively Robust
Representations) is a clever variant of inverse
iteration without the need for reorthogonalization.
{\tt stegr}, the current version of MRRR in LAPACK 3.0,
does not allow for subset computations. The next
release of {\tt stegr} is designed to compute a
(sub-)set of $k$ eigenpairs with {$ O(k n) $}
operations.
Because of the special way in which eigenvectors are
computed, MRRR subset computations are more complicated
than when using inverse iteration. Unlike the latter,
MRRR sometimes cannot ignore the unwanted part of the
spectrum.
We describe the problems with what we call false
singletons. These are eigenvalues that appear to be
isolated with respect to the wanted eigenvalues but in
fact belong to a tight cluster of unwanted eigenvalues.
This paper analyzes these complications and ways to
deal with them.",
acknowledgement = ack-nhfb,
keywords = "false singleton; Multiple relatively robust
representations; numerically orthogonal eigenvectors;
subset computation; symmetric tridiagonal matrix",
}
@Article{Parlett:2005:BMD,
author = "Beresford N. Parlett",
title = "A bidiagonal matrix determines its hyperbolic {SVD} to
varied relative accuracy",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "26",
number = "4",
pages = "1022--1057",
year = "2005",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479803424980",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A18 (15A23 65F15)",
MRnumber = "MR2178210 (2006k:15033)",
MRreviewer = "Alan L. Andrew",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
ZMnumber = "02206316",
abstract = "Let {$ T = L \Omega L^t $} be an invertible,
unreduced, indefinite tridiagonal symmetric matrix with
{$ \Omega $} a diagonal signature matrix. We provide
error bounds on the (relative) change in an eigenvalue
and the angular change in its eigenvector when the
entries in {$L$} suffer small relative changes. Our
results extend those of Demmel and Kahan for {$ \Omega
= I $}. The relative condition number for an eigenvalue
exceeds by 1 its absolute condition number as an
eigenvalue of {$ \Omega L^t L $}. The condition number
of an eigenvector is a weighted sum of the relative
separations of the eigenvalue from each of the
others.\par
A small example shows that very small eigenpairs can be
robust even when the large eigenvalues are extremely
sensitive. When {$L$} is well conditioned for
inversion, then all eigenvalues are robust and the
eigenvectors depend only on the relative separations.",
acknowledgement = ack-nhfb,
classmath = "*15A18 Eigenvalues of matrices, etc. 15A23
Factorization of matrices",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
keywords = "bidiagonal; condition number; eigenvector; hyperbolic
SVD",
}
@Article{Zheng:2005:TLT,
author = "Xiaoqiang Zheng and Beresford N. Parlett and Alex
Pang",
title = "Topological Lines in {$3$D} Tensor Fields and
Discriminant {Hessian} Factorization",
journal = j-IEEE-TRANS-VIS-COMPUT-GRAPH,
volume = "11",
number = "4",
pages = "395--407",
month = jul # "\slash " # aug,
year = "2005",
CODEN = "ITVGEA",
DOI = "https://doi.org/10.1109/TVCG.2005.67",
ISSN = "1077-2626 (print), 1941-0506 (electronic), 2160-9306",
ISSN-L = "1077-2626",
bibdate = "Thu Nov 10 07:58:55 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Visualization and Computer
Graphics",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2945",
}
@InProceedings{Zheng:2005:TST,
author = "Xiaoqiang Zheng and Beresford N. Parlett and Alex T.
Pang",
booktitle = "{IEEE Visualization, 2005. VIS 05}",
title = "Topological structures of {$3$D} tensor fields",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "551--558",
year = "2005",
DOI = "https://doi.org/10.1109/VISUAL.2005.1532841",
bibdate = "Tue Mar 5 09:03:06 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1532841",
acknowledgement = ack-nhfb,
journal-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=10269",
}
@Article{Barlow:2006:PSI,
author = "Jesse L. Barlow and Beresford N. Parlett and Kresimir
Veseli{\'c}",
title = "Preface [Special issue on accurate solutions of
eigenvalue problems]",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "417",
number = "2--3",
pages = "381--381",
year = "2006",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2006.03.020",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65-06 (15A18 65F15)",
MRnumber = "MR2250319",
bibdate = "Fri May 14 12:29:46 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
http://www.sciencedirect.com/science/journal/00243795",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Dhillon:2006:DIM,
author = "Inderjit S. Dhillon and Beresford N. Parlett and
Christof V{\"o}mel",
title = "The design and implementation of the {MRRR}
algorithm",
journal = j-TOMS,
volume = "32",
number = "4",
pages = "533--560",
month = dec,
year = "2006",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1186785.1186788",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65F15 (65Y20)",
MRnumber = "MR2290445",
bibdate = "Sat Apr 14 09:48:57 MDT 2007",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
abstract = "In the 1990's, Dhillon and Parlett devised the
algorithm of multiple relatively robust representations
(MRRR) for computing numerically orthogonal
eigenvectors of a symmetric tridiagonal matrix {$T$}
with {$ O(n^2) $} cost. While previous publications
related to MRRR focused on theoretical aspects of the
algorithm, a documentation of software issues has been
missing. In this article, we discuss the design and
implementation of the new MRRR version STEGR that will
be included in the next LAPACK release. By giving an
algorithmic description of MRRR and identifying
governing parameters, we hope to make STEGR more easily
accessible and suitable for future performance tuning.
Furthermore, this should help users understand design
choices and tradeoffs when using the code.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
}
@Article{Marques:2006:CES,
author = "Osni A. Marques and Beresford N. Parlett and Christof
V{\"o}mel",
title = "Computations of eigenpair subsets with the {MRRR}
algorithm",
journal = j-NUM-LIN-ALG-APPL,
volume = "13",
number = "8",
pages = "643--653",
year = "2006",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.493",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
MRclass = "65F15",
MRnumber = "MR2259547 (2007h:65033)",
MRreviewer = "Marc Van Barel",
bibdate = "Fri May 14 12:30:20 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
}
@Article{Parlett:2006:AOM,
author = "B. N. Parlett and E. Barszcz",
title = "Another orthogonal matrix",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "417",
number = "2-3",
pages = "342--346",
year = "2006",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2005.03.032",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A57 (15A23)",
MRnumber = "MR2250316 (2007e:15020)",
MRreviewer = "Zhongxiao Jia",
bibdate = "Fri May 14 12:30:52 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@TechReport{Demmel:2007:PAL,
author = "James W. Demmel and Osni A. Marques and Beresford N.
Parlett and Christof V{\"o}mel",
title = "Performance and Accuracy of {LAPACK}'s Symmetric
Tridiagonal Eigensolvers",
type = "LAPACK Working Note",
number = "183",
institution = inst-UCB-EECS,
address = inst-UCB-EECS:adr,
month = apr,
year = "2007",
MRclass = "15A18, 15A23",
bibdate = "Fri Apr 24 12:25:43 2009",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://www.netlib.org/lapack/lawnspdf/lawn183.pdf",
abstract = "We compare four algorithms from the latest LAPACK 3.1
release for computing eigenpairs of a symmetric
tridiagonal matrix. These include QR iteration,
bisection and inverse iteration (BI), the
Divide-and-Conquer method (DC), and the method of
Multiple Relatively Robust Representations
(MR).\par
Our evaluation considers speed and accuracy when
computing all eigenpairs, and additionally subset
computations. Using a variety of carefully selected
test problems, our study includes a variety of today's
computer architectures.\par
Our conclusions can be summarized as follows. (1) DC
and MR are generally much faster than QR and BI on
large matrices. (2) MR almost always does the fewest
floating point operations, but at a lower MFlop rate
than all the other algorithms. (3) The exact
performance of MR and DC strongly depends on the matrix
at hand. (4) DC and QR are the most accurate algorithms
with observed accuracy {$ O(\sqrt {n} \epsilon) $}. The
accuracy of BI and MR is generally {$ O(n \epsilon) $}.
(5) MR is preferable to BI for subset computations.",
acknowledgement = ack-nhfb,
}
@TechReport{Demmel:2007:PNL,
author = "James W. Demmel and Jack J. Dongarra and Beresford N.
Parlett and William Kahan and Ming Gu and David S.
Bindel and Yozo Hida and Xiaoye S. Li and Osni A.
Marques and E. Jason Riedy and Christof V{\"o}mel and
Julien Langou and Piotr Luszczek and Jakub Kurzak and
Alfredo Buttari and Julie Langou and Stanimire Tomov",
title = "Prospectus for the Next {LAPACK} and {ScaLAPACK}
Libraries",
type = "LAPACK Working Note",
number = "181",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
day = "11",
month = mar,
year = "2007",
bibdate = "Fri Apr 24 12:25:43 2009",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://www.netlib.org/lapack/lawnspdf/lawn181.pdf",
acknowledgement = ack-nhfb,
utknumber = "UT-CS-07-592",
}
@TechReport{Demmel:2007:TIL,
author = "James W. Demmel and Osni A. Marques and Beresford N.
