%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "1.45",
%%%     date            = "05 March 2013",
%%%     time            = "08:26:46 MST",
%%%     filename        = "kahan-william.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             = "http://www.math.utah.edu/~beebe",
%%%     checksum        = "42957 6128 23659 251034",
%%%     email           = "beebe at math.utah.edu, beebe at acm.org,
%%%                        beebe at computer.org (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "bibliography; BibTeX; William M. Kahan",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography of the publications
%%%                        of William (Velvel) M. Kahan, plus a few that
%%%                        refer to them in their titles, or cross
%%%                        reference them.  Informal class notes are
%%%                        included as well, because they are sometimes
%%%                        cited by other authors.
%%%
%%%                        W. M. Kahan is the recipient of several
%%%                        awards, including the 1990 ACM Turing Award
%%%                        and the 1997 SIAM John von Neumann Prize.  He
%%%                        is the guiding force behind IEEE 754
%%%                        floating-point arithmetic, which has been
%%%                        implemented on billions of computer chips,
%%%                        and which has contributed substantially to
%%%                        the much-needed improvement of the
%%%                        floating-point environment on digital
%%%                        computers.  His personal Web site at
%%%
%%%                            http://www.cs.berkeley.edu/~wkahan/
%%%
%%%                        contains many published and unpublished
%%%                        documents and software.
%%%
%%%                        At version 1.45, the year coverage looked
%%%                        like this:
%%%
%%%                             1955 (   1)    1975 (   3)    1995 (   3)
%%%                             1956 (   0)    1976 (   2)    1996 (   9)
%%%                             1957 (   0)    1977 (   3)    1997 (   9)
%%%                             1958 (   1)    1978 (   2)    1998 (  25)
%%%                             1959 (   0)    1979 (   5)    1999 (  35)
%%%                             1960 (   0)    1980 (   6)    2000 (  23)
%%%                             1961 (   0)    1981 (   3)    2001 (   8)
%%%                             1962 (   0)    1982 (   6)    2002 (  22)
%%%                             1963 (   4)    1983 (   7)    2003 (   2)
%%%                             1964 (   1)    1984 (   1)    2004 (  16)
%%%                             1965 (   6)    1985 (   4)    2005 (   6)
%%%                             1966 (   6)    1986 (   5)    2006 (   3)
%%%                             1967 (   2)    1987 (   7)    2007 (   5)
%%%                             1968 (   3)    1988 (   3)    2008 (   1)
%%%                             1969 (   5)    1989 (   4)    2009 (   1)
%%%                             1970 (   3)    1990 (   8)    2010 (   0)
%%%                             1971 (   3)    1991 (   8)    2011 (   0)
%%%                             1972 (   4)    1992 (   7)    2012 (   1)
%%%                             1973 (   4)    1993 (   3)
%%%                             1974 (   1)    1994 (   6)
%%%
%%%                             Article:         62
%%%                             Book:             2
%%%                             InCollection:     4
%%%                             InProceedings:   19
%%%                             Manual:           1
%%%                             MastersThesis:    1
%%%                             Misc:           126
%%%                             PhdThesis:        1
%%%                             Proceedings:     16
%%%                             TechReport:      41
%%%                             Unpublished:     34
%%%
%%%                             Total entries:  307
%%%
%%%                        This bibliography has been prepared from the
%%%                        extensive BibNet Project and TeX User Group
%%%                        bibliography archives, from the IEEE Explore
%%%                        database, from the ACM Portal database, from
%%%                        several different university and government
%%%                        library catalogs, and from assorted Web sites
%%%                        and technical articles found by Web searches.
%%%
%%%                        BibTeX citation tags are uniformly chosen
%%%                        as name:year:abbrev, where name is the
%%%                        family name of the first author or editor,
%%%                        year is a 4-digit number, and abbrev is a
%%%                        3-letter condensation of important title
%%%                        words. Citation tags were automatically
%%%                        generated by software developed for the
%%%                        BibNet Project.
%%%
%%%                        In this bibliography, entries are sorted
%%%                        first by ascending year, and within each
%%%                        year, alphabetically by author or editor,
%%%                        and then, if necessary, by the 3-letter
%%%                        abbreviation at the end of the BibTeX
%%%                        citation tag, using the bibsort -byyear
%%%                        utility.  Cross-referenced proceedings
%%%                        entries appear at the end, because of a
%%%                        restriction in the current BibTeX.
%%%
%%%                        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{
    "\input path.sty" #
    "\hyphenation{manu-script Manu-script UCB-TEST}"
}