Parlett and Christof V{\"o}mel",
title = "A Testing Infrastructure for {LAPACK}'s Symmetric
Eigensolvers",
type = "LAPACK Working Note",
number = "182",
institution = inst-UCB-EECS,
address = inst-UCB-EECS:adr,
month = apr,
year = "2007",
MRclass = "15A18, 15A23",
bibdate = "Fri Apr 24 12:25:43 2009",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://www.netlib.org/lapack/lawnspdf/lawn182.pdf",
abstract = "LAPACK is often mentioned as a positive example of a
software library that encapsulates complex, robust, and
widely used numerical algorithms for a wide range of
applications. At installation time, the user has the
option of running a (limited) number of test cases to
verify the integrity of the installation process. On
the algorithm developer's side, however, more
exhaustive tests are usually performed to study
algorithm behavior on a variety of problem settings and
also computer architectures. In this process, difficult
test cases need to be found that reflect particular
challenges of an application or push algorithms to
extreme behavior. These tests are then assembled into a
comprehensive collection, therefore making it possible
for any new or competing algorithm to be stressed in a
similar way. This note describes such an infrastructure
for exhaustively testing the symmetric tridiagonal
eigensolvers implemented in LAPACK. It consists of two
parts: a selection of carefully chosen test matrices
with particular idiosyncrasies and a portable testing
framework that allows easy testing and data processing.
The tester facilitates experiments with algorithmic
choices, parameter and threshold studies, and
performance comparisons on different architectures.",
acknowledgement = ack-nhfb,
}
@Article{Parlett:2007:WHM,
author = "Beresford N. Parlett",
title = "What {Hadamard} missed",
journal = "Internat. J. Appl. Sci. Comput.",
volume = "14",
number = "3",
pages = "116--136",
year = "2007",
ISSN = "1089-0025",
MRclass = "65F15",
MRnumber = "MR2374179 (2008j:65060)",
bibdate = "Fri May 14 12:31:28 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Applied Science and
Computations",
}
@Article{Demmel:2008:PAL,
author = "James W. Demmel and Osni A. Marques and Beresford N.
Parlett and Christof V{\"o}mel",
title = "Performance and accuracy of {LAPACK}'s symmetric
tridiagonal eigensolvers",
journal = j-SIAM-J-SCI-COMP,
volume = "30",
number = "3",
pages = "1508--1526",
year = "2008",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/070688778",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F15 (65Y20)",
MRnumber = "MR2398876 (2008m:65116)",
MRreviewer = "Ross A. Lippert",
bibdate = "Fri May 14 12:31:44 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Liesen:2008:NSP,
author = "J{\"o}rg Liesen and Beresford N. Parlett",
title = "On nonsymmetric saddle point matrices that allow
conjugate gradient iterations",
journal = j-NUM-MATH,
volume = "108",
number = "4",
pages = "605--624",
month = feb,
year = "2008",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-007-0131-9",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F10",
MRnumber = "MR2369206 (2009c:65076)",
MRreviewer = "Rafael J. Villanueva",
bibdate = "Tue Jul 8 09:49:13 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Parlett:2008:MPR,
author = "Beresford Parlett and Gilbert Strang",
title = "Matrices with prescribed {Ritz} values",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "428",
number = "7",
pages = "1725--1739",
year = "2008",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2007.10.040",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A18 (15A29)",
MRnumber = "MR2388652 (2009c:15015)",
MRreviewer = "Claude M. Vall{\'e}e",
bibdate = "Fri May 14 12:33:07 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Misc{Parlett:2008:RDE,
author = "Beresford N. Parlett",
title = "Recollections (designed to entertain or enlighten)",
howpublished = "Web document",
day = "30",
month = mar,
year = "2008",
bibdate = "Mon Mar 31 16:55:05 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "The Bay Area Scientific Computing Day, BASCD08,
honoring Profs. Kahan and Parlett, 29--30 March,
2008.",
URL = "http://math.berkeley.edu/bascd08",
acknowledgement = ack-nhfb,
}
@Article{Ferreira:2009:CAO,
author = "Carla Ferreira and Beresford Parlett",
title = "Convergence of {$ L R $} algorithm for a one-point
spectrum tridiagonal matrix",
journal = j-NUM-MATH,
volume = "113",
number = "3",
pages = "417--431",
month = sep,
year = "2009",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-009-0238-2",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F15",
MRnumber = "MR2534131",
bibdate = "Fri May 14 08:10:17 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=????&volume=113&issue=3;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=????&volume=113&issue=3&spage=417",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Marques:2009:ATI,
author = "Osni A. Marques and Christof V{\"o}mel and James W.
Demmel and Beresford N. Parlett",
title = "{Algorithm 880}: a testing infrastructure for
symmetric tridiagonal eigensolvers",
journal = j-TOMS,
volume = "35",
number = "1",
pages = "8:1--8:13",
month = jul,
year = "2009",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1377603.1377611",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65F15 (65Y20)",
MRnumber = "MR2501873",
bibdate = "Tue Aug 5 18:12:48 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "LAPACK is often mentioned as a positive example of a
software library that encapsulates complex, robust, and
widely used numerical algorithms for a wide range of
applications. At installation time, the user has the
option of running a (limited) number of test cases to
verify the integrity of the installation process. On
the algorithm developer's side, however, more
exhaustive tests are usually performed to study
algorithm behavior on a variety of problem settings and
also computer architectures. In this process, difficult
test cases need to be found that reflect particular
challenges of an application or push algorithms to
extreme behavior. These tests are then assembled into a
comprehensive collection, therefore making it possible
for any new or competing algorithm to be stressed in a
similar way. This article describes an infrastructure
for exhaustively testing the symmetric tridiagonal
eigensolvers implemented in LAPACK. It consists of two
parts: a selection of carefully chosen test matrices
with particular idiosyncrasies and a portable testing
framework that allows for easy testing and data
processing. The tester facilitates experiments with
algorithmic choices, parameter and threshold studies,
and performance comparisons on different
architectures.",
acknowledgement = ack-nhfb,
articleno = "8",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
keywords = "accuracy; design; eigenvalues; eigenvectors;
implementation; LAPACK; numerical software;
performance; symmetric matrix; test matrices; testing",
}
@Article{Parlett:2009:RCG,
author = "Beresford N. Parlett",
title = "A result complementary to {Gersgorin}'s {Circle
Theorem}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "431",
number = "1-2",
pages = "20--27",
year = "2009",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2009.01.030",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A18 (15A42)",
MRnumber = "MR2522553 (2010e:15009)",
MRreviewer = "Fuad Kittaneh",
bibdate = "Fri May 14 12:36:11 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Parlett:2009:RFM,
author = "Beresford N. Parlett",
title = "Review of {{\em Functions of Matrices: Theory and
Computation}, Nicholas J. Higham. SIAM, Philadelphia,
PA (2008), xx + 425 pp}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "430",
number = "11--12",
pages = "3139--3140",
day = "1",
month = jun,
year = "2009",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Wed Mar 30 14:20:44 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
http://www.sciencedirect.com/science/journal/00243795",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Parlett:2009:SGM,
author = "Beresford N. Parlett and Christof V{\"o}mel",
title = "The spectrum of a glued matrix",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "1",
pages = "114--132",
year = "2009",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/070687062",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A18 (15A23)",
MRnumber = "MR2487053",
MRreviewer = "Ion Zaballa",
bibdate = "Fri May 14 12:36:19 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Shomron:2009:LAM,
author = "Noam Shomron and Beresford N. Parlett",
title = "Linear algebra meets {Lie} algebra: the
{Kostant--Wallach} theory",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "431",
number = "10",
pages = "1745--1767",
year = "2009",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2009.06.007",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A18 (14R20 17Bxx)",
MRnumber = "MR2567787",
bibdate = "Fri May 14 12:40:55 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Dubrulle:2010:RTM,
author = "A. A. Dubrulle and B. N. Parlett",
title = "Revelations of a transposition matrix",
journal = j-J-COMPUT-APPL-MATH,
volume = "233",
number = "5",
pages = "1217--1219",
day = "1",
month = jan,
year = "2010",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/j.cam.2008.11.018",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65F15 (15A18)",
MRnumber = "MR2559358",
bibdate = "Sat Feb 25 13:24:20 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042709001745",
ZMnumber = "1179.15003",
abstract = "Matrix transposition, which is most commonly thought
of as a simple exchange of the entries of a matrix, is
a similarity transformation. While this transformation
is not unique, its composition is determined by the
spectral configuration of the matrix to which it
applies. We use this relationship here to show that,
conversely, certain properties of the spectrum of a
matrix can be inferred from some knowledge of its
transposition matrices.\par
The paper is organised as follows. Section 2 is a
detailed analysis of the relationship between the
spectrum of a matrix and the constituents of an
associated transposition matrix. In Section 3, we
discuss the spectral properties revealed by
transposition matrices and an application to the
product of two skew-symmetric matrices.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Parlett:2010:BRB,
author = "Beresford Parlett",
title = "Book Review: {{\booktitle{The matrix eigenvalue
problem: GR and Krylov subspace methods}} [book review
of MR2383888]; \booktitle{Numerical methods for general
and structured eigenvalue problems} [book review of
MR2164298]}",
journal = j-SIAM-REVIEW,
volume = "52",
number = "4",
pages = "771--774",
month = "????",
year = "2010",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "00A17",
MRnumber = "2743241",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Gutknecht:2011:HWA,
author = "Martin H. Gutknecht and Beresford N. Parlett",
title = "From qd to {$ L R $}, or, how were the qd and {$ L R
$} algorithms discovered?",
journal = j-IMA-J-NUMER-ANAL,
volume = "31",
number = "3",
pages = "741--754",
month = jul,
year = "2011",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/drq003",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65-03 (01A60 15A21 65F15 65H04)",
MRnumber = "2832778",
MRreviewer = "Fabio Di Benedetto",
bibdate = "Fri Jul 15 12:37:42 MDT 2011",
bibsource = "http://imanum.oxfordjournals.org/content/31/3.toc;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://imajna.oxfordjournals.org/content/31/3/741.full.pdf+html",
ZMnumber = "1222.65032",
abstract = "Perhaps, the most astonishing idea in eigenvalue
computation is Rutishauser's idea of applying the {$ L
R $} transform to a matrix for generating a sequence of
similar matrices that become more and more triangular.
The same idea is the foundation of the ubiquitous {$ Q
R $} algorithm. It is well known that this idea
originated in Rutishauser's qd algorithm, which
precedes the {$ L R $} algorithm and can be understood
as applying {$ L R $} to a tridiagonal matrix. But how
did Rutishauser discover qd and when did he find
the qd-{$ L R $} connection? We checked some of
the early sources and have come up with an
explanation.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
onlinedate = "May 27, 2010",
}
@Article{Morzfeld:2011:TSO,
author = "Matthias Morzfeld and Fai Ma and Beresford N.
Parlett",
title = "The Transformation of Second-Order Linear Systems into
Independent Equations",
journal = j-SIAM-J-APPL-MATH,
volume = "71",
number = "4",
pages = "1026--1043",
month = "????",
year = "2011",
CODEN = "SMJMAP",
DOI = "https://doi.org/10.1137/100818637",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
MRclass = "34C20 (34A30 70J10)",
MRnumber = "2819506",
MRreviewer = "O. A. Sebakhy",
bibdate = "Fri Jul 22 09:01:56 MDT 2011",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIAP/71/4;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
URL = "http://epubs.siam.org/siap/resource/1/smjmap/v71/i4/p1026_s1",
ZMnumber = "1232.34060",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
onlinedate = "July 07, 2011",
}
@Article{Vomel:2011:DLI,
author = "Christof V{\"o}mel and Beresford N. Parlett",
title = "Detecting Localization in an Invariant Subspace",
journal = j-SIAM-J-SCI-COMP,
volume = "33",
number = "6",
pages = "3447--3467",
month = "????",
year = "2011",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/09077624X",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F15 (15A18)",
MRnumber = "2862021",
MRreviewer = "Fabio Di Benedetto",
bibdate = "Thu Feb 9 06:05:59 MST 2012",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/33/6;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
URL = "http://epubs.siam.org/sisc/resource/1/sjoce3/v33/i6/p3447_s1",
ZMnumber = "1232.15011",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "December 13, 2011",
}
@Article{Ferreira:2012:SEU,
author = "Carla Ferreira and Beresford Parlett and Froil{\'a}n
M. Dopico",
title = "Sensitivity of eigenvalues of an unsymmetric
tridiagonal matrix",
journal = j-NUM-MATH,
volume = "122",
number = "3",
pages = "527--555",
month = nov,
year = "2012",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-012-0470-z",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "15A42 (15A12 65F15)",
MRnumber = "2983090",
MRreviewer = "Chun-Hua Guo",
bibdate = "Tue Nov 6 10:54:38 MST 2012",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=122&issue=3;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/nummath2010.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=122&issue=3&spage=527",
ZMnumber = "06134329",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Li:2014:IDA,
author = "Shengguo Li and Ming Gu and Beresford N. Parlett",
title = "An Improved {DQDS} Algorithm",
journal = j-SIAM-J-SCI-COMP,
volume = "36",
number = "3",
pages = "C290--C308",
month = "????",
year = "2014",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/120881087",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F15",
MRnumber = "3224580",
MRreviewer = "Heike Fa\ss bender",
bibdate = "Sat Sep 13 12:24:04 MDT 2014",
bibsource = "http://epubs.siam.org/toc/sjoce3/36/3;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
ZMnumber = "06340661",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2014",
}
@Article{Parlett:2016:IEP,
author = "Beresford Parlett and Froil{\'a}n M. Dopico and Carla
Ferreira",
title = "The Inverse Eigenvector Problem for Real Tridiagonal
Matrices",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "37",
number = "2",
pages = "577--597",
month = "????",
year = "2016",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/15M1025293",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A29 (15A18 65F15 65F18)",
MRnumber = "3490889",
MRreviewer = "Hua Dai",
bibdate = "Fri Sep 23 08:21:42 MDT 2016",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/37/2;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "January 2016",
}
@Article{Ferreira:2020:EWM,
author = "Carla Ferreira and Beresford Parlett",
title = "Eigenpairs of {Wilkinson} Matrices",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "41",
number = "3",
pages = "1388--1415",
month = "????",
year = "2020",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/20M1327343",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (15A18)",
MRnumber = "4151476",
MRreviewer = "Jin Yun Yuan",
bibdate = "Fri Mar 12 10:18:03 MST 2021",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/41/3;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "January 2020",
}
@Article{Ferreira:2022:RTD,
author = "Carla Ferreira and Beresford Parlett",
title = "A real triple dqds algorithm for the nonsymmetric
tridiagonal eigenvalue problem",
journal = j-NUM-MATH,
volume = "150",
number = "2",
pages = "373--422",
month = feb,
year = "2022",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-021-01254-z",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Thu Feb 10 08:03:50 MST 2022",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/nummath2020.bib",
URL = "http://link.springer.com/article/10.1007/s00211-021-01254-z",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
%%% ====================================================================
%%%
%%% Part 2 (of 2): publications about Beresford Parlett and his works
%%%
%%% Bibliography entries, sorted by year, and then by citation label
%%% (with ``bibsort -byyear'')
@Article{Bunch:1995:EDB,
author = "James R. Bunch",
title = "Editorial: Dedicated to {Beresford Parlett} and
{William Kahan}",
journal = j-NUM-LIN-ALG-APPL,
volume = "2",
number = "2",
pages = "85--85",
year = "1995",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.1680020202",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
bibdate = "Sat Jan 20 06:15:41 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/numlinaa.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
}
@Article{Davies:2003:SPA,
author = "P. I. Davies and N. J. Higham",
title = "A {Schur--Parlett} algorithm for computing matrix
functions",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "25",
number = "2",
pages = "464--485",
month = "????",
year = "2003",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479802410815",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F30",
MRnumber = "2047429",
bibdate = "Thu Jun 6 12:11:59 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Koikari:2009:ABS,
author = "Souji Koikari",
title = "{Algorithm 894}: {On} a block {Schur--Parlett}
algorithm for $ \varphi $-functions based on the
sep-inverse estimate",
journal = j-TOMS,
volume = "36",
number = "2",
pages = "12:1--12:20",
month = mar,
year = "2009",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1499096.1499101",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65P10",
MRnumber = "2738193",
bibdate = "Fri Apr 3 17:44:12 MDT 2009",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "FORTRAN 95 software is provided for computing the
matrix values of $ \varphi $-functions required in
exponential integrators. The subroutines in the library
accept as their argument a full, diagonal, or upper
quasitriangular matrix with real or complex entries in
one of four precisions. Two different algorithms are
implemented, one is the scaling and squaring method,
and the other is a modified block Schur--Parlett
algorithm. In the latter algorithm, a recursive
three-by-three blocking is applied to the argument
based on an estimate of the sep-inverse function. The
estimation of the sep-inverse function is carried out
by Hager--Higham estimator implemented as the
subroutine xLACON in LAPACK. Our modifications to the
block Schur--Parlett algorithm are described together
with the results of numerical experiments.",
acknowledgement = ack-nhfb,
articleno = "12",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
keywords = "$\varphi$-functions; block Schur--Parlett algorithm;
exponential integrators; matrix functions",
}
@Article{Schulman:2017:ACM,
author = "Leonard J. Schulman and Alistair Sinclair",
title = "Analysis of a Classical Matrix Preconditioning
Algorithm",
journal = j-J-ACM,
volume = "64",
number = "2",
pages = "9:1--9:23",
month = jun,
year = "2017",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/2988227",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
bibdate = "Fri Sep 8 08:45:18 MDT 2017",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/jacm.bib",
abstract = "We study a classical iterative algorithm for balancing
matrices in the $ L_\infty $ norm via a scaling
transformation. This algorithm, which goes back to
Osborne and Parlett 8 Reinsch in the 1960s, is
implemented as a standard preconditioner in many
numerical linear algebra packages. Surprisingly,
despite its widespread use over several decades, no
bounds were known on its rate of convergence. In this
article, we prove that, for any irreducible $ n \times
n $ (real or complex) input matrix $A$, a natural
variant of the algorithm converges in $ O(n^3 \log (n
\rho / \epsilon))$ elementary balancing operations,
where $ \rho $ measures the initial imbalance of $A$
and $ \epsilon $ is the target imbalance of the output
matrix. (The imbalance of $A$ is $ | \log (a_i^{\rm
out} / a_i^{\rm in})|$, where $ a_i^{\rm out}$, $
a_i^{\rm in}$ are the maximum entries in magnitude in
the $i$ th row and column, respectively.) This bound is
tight up to the $ \log n$ factor. A balancing operation
scales the $i$ th row and column so that their maximum
entries are equal, and requires $ O(m / n)$ arithmetic
operations on average, where $m$ is the number of
nonzero elements in $A$. Thus, the running time of the
iterative algorithm is $ {\tilde {O}}(n^2 m)$. This is
the first time bound of any kind on any variant of the
Osborne--Parlett--Reinsch algorithm. We also prove a
conjecture of Chen that characterizes those matrices
for which the limit of the balancing process is
independent of the order in which balancing operations
are performed.",
acknowledgement = ack-nhfb,
articleno = "9",
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Wang:2020:KPJ,
author = "Yunjie Wang and Gang Wu",
title = "On the {Kahan--Parlett--Jiang} theorem --- a globally
optimal backward perturbation error for two-sided
invariant subspaces",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "602",
number = "??",
pages = "73--92",
day = "1",
month = oct,
year = "2020",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2020.05.003",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Fri Mar 12 08:38:22 MST 2021",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/linala2020.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0024379520302342",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
%%% ====================================================================
%%% Cross-referenced entries must come last:
@Proceedings{Ralston:1967:MMD,
editor = "Anthony Ralston and Herbert S. Wilf",
booktitle = "Mathematical Methods for Digital Computers",
title = "Mathematical Methods for Digital Computers",
volume = "II",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "x + 287",
year = "1967",
ISBN = "0-471-70686-8 (vol. 1), 0-471-70689-2 (vol. 2),
0-471-70690-6 (vol. 3)",
ISBN-13 = "978-0-471-70686-1 (vol. 1), 978-0-471-70689-2 (vol.