%%% ====================================================================
%%% Institution abbreviations:

@String{inst-ANL-MCS            = "Mathematics and Computer Science Division,
                                  Argonne National Laboratory"}
@String{inst-ANL-MCS:adr        = "9700 South Cass Avenue, Argonne, IL
                                  60439-4801, USA"}

@String{inst-BERKELEY           = "University of California"}
@String{inst-BERKELEY:adr       = "Berkeley, CA, USA"}

@String{inst-BERKELEY-CPAM      = "Center for Pure and Applied Mathematics,
                                  University of California"}
@String{inst-BERKELEY-CPAM:adr  = "Berkeley, CA, USA"}

@String{inst-BERKELEY-CS        = "Department of Computer Science, University
                                  of California"}
@String{inst-BERKELEY-CS:adr    = "Berkeley, CA, USA"}

@String{inst-BERKELEY-EECS      = "Department of Electrical Engineering and
                                  Computer Science, University of California,
                                  Berkeley"}
@String{inst-BERKELEY-EECS:adr  = "Berkeley, CA, USA"}

@String{inst-BERKELEY-MATH-EECS = "Department of Mathematics and Department of
                                  Electrical Engineering and Computer Science,
                                  University of California, Berkeley"}
@String{inst-BERKELEY-MATH-EECS:adr = "Berkeley, CA, USA"}

@String{inst-STANFORD-CS        = "Department of Computer Science, Stanford
                                  University"}
@String{inst-STANFORD-CS:adr    = "Stanford, 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-ANAL-MATH             = "J. Anal. Math."}

@String{j-ANNALS-FOURIER        = "Ann. Inst. Fourier (Grenoble)"}

@String{j-APPL-NUM-MATH         = "Applied Numerical Mathematics: Transactions
                                  of IMACS"}

@String{j-APPROX-TH             = "J. Approx. Th."}

@String{j-BULL-AMS              = "Bulletin of the American Mathematical
                                  Society"}

@String{j-BULL-LONDON-MS        = "Bull. London Math. Soc."}

@String{j-CACM                  = "Communications of the Association for
                                  Computing Machinery"}

@String{j-CAN-MATH-BULL         = "Canadian mathematical bulletin = Bulletin
                                  canadien de math{\'e}matiques"}

@String{j-COLLOQ-MATH           = "Colloq. Math."}

@String{j-COMP-NET-AMSTERDAM    = "Computer Networks (Amsterdam, Netherlands:
                                  1999)"}

@String{j-COMP-NET-ISDN         = "Computer Networks and ISDN Systems"}

@String{j-COMPUTER              = "Computer"}

@String{j-CPE                   = "Concurrency: Prac\-tice and Experience"}

@String{j-CR-ACADSCI-PARIS      = "C.R. Acad. Sci. Paris"}

@String{j-DDJ                   = "Dr. Dobb's Journal of Software Tools"}

@String{j-HEWLETT-PACKARD-J     = "Hew\-lett-Pack\-ard Journal: technical
                                  information from the laboratories of
                                  Hew\-lett-Pack\-ard Company"}

@String{j-IBM-JRD               = "IBM Journal of Research and Development"}

@String{j-IBM-SYS-J             = "IBM Systems Journal"}

@String{j-IEEE-COMPUT-SCI-ENG   = "IEEE Computational Science \& Engineering"}

@String{j-IEEE-MICRO            = "IEEE Micro"}

@String{j-IEEE-TRANS-COMPUT     = "IEEE Transactions on Computers"}

@String{j-IEEE-TRANS-PATT-ANAL-MACH-INTEL = "IEEE Trans. on Pattern Anal. and
                                  Machine Intel."}

@String{j-IEEE-TRANS-PATT-ANAL-MACH-INTEL = "IEEE Transactions on Pattern
                                  Analysis and Machine Intelligence"}

@String{j-INFO-PROC             = "Journal of Information Processing (of
                                  Japan??)"}

@String{j-J-COMPUT-PHYS         = "Journal of computational physics"}

@String{j-J-CRYPTOLOGY          = "Journal of Cryptology: the journal of the
                                  International Association for Cryptologic
                                  Research"}

@String{j-J-MATH-ANAL-APPL      = "Journal of Mathematical Analysis and
                                  Applications"}