2), 978-0-471-70690-8 (vol. 3)",
LCCN = "????",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Morrell:1969:IPP,
editor = "A. J. H. Morrell",
booktitle = "{Information processing 68: proceedings of IFIP
congress 1968, organized by the International
Federation for Information Processing, Edinburgh, 5--10
August 1968}",
title = "{Information processing 68: proceedings of IFIP
congress 1968, organized by the International
Federation for Information Processing, Edinburgh, 5--10
August 1968}",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "????",
year = "1969",
ISBN = "0-7204-2032-6",
ISBN-13 = "978-0-7204-2032-6",
LCCN = "QA76 .I578",
bibdate = "Fri Nov 11 07:22:32 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
remark = "Volume 1. Mathematics, software. Volume 2. Hardware,
applications.",
subject = "Electronic data processing; Congresses; Electronic
digital computers; Congresses; Machine theory;
Congresses",
}
@Book{Wilkinson:1971:LA,
editor = "James H. Wilkinson and Christian Reinsch",
booktitle = "Linear Algebra",
title = "Linear Algebra",
volume = "II",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 439",
year = "1971",
ISBN = "0-387-05414-6, 3-540-05414-6",
ISBN-13 = "978-0-387-05414-8, 978-3-540-05414-6",
LCCN = "QA251 .W67",
bibdate = "Wed Dec 15 18:44:50 1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/householder-alston-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/gnu.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
series = "Handbook for Automatic Computation, Editors: {F. L.
Bauer, A. S. Householder, F. W. J. Olver, H.
Rutishauser, K. Samelson and E. Stiefel}",
acknowledgement = ack-nhfb,
author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022);
James H. Wilkinson (27 September 1919--5 October
1986)",
tableofcontents = "Part I: Linear systems, least squares and linear
programming \\
J. H. Wilkinson / Introduction to Part I / 1--8 \\
1. Introduction \\
2. List of procedures \\
3. Positive definite symmetric matrices \\
4. Non-positive definite symmetric matrices \\
5. Non-Hermitian matrices \\
6. Least squares and related problems \\
7. The linear programming problem \\
R. S. Martin, G. Peters and J. H. Wilkinson / Symmetric
decomposition of a positive definite matrix / 9--30 \\
Martin, Peters and Wilkinson / Iterative refinement of
the solution of a positive definite system of equations
/ 31--44 \\
F. L. Bauer and C. Reinsch / Inversion of positive
definite matrices by the Gauss-Jordan method / 45--49
\\
Martin and Wilkinson / Symmetric decomposition of
positive definite band matrices / 50--56 \\
T. Ginsburg / The conjugate gradient method / 57--69
\\
Martin and Wilkinson / Solution of symmetric and
unsymmetric band equations and the calculation of
eigenvectors of band matrices / 70--92 \\
H. J. Bowdler, Martin, Peters and Wilkinson / Solution
of real and complex systems of linear equations /
93--110 \\
P. Businger and G. H. Golub / Linear least squares
solutions by Householder transformations / 111--118 \\
Bauer / Elimination with weighted row combinations for
solving linear equations and least squares problems /
119--133 \\
Golub and Reinsch / Singular value decomposition and
least squares solutions / 134--151 \\
R. H. Bartels, J. Stoer and Ch. Zenger / A realization
of the simplex method based on triangular
decompositions / 152--190 \\
Part II: The algebraic eigenvalue problem \\
Wilkinson / Introduction to Part II / 191--201 \\
1. Introduction \\
2. List of procedures \\
3. Real, dense, symmetric matrices \\
4. Symmetric band matrices \\
5. Simultaneous determination of dominant eigenvalues
and eigenvectors of a symmetric sparse matrix \\
6. The generalized symmetric eigenvalue problems $A x =
\lambda B x$ and $A B x = \lambda x$ \\
7. Hermitian matrices \\
8. Real dense unsymmetric matrices \\
9. Unsymmetric band matrices \\
10. Dense unsymmetric matrices with complex elements,
H. Rutishauser / The Jacobi method for real symmetric
matrices / 202--211 \\
Martin, Reinsch and Wilkinson / Householder's
tridiagonalization of a symmetric matrix / 212--226 \\
H. Bowdler, Martin, Reinsch and Wilkinson / The $QR$
and $QL$ algorithms for symmetric matrices / 227--240
\\
A. Dubrulle, Martin and Wilkinson / The implicit $QL$
algorithm / 241--248 \\
W. Barth, Martin, and Wilkinson / Calculation of the
eigenvalues of a symmetric tridiagonal matrix by the
method of bisection / 249--256 \\
Reinsch and Bauer / Rational $QR$ transformation with
Newton shift for symmetric tridiagonal matrices /
257--265 \\
Martin, Reinsch and Wilkinson / The $QR$ algorithm for
band symmetric matrices / 266--272 \\
H. R. Schwarz / Tridiagonalization of a symmetric band
matrix / 273--283 \\
Rutishauser / Simultaneous iteration method for
symmetric matrices / 284--302 \\
Martin and Wilkinson / Reduction of the symmetric
eigenproblem $A x = \lambda B x$ and related problems
to standard form / 303--314 \\
B. N. Parlett and Reinsch / Balancing a matrix for
calculation of eigenvalues and eigenvectors / 315--326
\\
P. J. Eberlein and J. Boothroyd / Solution to the
eigenproblem by a norm reducing Jacobi type method /
327--338 \\
Martin and Wilkinson / Similarity reduction of a
general matrix to Hessenberg form / 339--358 \\
Martin, Peters and Wilkinson / The $QR$ algorithm for
real Hessenberg matrices / 359--371 \\
Peters and Wilkinson / Eigenvectors of real and complex
matrices by $LR$ and $QR$ triangularizations / 372--395
\\
Martin and Wilkinson / The modified $LR$ algorithm for
complex Hessenberg matrices / 396--403 \\
Eberlein / Solution to the complex eigenproblem by a
norm reducing Jacobi type method / 404--417 \\
Peters and Wilkinson / The calculation of specified
eigenvectors by inverse iteration / 418--439",
}
@Proceedings{Greville:1972:PDP,
editor = "T. N. E. (Thomas Nall Eden) Greville",
booktitle = "{Population dynamics: proceedings of a symposium
conducted by the Mathematics Research Center, the
University of Wisconsin, Madison, June 19--21, 1972}",
title = "{Population dynamics: proceedings of a symposium
conducted by the Mathematics Research Center, the
University of Wisconsin, Madison, June 19--21, 1972}",
volume = "29",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "ix + 445",
year = "1972",
ISBN = "0-12-302940-6",
ISBN-13 = "978-0-12-302940-9",
bibdate = "Fri Nov 11 07:27:17 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
melvyl.cdlib.org:210/CDL90",
note = "Some catalogs show ISBN 0-12-302940-1 with invalid
checksum.",
series = "Mathematics Research Center Publications",
acknowledgement = ack-nhfb,
meetingname = "Symposium on Population Dynamics (1972 : Mathematics
Research Center, University of Wisconsin)",
subject = "Population; Congresses; Mathematics; Congresses;
Models, Theoretical; Congresses",
}
@Proceedings{Bunch:1976:SMC,
editor = "James R. Bunch and Donald J. Rose",
booktitle = "{Sparse Matrix Computations: Proceedings of the
Symposium on Sparse Matrix Computations at Argonne
National Laboratory on September 9--11, 1975}",
title = "{Sparse Matrix Computations: Proceedings of the
Symposium on Sparse Matrix Computations at Argonne
National Laboratory on September 9--11, 1975}",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xi + 453",
year = "1976",
ISBN = "0-12-141050-1",
ISBN-13 = "978-0-12-141050-6",
LCCN = "QA188 .S989 1975",
bibdate = "Sat Oct 22 18:13:05 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Contributors / / ix \\
Preface / / xi \\
I. Design and Analysis of Elimination Algorithms / / 1
\\
1. Graph Theory and Gaussian Elimination / Robert Endre
Tarjan / 3 \\
2. Partitioning Using PAQ / Thomas D. Howell / 23 \\
3. Block Methods for Solving Sparse Linear Systems /
James R. Bunch / 39 \\
4. A Recursive Analysis of Dissection Strategies /
Donald J. Rose and Gregory F. Whitten / 59 \\
5. Applications of an Element Model for Gaussian
Elimination / S. C. Eisenstat, M. H. Schultz, and 4. H.