@String{j-J-MATH-PHYS           = "Journal of Mathematical Physics"}

@String{j-LECT-NOTES-COMP-SCI   = "Lecture Notes in Computer Science"}

@String{j-LIN-MULT-ALGEBRA      = "Linear and Multilinear Algebra"}

@String{j-LINEAR-ALGEBRA-APPL   = "Linear Algebra and its Applications"}

@String{j-MATH-COMPUT           = "Mathematics of Computation"}

@String{j-NORDISK-TIDSKR-INFORM-BEHAND = "Nordisk tidskrift for
                                  informationsbehandling"}

@String{j-NUM-MATH              = "Numerische Mathematik"}

@String{j-PROC-AM-MATH-SOC      = "Proceedings of the American Mathematical
                                  Society"}

@String{j-SIAM-J-MAT-ANA-APPL   = "SIAM Journal on Matrix Analysis and
                                  Applications"}

@String{j-SIAM-J-NUM-ANALYSIS-B = "Journal of the Society for Industrial and
                                  Applied Mathematics: Series B, Numerical
                                  Analysis"}

@String{j-SIAM-J-NUMER-ANAL     = "SIAM Journal on Numerical Analysis"}

@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-SIGPLAN               = "ACM SIG{\-}PLAN Notices"}

@String{j-SIGSAM                = "SIGSAM Bulletin (ACM Special Interest Group
                                  on Symbolic and Algebraic Manipulation)"}

@String{j-SYS-COMP-JAPAN        = "Systems and Computers in Japan"}

@String{j-TOMS                  = "ACM Transactions on Mathematical Software"}

@String{j-TOSEM                 = "ACM Transactions on Software Engineering
                                  and Methodology"}

@String{j-Z-ANGE-MATH-MECH      = "Zeitschrift f{\"u}r Angewandte Mathematik
                                  und Mechanik"}

%%% ====================================================================
%%% Miscellaneous abbreviations:

@String{type-CSDTR              = "Computer Science Dept. Technical Report"}

%%% ====================================================================
%%% Publisher abbreviations:

@String{pub-ACM                 = "ACM Press"}
@String{pub-ACM:adr             = "New York, NY 10036, USA"}

@String{pub-AP                  = "Academic Press"}
@String{pub-AP:adr              = "New York, NY, USA"}

@String{pub-ENH                 = "Elsevier North-Holland, Inc."}
@String{pub-ENH:adr             = "New York, NY, USA"}

@String{pub-HRW                 = "Holt, Rinehart and Winston"}
@String{pub-HRW:adr             = "New York"}

@String{pub-IEEE                = "IEEE Computer Society Press"}
@String{pub-IEEE:adr            = "1109 Spring Street, Suite 300, Silver
                                  Spring, MD 20910, USA"}

@String{pub-LONGMAN-ST          = "Longman Scientific and Technical"}
@String{pub-LONGMAN-ST:adr      = "Harlow, Essex, UK"}

@String{pub-NH                  = "North-Hol{\-}land"}
@String{pub-NH:adr              = "Amsterdam, The Netherlands"}

@String{pub-OXFORD              = "Oxford University Press"}
@String{pub-OXFORD:adr          = "Walton Street, Oxford OX2 6DP, UK"}

@String{pub-SV                  = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr              = "Berlin, Germany~/ Heidelberg,
                                  Germany~/ London, UK~/ etc."}

%%% ====================================================================
%%% Bibliography entries, sorted by year and by citation key:

@MastersThesis{Kahan:1955:SMS,
  author =       "William Morton Kahan",
  title =        "A survey of methods of solving {Poisson}'s equation
                 suitable for electronic computers",
  type =         "{M.A.}",
  school =       "University of Toronto",
  address =      "Toronto, ON, Canada",
  pages =        "ii + 44 + 8",
  year =         "1955",
  bibdate =      "Mon Apr 25 05:21:08 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic calculating-machines; harmonic functions",
}

@PhdThesis{Kahan:1958:GSM,
  author =       "William Morton Kahan",
  title =        "{Gauss--Seidel} methods of solving large systems of
                 linear equations",
  type =         "{Ph.D.} Thesis",
  school =       "University of Toronto",
  address =      "Toronto, ON, Canada",
  year =         "1958",
  bibdate =      "Mon Apr 25 07:26:34 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Article{Davis:1963:REP,
  author =       "Chandler Davis",
  title =        "The Rotation of Eigenvectors By a Perturbation. {I}",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "6",
  pages =        "159--173",
  year =         "1963",
  CODEN =        "JMANAK",
  ISSN =         "0022-247X",
  ISSN-L =       "0022-247X",
  MRclass =      "47.48",
  MRnumber =     "MR0149309 (26 \#6799)",
  MRreviewer =   "J. Rovnyak",
  bibdate =      "Mon Apr 25 05:36:25 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "See \cite{Davis:1965:REP,Davis:1970:REP}.",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1963:ACC,
  author =       "W. Kahan and I. Farkas",
  title =        "{Algorithm 167}: {Calculation} of Confluent Divided
                 Differences",
  journal =      j-CACM,
  volume =       "6",
  number =       "4",
  pages =        "164--165",
  month =        apr,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Nov 26 10:57:46 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1963:ANIa,
  author =       "W. Kahan and I. Farkas",
  title =        "{Algorithm 169}: {Newton} Interpolation with Forward
                 Divided Differences",
  journal =      j-CACM,
  volume =       "6",
  number =       "4",
  pages =        "165--165",
  month =        apr,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Nov 26 10:58:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1963:ANIb,
  author =       "W. Kahan and I. Farkas",
  title =        "{Algorithm 168}: {Newton} Interpolation with Backward
                 Divided Differences",
  journal =      j-CACM,
  volume =       "6",
  number =       "4",
  pages =        "165--165",
  month =        apr,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Nov 26 10:59:17 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1964:FPM,
  author =       "W. Kahan and J. J. Leppik",
  title =        "A {FORTRAN} Post-Mortem Procedure",
  journal =      j-CACM,
  volume =       "7",
  number =       "1",
  pages =        "15--15",
  month =        jan,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Nov 26 11:00:17 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Article{Davis:1965:REP,
  author =       "Chandler Davis",
  title =        "The Rotation of Eigenvectors By a Perturbation. {II}",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "11",
  pages =        "20--27",
  year =         "1965",
  CODEN =        "JMANAK",
  ISSN =         "0022-247X",
  ISSN-L =       "0022-247X",
  MRclass =      "47.48",
  MRnumber =     "MR0180852 (31 \#5082)",
  MRreviewer =   "J. Rovnyak",
  bibdate =      "Mon Apr 25 05:36:25 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "See \cite{Davis:1963:REP,Davis:1970:REP}.",
  acknowledgement = ack-nhfb,
}

@Article{Golub:1965:CSV,
  author =       "G. H. Golub and W. Kahan",
  title =        "Calculating the Singular Values and Pseudo-Inverse of
                 a Matrix",
  journal =      j-SIAM-J-NUM-ANALYSIS-B,
  volume =       "2",
  number =       "2",
  pages =        "205--224",
  month =        "????",
  year =         "1965",
  ISSN =         "0887-459X (print), 1095-7170 (electronic)",
  MRclass =      "65.35",
  MRnumber =     "MR0183105 (32 \#587)",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/gvl.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  keywords =     "nla, svd, ginv",
  mynote =       "I have not seen.",
}

@InCollection{Kahan:1965:FPO,
  author =       "W. Kahan",
  booktitle =    "Programmer's Reference Manual",
  title =        "The Floating-Point Over\slash Underflow Trap Routine
                 {{\tt FPTRP}}",
  publisher =    "Institute of Computer Science, University of Toronto",
  address =      "Toronto, Ontario, Canada",
  year =         "1965",
  LCCN =         "????",
  bibdate =      "Wed Feb 14 19:11:11 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Section 4.1.",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1965:PFR,
  author =       "W. Kahan",
  title =        "Pracniques: {Further} Remarks on Reducing Truncation
                 Errors",
  journal =      j-CACM,
  volume =       "8",
  number =       "1",
  pages =        "40--40",
  month =        jan,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Nov 26 11:01:01 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/bit.bib;
                 http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nj,
  keywords =     "floating-point arithmetic; truncation errors",
  remark =       "Gives summation error estimate formula `s = fl(a + b);
                 error = (a - s) + b', also discovered independently by
                 \cite{Moller:1965:QDP}. Extends Gill's earlier
                 fixed-point result \cite{Gill:1951:PSS}. See
                 improvement \cite{Ozawa:1993:SAE}.",
}

@Article{Moller:1965:NQD,
  author =       "Ole M{\o}ller",
  title =        "Note on Quasi Double-Precision",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "5",
  number =       "4",
  pages =        "251--255",
  year =         "1965",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  bibdate =      "Sat Nov 14 09:14:57 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "See \cite{Moller:1965:QDP}.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
}