Sherman / 85 \\
6. An Optimization Problem Arising from Tearing Methods
/ Alberto Sangiovanni-Vincentelli / 97 \\
II. Eigenvalue Problems . / / 111 \\
1. A Bibliographical Tour of the Large, Sparse
Generalized Eigenvalue Problem / G. W. Stewart / 113
\\
2. How Far Should You Go With the Lanczos Process? / W.
Kahan and B. N. Parlett / 131 \\
III. Optimization, Least Squares and Linear Programming
/ / 145 \\
1. Optimization for Sparse Systems / T. L. Magnanti /
147 \\
2. Methods for Sparse Linear Least Squares Problems /
{AA}ke Bj{\"o}rck / 177 \\
3. The Orthogonal Factorization of a Large Sparse
Matrix / Philip E. Gill and Walter Murray / 201 \\
4. A Fast, Stable Implementation of the Simplex Method
Using Bartels-Golub Updating / Michael A. Saunders /
213 \\
5. Using the Steepest-edge Simplex Algorithm to Solve
Sparse Linear Programs / D. Goldfarb / 227 \\
IV. Mathematical Software / / 241 \\
1. Sparse Matrix Software / W. Morven Gentleman and
Alan George / 243 \\
2. Considerations in the Design of Software for Sparse
Gaussian Elimination / S. C. Eisenstat, M. H. Schultz,
and A. H. Sherman / 263 \\
3. Finding the Block Lower Triangular Form of a Sparse
Matrix / Fred Gustavson / 275 \\
V. Matrix Methods for Partial Difference Equations / /
291 \\
1. Marching Algorithms and Block Gaussian Elimination /
Randolph E. Bank / 293 \\
2. A Generalized Conjugate Gradient Method for the
Numerical Solution of Elliptic Partial Differential
Equations / Paul Concus, Gene H. Golub, and Dianne P.
O'Leary / 309 \\
3. Preconditioned Conjugate Gradient Iteration Applied
to Galerkin Methods for a Mildly-Nonlinear Dirichlet
Problem / Jim Douglas, Jr. and Todd Dupont / 333 \\
4. The Sparse Tableau Approach to Finite Element
Assembly / Gary Hachtel / 349 \\
5. A Capacitance Matrix Technique / B. L. Buzbee / 365
\\
6. M-Matrix Theory and Recent Results in Numerical
Linear Algebra / Richard S. Varga / 375 \\
VI. Applications / / 389 \\
1. Sparse Matrix Problems in a Finite Element Open
Ocean Model / Joel E. Hirsh and William L. Briggs / 391
\\
2. Calculation of Normal Modes of Oceans Using a
Lanczos Method / Alan K. Cline, Gene H. Golub, and
George W. Platzman / 409 \\
3. Application of Sparse Matrix Techniques to Reservoir
Simulation / P. T. Woo, S. C. Eisenstat, M. H. Schultz,
and A. H. Sherman / 427 \\
4. On the Origins and Numerical Solution of Some Sparse
Nonlinear Systems / T. A. Porsching / 439",
}
@Proceedings{Bathe:1977:FCA,
editor = "Klaus-J{\"u}rgen Bathe and J. Tinsley (John Tinsley)
Oden and Edward L. Wilson",
booktitle = "{Formulations and computational algorithms in finite
element analysis: U.S.--Germany symposium}",
title = "{Formulations and computational algorithms in finite
element analysis: U.S.--Germany symposium}",
publisher = pub-MIT,
address = pub-MIT:adr,
pages = "xvi + 1091",
year = "1977",
ISBN = "0-262-02127-7",
ISBN-13 = "978-0-262-02127-2",
LCCN = "TA347.F5 F67; TA347.F5 F67",
bibdate = "Fri Nov 11 07:31:16 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
remark = "This book contains the papers presented at the
U.S.--German symposium on finite element methods, held
at MIT, August, 1976.",
subject = "Finite element method; Congresses",
}
@Proceedings{Absi:1980:NME,
editor = "{\'E}lie Absi",
booktitle = "Numerical methods for engineering: 2nd International
Congress = {M{\'e}thodes num{\'e}riques dans les
sciences de l'ing{\'e}nieur: 2e Congr{\`e}s
international}",
title = "Numerical methods for engineering: 2nd International
Congress = {M{\'e}thodes num{\'e}riques dans les
sciences de l'ing{\'e}nieur: 2e Congr{\`e}s
international}",
publisher = pub-DUNOD,
address = pub-DUNOD:adr,
pages = "????",
year = "1980",
ISBN = "2-04-012165-X (vol. 1), 2-04-012194-3 (vol. 2)",
ISBN-13 = "978-2-04-012165-5 (vol. 1), 978-2-04-012194-5 (vol.
2)",
LCCN = "TA329 .C64 1980; TA329 .C64 1980",
bibdate = "Fri Nov 11 07:42:06 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
umlibr.library.umass.edu:210/INNOPAC",
acknowledgement = ack-nhfb,
meetingname = "Colloque international sur les m{\'e}thodes
num{\'e}riques dans les sciences de l'ing{\'e}nieur
(2nd: 1980: Paris)",
remark = "English or French. Organized by the Groupe pour
l'avancement des m{{\'e}}thodes num{\'e}riques dans les
sciences de l'ing{\'e}nieur.",
subject = "Engineering mathematics; Congresses; Numerical
analysis; Congresses",
}
@Book{Arden:1980:WCA,
editor = "Bruce W. Arden",
booktitle = "What can be automated?: The computer science and
engineering research study ({COSERS})",
title = "What can be automated?: The computer science and
engineering research study ({COSERS})",
volume = "3",
publisher = pub-MIT,
address = pub-MIT:adr,
pages = "934",
year = "1980",
ISBN = "0-262-01060-7",
ISBN-13 = "978-0-262-01060-3",
LCCN = "QA76 .W49",
bibdate = "Sun Dec 30 00:09:10 MST 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/signum.bib;
z3950.loc.gov:7090/Voyager",
series = "The MIT Press series in computer science",
acknowledgement = ack-nhfb,
subject = "Computers; Electronic data processing",
}
@Proceedings{Glowinski:1982:CMA,
editor = "R. Glowinski and Jacques Louis Lions",
booktitle = "{Computing methods in applied sciences and
engineering, V: proceedings of the Fifth International
Symposium on Computing Methods in Applied Sciences and
Engineering, Versailles, France, December 14--18,
1981}",
title = "{Computing methods in applied sciences and
engineering, V: proceedings of the Fifth International
Symposium on Computing Methods in Applied Sciences and
Engineering, Versailles, France, December 14--18,
1981}",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "x + 668",
year = "1982",
ISBN = "0-444-86450-4",
ISBN-13 = "978-0-444-86450-5",
LCCN = "QA297 .E53 1981",
bibdate = "Fri Nov 11 07:52:56 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib1;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "International Symposium on Computing Methods in
Applied Sciences and Engineering (5th : 1981 :
Versailles, France)",
remark = "Organized by Institut national de recherche en
informatique et en automatique.. English or French.",
subject = "Numerical analysis; Data processing; Congresses;
Science; Data processing; Congresses; Engineering; Data
processing; Congresses",
}
@Proceedings{Glowinski:1984:CMA,
editor = "R. Glowinski and J.-L. Lions",
booktitle = "Computing Methods in Applied Sciences and Engineering,
{VI}: Proceedings of the Sixth International Symposium
on Computing Methods in Applied Sciences and
Engineering, Versailles, France, December 12--16,
1983",
title = "Computing Methods in Applied Sciences and Engineering,
{VI}: Proceedings of the Sixth International Symposium
on Computing Methods in Applied Sciences and
Engineering, Versailles, France, December 12--16,
1983",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "xiii + 728",
year = "1984",
ISBN = "0-444-87597-2",
ISBN-13 = "978-0-444-87597-6",
LCCN = "QA297 .I57 1983",
bibdate = "Mon Jan 15 11:05:19 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Numrich:1985:SA,
editor = "Robert W. Numrich",
booktitle = "Supercomputer applications",
title = "Supercomputer applications",
publisher = pub-PLENUM,
address = pub-PLENUM:adr,
pages = "viii + 307",
year = "1985",
ISBN = "0-306-42013-9",
ISBN-13 = "978-0-306-42013-9",
LCCN = "QA76.5.S8944 1984a",
bibdate = "Fri Aug 30 08:01:51 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
University of California MELVYL catalog.",
note = "Proceedings of the Supercomputer Applications
Symposium cosponsored by the Purdue University
Computing Center, the Purdue Center for Parallel and
Vector Computing, and Control Data, held October
31--November 1, 1984, in West Lafayette, Indiana.",
acknowledgement = ack-nhfb,
annote = "Published in Proceedings of the Supercomputer
Applications Symposium cosponsored by the Purdue
University Computing Center, the Purdue Center for
Parallel and Vector Computing, and Control Data, held
October 31--November 1, 1984, in West Lafayette,
Indiana.",
keywords = "CYBER 205 (Computer) --- Congresses; Supercomputer
systems --- Applications; Supercomputers ---
Congresses",
}
@Proceedings{Glowinski:1986:CMA,
editor = "R. (Roland) Glowinski and Jacques Louis Lions",
booktitle = "{Computing methods in applied sciences and
engineering, VII: proceedings of the Seventh
International Symposium on Computing Methods in Applied
Sciences and Engineering, Versailles, France, December
9--13, 1985}",
title = "{Computing methods in applied sciences and
engineering, VII: proceedings of the Seventh
International Symposium on Computing Methods in Applied
Sciences and Engineering, Versailles, France, December
9--13, 1985}",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "xii + 648",
year = "1986",
ISBN = "0-444-70059-5",
ISBN-13 = "978-0-444-70059-9",
LCCN = "TA345",
bibdate = "Fri Nov 11 08:21:06 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
library.ox.ac.uk:210/ADVANCE",
acknowledgement = ack-nhfb,
meetingname = "International Symposium on Computing Methods in
Applied Sciences and Engineering 1985 : Versailles,
France, 7th.",
remark = "Includes 1 chapter in French.. There are English and
French forewords.",
subject = "Engineering; Data processing; Congresses; Technology;
Data processing; Congresses",
}
@Proceedings{Glowinski:1988:FIS,
editor = "Roland Glowinski and Gene H. Golub and G{\'e}rard
Meurant and Jacques P{\'e}riaux",