@Article{Moller:1965:QDP,
  author =       "Ole M{\o}ller",
  title =        "Quasi Double-Precision in Floating Point Addition",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "5",
  number =       "1",
  pages =        "37--50",
  year =         "1965",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  MRclass =      "65.80",
  MRnumber =     "31\#5359",
  bibdate =      "Sat Nov 14 09:14:57 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/bit.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "See also \cite{Moller:1965:NQD}.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  annote =       "Gives summation error estimate formula `s = fl(a + b);
                 error = (a - s) + b', also discovered independently by
                 \cite{Kahan:1965:FRR}. Extends Gill's earlier
                 fixed-point result \cite{Gill:1951:PSS}.",
  remark =       "Gives summation error estimate formula `s = fl(a + b);
                 error = (a - s) + b', also discovered independently by
                 \cite{Kahan:1965:FRR}. Extends Gill's earlier
                 fixed-point result \cite{Gill:1951:PSS}.",
}

@TechReport{Kahan:1966:AES,
  author =       "W. Kahan",
  title =        "Accurate Eigenvalues of a Symmetric Tri-Diagonal
                 Matrix",
  type =         "Technical Report",
  number =       "CS41",
  institution =  inst-STANFORD-CS,
  address =      inst-STANFORD-CS:adr,
  pages =        "????",
  day =          "22",
  month =        jul,
  year =         "1966",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Revised June 1968",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1966:CEB,
  author =       "W. M. Kahan",
  title =        "A Computable Error-Bound for Systems of Ordinary
                 Differential Equations (Abstract)",
  journal =      j-SIAM-REVIEW,
  volume =       "8",
  pages =        "568--569",
  year =         "1966",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-jr,
}

@TechReport{Kahan:1966:FIS,
  author =       "W. Kahan",
  title =        "The {FORTRAN IV} subroutine {QDRTC}",
  institution =  "Computer library, McLennan Laboratories, University of
                 Toronto",
  address =      "Toronto, ON, Canada",
  year =         "1966",
  bibdate =      "Fri Jul 03 08:59:48 2009",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited by G. E. Forsythe in ``What is a satisfactory
                 quadratic equation solver?'' (1969)",
}

@Article{Kahan:1966:NLA,
  author =       "W. M. Kahan",
  title =        "Numerical Linear Algebra",
  journal =      j-CAN-MATH-BULL,
  volume =       "9",
  number =       "??",
  pages =        "757--801",
  month =        "????",
  year =         "1966",
  CODEN =        "CMBUA3",
  DOI =          "http://dx.doi.org/10.4153/CMB-1966-083-2",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  bibdate =      "Thu Sep 8 10:03:18 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/gvl.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 http://cms.math.ca/cmb/v9/",
  acknowledgement = ack-nhfb,
  fjournal =     "Canadian mathematical bulletin = Bulletin canadien de
                 math{\'e}matiques",
}

@Misc{Kahan:1966:ISS,
  author =       "W. Kahan",
  title =        "{7094-II} System Support for Numerical Analysis",
  howpublished = "SHARE Secretary Distribution 159, C4537",
  pages =        "1--54",
  day =          "12",
  month =        dec,
  year =         "1966",
  bibdate =      "Wed Nov 07 08:39:33 2007",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  remark =       "Warning: various online documents cite this with years
                 1965, 1966, and 1968. The correct year appears to be
                 1966, based on citations in other documents to other
                 papers in volume C4537, including one from 1967 (which
                 therefore eliminates 1968).  Forsythe gives 1966 in his
                 paper ``What is a satisfactory quadratic equation
                 solver?''",
}

@TechReport{Kahan:1966:WND,
  author =       "W. Kahan",
  title =        "When to neglect off-diagonal elements of symmetric
                 tri-diagonal matrices",
  type =         "Technical report",
  number =       "CS42",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  day =          "25",
  month =        jul,
  year =         "1966",
  bibdate =      "Mon Apr 25 05:31:38 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "ftp://reports.stanford.edu/pub/cstr/reports/cs/tr/66/42/CS-TR-66-42.pdf",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:196x:ACM,
  author =       "W. M. Kahan",
  title =        "Note on bounds for generating {Bessel} functions by
                 recurrence",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  year =         "196x",
  bibdate =      "Wed Apr 30 11:14:58 2008",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in reference 28 of Walter Gautschi, {\em
                 Computational Aspects of Three-Term Recurrence
                 Relations}, SIAM Review 9(1) 24--82 January (1967), and
                 reference 7 of F. W. J. Olver and D. J. Sookne, {\em
                 Note on Backward Recurrence Algorithms}, Mathematics of
                 Computation, 26(120) 941--947, October 1972. Web
                 searches do not find mention of this before 1967, so
                 the date, and contents, remain uncertain.",
}

@TechReport{Kahan:1967:ITC,
  author =       "W. Kahan",
  title =        "Inclusion Theorems for Clusters of Eigenvalues of
                 {Hermitian} Matrices",
  type =         "report",
  institution =  "Computer Science, University of Toronto",
  address =      "Toronto, Canada",
  year =         "1967",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/gvl.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1967:LMC,
  author =       "W. Kahan",
  title =        "{Laguerre}'s Method and a Circle Which Contains at
                 Least One Zero of a Polynomial",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "4",
  number =       "3",
  pages =        "474--482",
  month =        sep,
  year =         "1967",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65.50",
  MRnumber =     "MR0216743 (35 \#7572)",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
}

@Article{Kahan:1968:CEA,
  author =       "W. M. Kahan",
  title =        "Circumscribing an ellipsoid about the intersection of
                 two ellipsoids",
  journal =      j-CAN-MATH-BULL,
  volume =       "11",
  number =       "??",
  pages =        "437--441",
  month =        "????",
  year =         "1968",
  CODEN =        "CMBUA3",
  DOI =          "http://dx.doi.org/10.4153/CMB-1968-050-2",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  MRclass =      "15.58 (65.00)",
  MRnumber =     "MR0232788 (38 \#1111)",
  MRreviewer =   "W. C. Rheinboldt",
  bibdate =      "Thu Sep 8 10:03:30 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 http://cms.math.ca/cmb/v11/",
  acknowledgement = ack-jr # "\slash " # ack-nhfb,
  fjournal =     "Canadian mathematical bulletin = Bulletin canadien de
                 math{\'e}matiques",
  xxpages =      "437--442",
}

@Article{Kahan:1968:FAC,
  author =       "W. Kahan",
  title =        "Four aphorisms concerning floating point hardware
                 design",
  journal =      j-SIGNUM,
  volume =       "3",
  number =       "2",
  pages =        "??--??",
  month =        jul,
  year =         "1968",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Mon Mar 5 17:26:27 MST 2007",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  articleno =    "2",
}

@TechReport{Kahan:1968:MCI,
  author =       "W. M. Kahan",
  title =        "A More Complete Interval Arithmetic: Lecture Notes for
                 an {Engineering Summer Course in Numerical Analysis} at
                 the {University of Michigan}",
  institution =  "University of Michigan",
  year =         "1968",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-jr,
}

@Article{Davis:1969:SNB,
  author =       "Chandler Davis and W. M. Kahan",
  title =        "Some new bounds on perturbation of subspaces",
  journal =      j-BULL-AMS,
  volume =       "75",
  number =       "4",
  pages =        "863--868",
  month =        "????",
  year =         "1969",
  CODEN =        "BAMOAD",
  ISSN =         "0002-9904 (print), 1936-881X (electronic)",
  ISSN-L =       "0002-9904",
  MRclass =      "47.48",
  MRnumber =     "MR0246155 (39 \#7460)",
  MRreviewer =   "A. McIntosh",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://projecteuclid.org/euclid.bams/1183530664",
  acknowledgement = ack-nhfb,
  ZMnumber =     "0175.43204",
}

@InProceedings{Kahan:1969:ICC,
  author =       "W. M. Kahan",
  editor =       "A. Morrell",
  booktitle =    "Proc. of IFIP Congress 1968, Vol. I",
  title =        "Invited Commentary (Concerning the Invited Paper of
                 {K. Nickel}: Error Bounds and Computer Arithmetic)",
  publisher =    "North-Holland Publ. Comp.",
  address =      "Amsterdam, New York, Oxford",
  pages =        "60--62",
  year =         "1969",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-jr,
}

@InProceedings{Nickel:1969:EBC,
  author =       "K. Nickel",
  editor =       "A. J. H. Morrell",
  booktitle =    "Proc. of IFIP-Congress 1968, Vol. I",
  title =        "Error Bounds and Computer-Arithmetic",
  publisher =    "North-Holland Publ. Comp.",
  address =      "Amsterdam, New York, Oxford",
  pages =        "54--60",
  year =         "1969",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Cf.: Kahan, W. M., Invited Commentary, Ibidem 60-62",
  acknowledgement = ack-jr,
}

@TechReport{Nickel:1969:KBS,
  author =       "K. Nickel",
  title =        "{Das Kahan-Babuska'sche Summierungsverfahren In
                 Triplex-Algol 60}. ({German}) [{The}
                 {Kahan-Babu{\v{s}}ka} Summation Method in
                 {Triplex-Algol 60}]",
  type =         "Interner Bericht Des Inst. F. Informatik",
  number =       "69/3",
  institution =  "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  year =         "1969",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Published in \cite{Nickel:1970:KBS}.",
  acknowledgement = ack-jr,
}