booktitle = "{First International Symposium on Domain Decomposition
Methods for Partial Differential Equations: Proceedings
of the First International Symposium on Domain
Decomposition Methods for Partial Differential
Equations, Ecole Nationale des Ponts et Chauss{\'e}es,
Paris, France, January 7--9, 1987}",
title = "{First International Symposium on Domain Decomposition
Methods for Partial Differential Equations: Proceedings
of the First International Symposium on Domain
Decomposition Methods for Partial Differential
Equations, Ecole Nationale des Ponts et Chauss{\'e}es,
Paris, France, January 7--9, 1987}",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "x + 431",
year = "1988",
ISBN = "0-89871-220-3",
ISBN-13 = "978-0-89871-220-9",
LCCN = "QA402.2 .I571 1987",
MRclass = "65-06 (76-06)",
MRnumber = "89f:65005",
bibdate = "Sun Jan 14 09:19:15 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Cox:1990:RNC,
editor = "M. G. Cox and S. Hammarling",
booktitle = "Reliable numerical computation",
title = "Reliable numerical computation",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xvi + 339",
year = "1990",
ISBN = "0-19-853564-3",
ISBN-13 = "978-0-19-853564-5",
LCCN = "QA297 .R435 1990",
MRclass = "65-06",
MRnumber = "91k:65011",
bibdate = "Fri Dec 20 18:34:52 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Based on papers from a conference in honour of the
late James Hardy Wilkinson (died Sunday 5th October
1986) held at National Physical Laboratory, Teddington,
Middlesex, UK, 8th--10th July 1987.",
price = "US\$75.00",
abstract = "Published to honor the late Jim Wilkinson, the
respected pioneer in numerical analysis, this book
includes contributions from his colleagues and
collaborators, leading experts in their own right. The
breadth of Wilkinson's research is reflected in the
topics covered, which include linear algebra, error
analysis and computer arithmetic algorithms, and
mathematical software. An invaluable reference, the
book is completely up-to-date with the latest
developments on the Lanczos algorithm,
QR-factorizations, error propagation models, parameter
estimation problems, sparse systems, and
shape-preserving splines. Reflecting the current growth
and vitality of this field, the volume is an essential
reference for all numerical analysts.",
acknowledgement = ack-nhfb,
author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)",
tableofcontents = "List of contributors / / xv \\
Prologue. Reflections on Jim Wilkinson / Gene Golub / 1
\\
1. Misconvergence in the Lanczos algorithm / Beresford
Parlett / 7 \\
2. The Lanczos algorithm for a pure imaginary Hermitian
matrix / Charles L. Lawson and Kajal K. Gupta / 25 \\
3. Nearest defective matrices and the geometry of
ill-conditioning / James Demmel / 35 \\
4. Computational aspects of the Jordan canonical form /
Theo Beelen and Paul Van Dooren / 57 \\
5. Some aspects of generalized QR factorizations / C.
C. Paige / 73 \\
6. The multifrontal method in a parallel environment /
I. S. Duff, N. I. M. Gould, M. Lescrenier, and J. K.
Reid / 93 \\
7. A Schur-complement method for sparse quadratic
programming / Philip E. Gill, Walter Murray, Michael A.
Saunders, and Margaret H. Wright / 113 \\
8. A probabilistic round-off error propagation model.
Application to the eigenvalue problem / Fran{\c{c}}oise
Chatelin and Marie Christine Brunet / 139 \\
9. Analysis of the Cholesky decomposition of a
semi-definite matrix / Nicholas J. Higham / 161 \\
10. On the conditioning of parameter estimation
problems / James M. Varah / 187 \\
11. Rounding errors in algebraic process-in level-index
arithmetic / F. W J. Olver / 197 \\
12. Experiments in tearing large sparse systems / Mario
Arioli and lain S. Duff / 207 \\
13. The least-squares solution of linear equations with
block-angular observation matrix / M. G. Cox / 227 \\
14. An iterative method for solving linear inequalities
/ G. W Stewart / 241 \\
15. Iterative refinement and reliable computing / Ake
Bjorck / 249 \\
16. Software for shape-preserving spline interpolation
/ Christian H. Reinsch / 267 \\
17. Experiences with some software engineering
practices in numerical software / D. A. H. Jacobs and
G. Markham / 277 \\
18. Evolution of numerical software for dense linear
algebra / Jack Dongarra and Sven Hammarling / 297 \\
Epilogue. Jim Wilkinson: some after-dinner sentiments /
L. Fox / 329",
}
@Proceedings{Kaashoek:1990:PIS,
editor = "M. A. Kaashoek and J. H. van Schuppen and A. C. M.
Ran",
booktitle = "{Proceedings of the International Symposium MTNS-89}",
title = "{Proceedings of the International Symposium MTNS-89}",
volume = "3--5",
publisher = pub-BIRKHAUSER-BOSTON,
address = pub-BIRKHAUSER-BOSTON:adr,
pages = "????",
year = "1990",
ISBN = "0-8176-3469-X (vol 1), 0-8176-3470-3 (vol. 2),
0-8176-3471-1 (vol. 3), 0-8176-3468-1 (set)",
ISBN-13 = "978-0-8176-3469-8 (vol 1), 978-0-8176-3470-4 (vol. 2),
978-0-8176-3471-1 (vol. 3), 978-0-8176-3468-1 (set)",
LCCN = "QA402 .P766 1989",
bibdate = "Fri Nov 11 07:56:03 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
melvyl.cdlib.org:210/CDL90",
series = "Progress in systems and control theory",
acknowledgement = ack-nhfb,
meetingname = "International Symposium on the Mathematical Theory of
Networks and Systems (9th : 1989 : Amsterdam,
Netherlands)",
remark = "The 1989 International Symposium on the Mathematical
Theory of Networks and Systems (MTNS) \ldots{} held in
Amsterdam, The Netherlands, June 19-23, 1989. Vol. 1.
Realization and modelling in system theory. Vol. 2.
Robust control of linear systems and nonlinear control.
Vol. 3. Signal processing, scattering and operator
theory, and numerical methods.",
subject = "System analysis; Congresses; Control theory;
Congresses",
}
@Proceedings{Nash:1990:HSC,
editor = "Stephen (Stephen G.) Nash",
booktitle = "A History of Scientific Computing",
title = "A History of Scientific Computing",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xix + 359",
year = "1990",
ISBN = "0-201-50814-1",
ISBN-13 = "978-0-201-50814-7",
LCCN = "QA76.17 .H59 1990",
bibdate = "Thu Nov 10 12:03:06 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
z3950.loc.gov:7090/Voyager",
series = "ACM Press history series",
acknowledgement = ack-nhfb,
remark = "Based on papers presented at the Conference on the
History of Scientific and Numeric Computation, held in
Princeton, NJ, 1987.",
subject = "Electronic data processing; History; Science; Data
processing; History",
}
@Proceedings{Albrecht:1991:NTE,
editor = "J. (Julius) Albrecht",
booktitle = "{Numerical treatment of eigenvalue problems: Workshop
in Oberwolfach, February 25-March 3, 1990 = Numerische
Behandlung von Eigenwertaufgaben: Tagung in
Oberwolfach, 25. Februar--3. M{\"a}rz 1990}",
title = "{Numerical treatment of eigenvalue problems: Workshop
in Oberwolfach, February 25-March 3, 1990 = Numerische
Behandlung von Eigenwertaufgaben: Tagung in
Oberwolfach, 25. Februar--3. M{\"a}rz 1990}",
volume = "96",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "ix + 243",
year = "1991",
ISBN = "3-7643-2575-5",
ISBN-13 = "978-3-7643-2575-6",
bibdate = "Fri Nov 11 08:23:50 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
melvyl.cdlib.org:210/CDL90",
series = "International series of numerical mathematics;
Numerical treatment of eigenvalue problems",
acknowledgement = ack-nhfb,
remark = "English and German.",
subject = "Differential equations; Numerical solutions; Data
processing; Congresses; Matrices; Data processing;
Congresses; Eigenvalues; Data processing; Congresses",
}
@Proceedings{Moonen:1993:LAL,
editor = "Marc S. Moonen and Gene H. Golub and Bart L. R. {De
Moor}",
booktitle = "{Linear Algebra for Large Scale and Real-Time
Applications: Proceedings of the NATO Advanced Study
Institute, Leuven, Belgium, August 3--14, 1992}",
title = "{Linear Algebra for Large Scale and Real-Time
Applications: Proceedings of the NATO Advanced Study
Institute, Leuven, Belgium, August 3--14, 1992}",
volume = "232",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "ix + 435",
year = "1993",
ISBN = "0-7923-2151-0",
ISBN-13 = "978-0-7923-2151-4",
LCCN = "QA185.D37 L56 1993",
MRclass = "65-06 (65Fxx 65Y05)",
MRnumber = "94e:65009",
bibdate = "Mon Jan 15 17:53:04 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib",
series = "NATO ASI series. Series E, Applied sciences",
URL = "http://catdir.loc.gov/catdir/enhancements/fy0823/92046135-d.html;
http://www.gbv.de/dms/hbz/toc/ht004938330.pdf;
http://zbmath.org/?q=an:0810.00029",
ZMnumber = "0810.00029",
abstract = "In recent years there has been great interest in large
scale and real-time matrix computations; these
computations arise in a variety of fields, such as
computer graphics, imaging, speech and image
processing, telecommunication, biomedical signal
processing, optimization and so on. This volume, which
is an outgrowth of a NATO ASI, held at Leuven, Belgium,
August 1992, gives an account of recent research
advances in numerical techniques used in large scale
and real-time computations and their implementation on
high performance computers.",
acknowledgement = ack-nhfb,
tableofcontents = "Preface / / xi \\
Invited Lectures / / 1 \\
Large scale structural analysis on massively parallel
computers / P. E. Bj{\o}rstad and J. Cook / 3 \\
Data-parallel BLAS as a basis for LAPACK on massively
parallel computers / P. E. Bj{\o}rstad and T.