@InCollection{Parlett:1969:CPA,
  author =       "B. N. Parlett and W. Kahan",
  booktitle =    "Information Processing 68 (Proc. IFIP Congress,
                 Edinburgh, 1968), Vol. 1: Mathematics, Software",
  title =        "On the convergence of a practical {${\rm QR}$}
                 algorithm. ({With} discussion)",
  publisher =    "North-Holland",
  address =      "Amsterdam",
  pages =        "114--118",
  year =         "1969",
  MRclass =      "65.40",
  MRnumber =     "MR0255035 (40 \#8242)",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Article{Davis:1970:REP,
  author =       "Chandler Davis and W. M. Kahan",
  title =        "The Rotation of Eigenvectors By a Perturbation.
                 {III}",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "7",
  number =       "1",
  pages =        "1--46",
  month =        mar,
  year =         "1970",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "47.48",
  MRnumber =     "MR0264450 (41 \#9044)",
  MRreviewer =   "C. A. Hall",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/gvl.bib
                 http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "See \cite{Davis:1963:REP,Davis:1965:REP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  ZMnumber =     "0198.47201",
}

@Unpublished{Kahan:1970:ACM,
  author =       "W. M. Kahan",
  title =        "Almost-Commuting Matrices are Near Commuting
                 Matrices",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  day =          "23",
  month =        jul,
  year =         "1970",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Article{Nickel:1970:KBS,
  author =       "K. Nickel",
  title =        "{Das Kahan-Babu{\v{s}}kasche Summierungsverfahren in
                 Trip\-lex-AL\-GOL 60}. ({German}) [{The
                 Kahan-Babu{\v{s}}ka} summation method in
                 {Trip\-lex-AL\-GOL 60}]",
  journal =      j-Z-ANGE-MATH-MECH,
  volume =       "50",
  pages =        "369--373",
  year =         "1970",
  CODEN =        "ZAMMAX",
  ISSN =         "0044-2267 (print), 1521-4001 (electronic)",
  ISSN-L =       "0044-2267",
  bibdate =      "Tue Aug 28 06:12:04 2001",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1971:P,
  author =       "W. Kahan",
  title =        "A Problem",
  journal =      j-SIGNUM,
  volume =       "6",
  number =       "3",
  pages =        "6--6",
  month =        nov,
  year =         "1971",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Mon Dec 12 21:50:03 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "See response \cite{Dorr:1973:REC}.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kahan:1971:SEA,
  author =       "W. M. Kahan",
  title =        "A Survey of Error Analysis",
  crossref =     "Freiman:1971:PIC",
  pages =        "1214--1239",
  year =         "1971",
  MRclass =      "65G05",
  MRnumber =     "MR0458845 (56 \#17045)",
  bibdate =      "Tue Aug 28 05:24:53 2001",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  series =       "Information Processing 71",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  remark =       "This paper contains the modified compensating
                 summation algorithm wherein `e = (temp - s) + y' is
                 replaced by `f = 0; if (sign(temp) == sign(y)) {f =
                 (0.46*s - s) + s} e = ((temp - f) - (s - f)) + y',
                 cited in e.g.,
                 \cite{Dalhquist:1974:NM,Higham:1993:AFP}.",
}

@InProceedings{Anderson:1972:HHI,
  author =       "Donald G. M. Anderson and Joseph Traub and W. Kahan",
  title =        "How to Help an Ill-Posed Problem Get Well",
  crossref =     "ACM:1972:PAA",
  pages =        "663--663",
  year =         "1972",
  bibdate =      "Mon Apr 25 14:54:19 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "The first annual George Forsythe Memorial Lecture,
                 presented by W. Kahan.",
  acknowledgement = ack-nhfb,
}