S{\o}revik / 13 \\
a Large-scale nonlinear constrained optimization / A.
R. Conn, N. Gould and Ph. L. Toint / 21 \\
Trading off parallelism and numerical stability / J. W.
Demmel / 49 \\
Subband filtering: CORDIC modulation and systolic
quadrature mirror filter tree / E. F. Deprettere / 69
\\
A parallel image rendering algorithm and architecture
based on ray tracing and radiosity shading / E. F.
Deprettere and L.-S. Shen / 91 \\
Reduction and approximation of linear computational
circuits / P. Dewilde and A.-J. van der Veen / 109 \\
The look-ahead Lanczos process for large nonsymmetric
matrices and related algorithms / R. W. Freund / 137
\\
Case studies of real-time processing in robotics / W.
M. Gentleman / 165 \\
Adaptive signal processing with emphasis on QRD-least
squares lattice / S. Haykin / 183 \\
A direct method for reordering eigenvalues in the
generalized real Schur form of a regular matrix pair
(A, B) / B. K{\aa}gstr{\"o}m / 195 \\
Block shift invariance and efficient system
identification algorithms / N. Kalouptsidis / 219 \\
Computing the singular value decomposition on a
fat-tree architecture / T. J. Lee, F. T. Luk and D. L.
Boley / 231 \\
A new matrix decomposition for signal processing / F.
T. Luk and S. Qiao / 241 \\
The linear algebra of perfect reconstruction filtering
/ M. Stewart and G. Cybenko / 249 \\
Determining rank in the presence of error / G. W.
Stewart / 275 \\
Approximation with Kronecker products / C. F. Van Loan
and N. Pitsianis / 293 \\
Some linear algebra issues in large-scale optimization
/ M. H. Wright / 315 \\
Contributed Lectures / / 339 \\
Direct and inverse unitary eigenproblems in signal
processing: an overview / G. S. Ammar, W. B. Gragg and
L. Reichel / 341 \\
Block implementations of the symmetric QR and Jacobi
algorithms / P. Arbenz and M. Oettli / 345 \\
Linear algebra for large-scale information retrieval
applications / M. W. Berry / 347 \\
Matched filter vs. least-squares approximation / L. H.
J. Bierens / 349 \\
Reordering diagonal blocks in real Schur form / A. W.
Bojanczyk and P. Van Dooren / 351 \\
Placing zeroes and the Kronecker canonical form / D. L.
Boley and P. Van Dooren / 353 \\
Analysis of the recursive least squares lattice
algorithm / J. R. Bunch and R. C. LeBorne / 355 \\
Adaptive Chebyshev iteration based on modified moments
/ D. Calvetti, G. H. Golub and L. Reichel / 357 \\
Continuous realization methods and their applications /
M. T. Chu / 359 \\
Asymptotic behavior of orthogonal polynomials / T. Dehn
/ 361 \\
CADCS and parallel computing / F. Dumortier, A. Van
Cauwenberghe and L. Boullart / 363 \\
Eigenvalue roulette and random test matrices / A.
Edelman / 365 \\
On numerical methods for unitary eigenvalue problems /
H. Fa{\sas}bender / 369 \\
Accurate singular values and differential qd algorithms
/ K. V. Fernando and B. N. Parlett / 371 \\
Orthogonal projection and total least squares / R. D.
Fierro and J. R. Bunch / 375 \\
Gauss quadratures associated with the Arnoldi process
and the Lanczos algorithm / R. W. Freund and M.
Hochbruck / 377 \\
An implementation of the QMR method based on coupled
two-term recurrences / R. W. Freund and N. M. Nachtigal
/ 381 \\
Computationally efficient homotopies for the H 2 model
order reduction problem / Y. Ge, L. T. Watson, E. G.
Collins, Jr. and L. D. Davis / 385 \\
A fast algorithm for QR decomposition of Toeplitz
matrices / G. O. Glentis / 387 \\
Unitary Hessenberg methods for Toeplitz approximations
and applications / Ch. He and A. Bunse-Gerstner / 389
\\
Perturbation theory and backward error for $A X - X B =
C$ / N. J. Higham / 391 \\
Fast transforms and elliptic problems / T. Huckle / 393
\\
An interior-point method for minimizing the maximum
eigenvalue of a linear combination of matrices / F.
Jarre / 395 \\
The lattice-ladder with generalized forgetting / J.
Kadlec / 397 \\
Solving a least squares problem with boundary
constraints / L. Kaufman / 399 \\
Estimating the extremal eigenvalues and condition
number by the Lanczos algorithm with a random start /
J. Kuczy{\'n}ski and H. Wo{\'z}niakowski / 401 \\
A generalized ADI iterative method / N. Levenberg and
L. Reichel / 403 \\
Quaternions and the symmetric eigenvalue problem / N.
Mackey / 405 \\
Application of the Gauss-Seidel iteration to the RLS
algorithm / {\"O}. Morg{\"u}l and A. Mala{\c{s}} / 407
\\
Ranks of submatrices of a matrix and its inverse / C.
C. Paige and M. Wei / 409 \\
A QRD-based least-squares algorithm for multipulse
antenna array signal processing / I. K. Proudler / 411
\\
On displacement structures for covariance matrices and
lossless functions / P. A. Regalia and F. Desbouvries /
413 \\
Application of vector extrapolation and conjugate
gradient type methods to the semiconductor device
problem / W. H. A. Schilders / 415 \\
Accurate symmetric eigenreduction by a Jacobi method /
I. Slapni{\v{c}}ar / 417 \\
The order-recursive Chandrasekhar equations for fast
square-root Kalman filtering / D. T. M. Slock / 419 \\
Hybrid iterative methods based on Faber polynomials /
G. Starke / 421 \\
Aspects of implementing a 'C' matrix library / D. E.
Stewart / 423 \\
Intermediate fill-in in sparse QR decomposition / M.
T{\r{u}}ma / 425 \\
Shifting strategies for the parallel QR algorithm / D.
S. Watkins / 427 \\
List of Participants / / 429 \\
Authors Index / / 437",
}
@Proceedings{Reichel:1993:NLA,
editor = "Lothar Reichel and Arden Ruttan and Richard S. Varga",
booktitle = "{Numerical linear algebra: proceedings of the
Conference in Numerical Linear Algebra and Scientific
Computation, Kent (Ohio), USA, March 13--14, 1992}",
title = "{Numerical linear algebra: proceedings of the
Conference in Numerical Linear Algebra and Scientific
Computation, Kent (Ohio), USA, March 13--14, 1992}",
publisher = pub-GRUYTER,
address = pub-GRUYTER:adr,
pages = "vii + 199",
year = "1993",
ISBN = "3-11-013784-4",
ISBN-13 = "978-3-11-013784-2",
LCCN = "QA184.C655 1993",
bibdate = "Fri Nov 11 08:28:39 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "Conference in Numerical Linear Algebra and Scientific
Computation (1992 : Kent, Ohio)",
subject = "Algebras, Linear; Congresses; Numerical analysis;
Congresses",
}
@Proceedings{Brown:1994:PCL,
editor = "J. David Brown and Moody T. Chu and Donald C. Ellison
and Robert J. Plemmons",
booktitle = "{Proceedings of the Cornelius Lanczos International
Centenary Conference, Raleigh, North Carolina, December
12--17, 1993}",
title = "{Proceedings of the Cornelius Lanczos International
Centenary Conference, Raleigh, North Carolina, December
12--17, 1993}",
volume = "73",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "lxv + 644",
year = "1994",
ISBN = "0-89871-339-0",
ISBN-13 = "978-0-89871-339-8",
LCCN = "QC19.2 .C67 1993",
bibdate = "Wed Jun 8 14:42:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/einstein.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Proceedings in Applied Mathematics",
acknowledgement = ack-nhfb,
meetingname = "Cornelius Lanczos International Centenary Conference
(1993:Raleigh, NC)",
subject = "Mathematical physics; Congresses; Astrophysics;
Mathematics; Lanczos, Cornelius; Physicists; Hungary;
Biography; Mathematicians",
subject-dates = "1893--1974",
tableofcontents = "The Life and Works of Cornelius Lanczos \\
\\
A Photographic Essay / / xvii \\
Cornelius Lanczos: A Biographical Essay / Barbara
Gellai / xxi \\
Cornelius Lanczos (1893-1974), and the Hungarian
Phenomenon in Science and Mathematics / Peter D. Lax /
xlix \\
The Roots of Cornelius Lanczos / George Marx / liii \\
Reminiscences of Cornelius Lanczos / Jon Todd / lviii
\\
Published Papers and Books of Cornelius Lanczos / / lx
\\
\\
Plenary Presentations: Computational Mathematics \\
\\
Lanczos and the FFT: A Discovery Before its Time /
James W. Cooley / 3 \\
Lanczos Algorithms for Large Scale Symmetric and
Nonsymmetric Matrix Eigenvalue Problems / Jane K.
Cullum / 11 \\
The Look-Ahead Lanczos Process for Nonsymmetric
Matrices and its Applications / Roland W Freund / 33
\\
The Lanczos and Conjugate Gradient Algorithms in Finite
Precision Arithmetic / Anne Greenbaum / 49 \\
The Lanczos Process and Pade Approximation / Martin H.
Gutknecht / 61 \\
The Tau Method and the Numerical Solution of
Differential Equations: Past Research and Recent
Research / Eduardo L. Ortiz / 77 \\
Krylov Subspace Processes, Krylov Subspace Methods, and
Iteration Polynomials / C. C. Paige / 83 \\
Do We Fully Understand the Symmetric Lanczos Algorithm
Yet? / Beresford N. Parlett / 93 \\
On Generalized Band Matrices and Their Inverses /
P{\'a}l R{\'o}sa, Francesco Romani, and Roberto
Bevilacqua / 109 \\
Theoretical Error Bounds and General Analysis of a Few
Lanczos-Type Algorithms / Youcef Saad / 123 \\
Lanczos and Linear Systems / G. W. Stewart / 135 \\
\\
Plenary Presentations: Theoretical Physics and
Astrophysics \\
\\
Integration on the Space of Connections Modulo Gauge
Transformations / Abbay Ashtekar, Donald Marolf, and
Jose Mourdo / 143 \\
Quasiclassical Domains in a Quantum Universe / James B.
Hartle / 161 \\
Gauge Invariant Energy-Momentum Tensor in Spinar
Electrodynamics / D. Petiot and Y. Takahashi / 173 \\
$\gamma$-Ray Bursts and Neutron Star Mergers / Tsvi
Piran / 187 \\
Lanczos's Early Contributions to Relativity and His
Relationship with Einstein / John Stachel / 201 \\
Topological Roots of Black Hole Entropy / Claudio
Teitelboim / 223 \\
Variational Principles, Local Symmetries, and Black
Hole Entropy / Robert M. Wald / 231 \\
\\
Mathematics Minisymposia \\
\\
Eigenvalue Computations: Theory and Algorithms / / 241
\\
Eigenvalue Computations: Applications / / 249 \\
Moments in Numerical Analysis / / 265 \\
Iterative Methods for Linear Systems / / 277 \\
Least Squares / / 301 \\
Software for Lanczos-based Algorithms / / 311 \\
Tau Method / / 335 \\
Chebyshev Polynomials / / 357 \\
Lanczos Methods in Control and Signal Processing / /
375 \\
Development of the FFT / / 393 \\
The FFT in Signal Processing / / 399 \\
Wavelets / / 411 \\
\\
Physics Minisymposia \\
\\
Computational Magnetohydrodynamics in Astrophysics / /
431 \\
Numerical Simulations of Collisionless Space Plasmas /
/ 453 \\
Detection of Gravitational Radiation from Astrophysical
Sources / / 477 \\
Lanczos $H$-tensor / / 489 \\
Cosmic Censorship / / 513 \\
Cauchy Problem of General Relativity / / 527 \\
Black Hole Evaporation and Thermodynamics / / 543 \\
The Problem of Time in Quantum Gravity / / 555 \\
New Variables and Loop Quantization / / 571 \\
Decoherence and the Foundations of Quantum Mechanics /
/ 589 \\
Open Questions in Particle Theory / / 603 \\
Supercollider Physics / / 621 \\
Symplectic Methods in Physics / / 633",
}
@Proceedings{Lewis:1994:ALA,
editor = "John G. Lewis",
booktitle = "Applied Linear Algebra: Proceedings of the Fifth
{SIAM} Conference on Applied Linear Algebra, Snowbird,
Utah, June 15--18, 1994",
title = "Applied Linear Algebra: Proceedings of the Fifth
{SIAM} Conference on Applied Linear Algebra, Snowbird,
Utah, June 15--18, 1994",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "x + 578",
year = "1994",
ISBN = "0-89871-336-6",
ISBN-13 = "978-0-89871-336-7",
LCCN = "QA184.S58 1994",
bibdate = "Fri May 14 12:41:12 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/i/ipsen-ilse-c-f.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Natori:1994:MAP,
editor = "M. Natori and T. Nodera",
booktitle = "Matrix analysis and parallel computing",
title = "Matrix analysis and parallel computing",
volume = "10",
publisher = "Keio University",
address = "Yokohama, Japan",
pages = "276",
year = "1994",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Nov 11 08:31:31 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
series = "Adv. Numer. Methods Large Sparse Sets Linear
Equations",
acknowledgement = ack-nhfb,
remark = "Papers presented at the 10th PCG symposium, held at
Keio University, Tokyo, Japan, March 14-16, 1994.",
}
@Proceedings{Bailey:1995:PSS,
editor = "D. H. Bailey and P. E. Bjorstad and J. R. Gilbert and
M. V. Mascagni and R. S. Schreiber and H. D. Simon and
V. J. Torczon and L. T. Watson",
booktitle = "{Proceedings of the Seventh SIAM Conference on
Parallel Processing for Scientific Computing (February
15--17, 1995, San Francisco, CA)}",
title = "{Proceedings of the Seventh SIAM Conference on
Parallel Processing for Scientific Computing (February
15--17, 1995, San Francisco, CA)}",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xviii + 875",
year = "1995",
ISBN = "0-89871-344-7",
ISBN-13 = "978-0-89871-344-2",
LCCN = "QA76.58.S55 1995",
bibdate = "Tue Sep 3 12:52:10 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
sponsor = "Society for Industrial and Applied Mathematics.",
}
@Book{Iserles:1995:AN,
editor = "A. Iserles",
booktitle = "{Acta Numerica 1995}",
title = "{Acta Numerica 1995}",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "491",
year = "1995",
ISBN = "0-521-48255-0",
ISBN-13 = "978-0-521-48255-4",
LCCN = "",
bibdate = "Fri Nov 11 07:13:56 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Renegar:1996:MNA,
editor = "James Renegar and Michael Shub and Steve Smale",
booktitle = "{The mathematics of numerical analysis: 1995 AMS--SIAM
Summer Seminar in Applied Mathematics, July 17--August
11, 1995, Park City, Utah}",
title = "{The mathematics of numerical analysis: 1995 AMS--SIAM
Summer Seminar in Applied Mathematics, July 17--August
11, 1995, Park City, Utah}",
volume = "32",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "xi + 927 + [1]",
year = "1996",
ISBN = "0-8218-0530-4",
ISBN-13 = "978-0-8218-0530-5",
ISSN = "0075-8485",
LCCN = "QA297 .A57 1995",
bibdate = "Tue Oct 27 18:18:33 MST 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
series = "Lectures in Applied Mathematics --- American
Mathematical Society",
acknowledgement = ack-nhfb,
keywords = "numerical analysis -- congresses",
sponsor = "American Mathematical Society. Society for Industrial
and Applied Mathematics.",
}
@Proceedings{Watson:1996:NA,
editor = "G. A. Watson and D. F. Griffiths",
booktitle = "Numerical analysis 1995",
title = "Numerical analysis 1995",
volume = "344",
publisher = pub-LONGMAN,
address = pub-LONGMAN:adr,
pages = "237",
year = "1996",
ISBN = "0-582-27633-0 (paperback)",
ISBN-13 = "978-0-582-27633-8 (paperback)",
ISSN = "0269-3674",
LCCN = "QA297.N854 1996",
bibdate = "Wed Nov 3 09:30:14 MST 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "Proceedings of the 16th Dundee Biennial Conference on
Numerical Analysis, University of Dundee, June 27--30,
1995.",
series = "Pitman research notes in mathematics series",
acknowledgement = ack-nhfb,
keywords = "numerical analysis -- research",
}
@Proceedings{Buhmann:1997:ATO,
editor = "M. D. (Martin Dietrich) Buhmann and A. Iserles and M.
J. D. (Michael James David) Powell",
booktitle = "Approximation theory and optimization: tributes to {M.
J. D. Powell}",
title = "Approximation theory and optimization: tributes to {M.
J. D. Powell}",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xiii + 220",
year = "1997",
ISBN = "0-521-58190-7 (hardback)",
ISBN-13 = "978-0-521-58190-5 (hardback)",
LCCN = "QA221 .A655 1997",
bibdate = "Fri Nov 11 07:17:57 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
sirsi.library.utoronto.ca:2200/UNICORN",
acknowledgement = ack-nhfb,
remark = "Ten invited papers presented at the Conference on
Numerical Mathematics in Cambridge, on 27--30 July 1996
on the occasion of the 60th birthday of M. J. D.
Powell.",
subject = "Approximation theory; Congresses; Mathematical
optimization; Congresses",
}
@Proceedings{Barlow:2000:PIW,
editor = "Jesse L. Barlow and Beresford N. Parlett",
booktitle = "{Proceedings of the International Workshop on Accurate
Solution of Eigenvalue Problems}",
title = "{Proceedings of the International Workshop on Accurate
Solution of Eigenvalue Problems}",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
pages = "iii + 361",
year = "2000",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
MRclass = "65-06 (15-06 65F15 65L15 65N25)",
MRnumber = "MR1758357 (2000m:65010)",
bibdate = "Thu Nov 10 18:37:11 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
note = "Held at Pennsylvania State University, University
Park, PA, July 20--23, 1998, Linear Algebra Appl. {\bf
309} (2000), no. 1--3.",
series = j-LINEAR-ALGEBRA-APPL,
acknowledgement = ack-nhfb,
}
%%% Last MathSciNet search: Thu Feb 10 08:11:55 2022