@TechReport{Kahan:1972:CCC,
  author =       "W. Kahan",
  title =        "Conserving Confluence Curbs Ill-Condition",
  type =         "Technical Report",
  number =       "6",
  institution =  "Computer Science Department, University of
                 California",
  address =      "Berkeley",
  pages =        "????",
  month =        aug,
  year =         "1972",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1972:MHK,
  author =       "W. Kahan",
  title =        "In memoriam: {Hirondo Kuki}: {Apr. 25, 1925--Dec. 28,
                 1971}",
  journal =      j-SIGNUM,
  volume =       "7",
  number =       "1",
  pages =        "8--10",
  month =        apr,
  year =         "1972",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:49:58 MDT 2005",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/signum.bib;
                 http://portal.acm.org/;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Article{Dorr:1973:REC,
  author =       "Fred W. Dorr and Cleve B. Moler",
  title =        "Roundoff error on the {CDC 6600\slash 7600}
                 computers",
  journal =      j-SIGNUM,
  volume =       "8",
  number =       "2",
  pages =        "24--26",
  month =        apr,
  year =         "1973",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:49:59 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "See \cite{Kahan:1971:P} for the original problem.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Univ. California, Los Alamos, NM, USA",
  keywords =     "arithmetic; CDC 6600/7600 computers; computer; digital
                 arithmetic; program; roundoff error",
  treatment =    "P Practical; X Experimental",
}

@Article{Kahan:1973:EMR,
  author =       "W. Kahan",
  title =        "Every {$n \times n$} Matrix {$Z$} with Real Spectrum
                 Satisfies {$\|Z-Z^*\| \le \|Z+Z^*\| (\log_2n+0.038)$}",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "39",
  pages =        "235--241",
  year =         "1973",
  CODEN =        "PAMYAR",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "15A60",
  MRnumber =     "MR0313278 (47 \#1833)",
  MRreviewer =   "David Carlson",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
}

@TechReport{Kahan:1973:IAC,
  author =       "W. M. Kahan",
  title =        "Implementation of Algorithms (Chapter 12)",
  number =       "AD 769-124",
  institution =  "National Technical Information Service",
  address =      "Springfield, Virginia",
  year =         "1973",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-jr,
}

@TechReport{Kahan:1973:IAL,
  author =       "W. Kahan",
  title =        "Implementation of Algorithms (Lecture Notes by {W. S.
                 Haugeland} and {D. Hough})",
  type =         "Technical Report",
  number =       "20",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "????",
  year =         "1973",
  bibdate =      "Tue Aug 28 05:28:07 2001",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  mynote =       "I have photocopy of Part I, secs 9 and 10 from Jeremy
                 Du Croz. Saw Philip Gill's complete copy, Dec 1994.
                 Nothing I wanted to copy.",
  remark =       "This paper contains the modified compensating
                 summation algorithm wherein `e = (temp - s) + y' is
                 replaced by `f = 0; if (sign(temp) == sign(y)) {f =
                 (0.46*s - s) + s} e = ((temp - f) - (s - f)) + y',
                 cited in e.g.,
                 \cite{Dalhquist:1974:NM,Higham:1993:AFP}. Kahan remarks
                 ``The mysterious constant 0.46, which could perhaps be
                 any number between 0.25 and 0.50, and the fact that the
                 proof requires a consideration of known machines
                 designs, indicate that this algorithm is not an advance
                 in computer science.''",
}

@TechReport{Kahan:1974:ALA,
  author =       "W. Kahan and B. N. Parlett",
  title =        "An Analysis of {Lanczos} Algorithms for Symmetric
                 Matrices",
  number =       "ERL-M467",
  institution =  "University of California, Berkeley",
  address =      "Berkeley, CA, USA",
  year =         "1974",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/gvl.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1975:EP,
  author =       "W. Kahan",
  title =        "An ellipse problem",
  journal =      j-SIGSAM,
  volume =       "9",
  number =       "3",
  pages =        "11--??",
  month =        aug,
  year =         "1975",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Mon Apr 25 05:53:53 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1975:SNH,
  author =       "W. Kahan",
  title =        "Spectra of nearly {Hermitian} matrices",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "48",
  pages =        "11--17",
  year =         "1975",
  CODEN =        "PAMYAR",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "15A42",
  MRnumber =     "MR0369394 (51 \#5627)",
  MRreviewer =   "B. N. Moyls",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/gvl.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
}

@InProceedings{Laveuve:1975:DKA,
  author =       "S. E. Laveuve",
  editor =       "K. Nickel",
  booktitle =    "Interval Mathematics",
  title =        "{Definition Einer Kahan-Arithmetik Und Ihre
                 Implementierung}. ({German}) [{Definition} of a {Kahan}
                 Arithmetic and its Implementation]",
  volume =       "29",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "236--245",
  year =         "1975",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  series =       "Lecture Notes In Computer Science",
  acknowledgement = ack-jr,
}

@InCollection{Kahan:1976:HFSa,
  author =       "W. Kahan and B. N. Parlett",
  booktitle =    "Sparse matrix computations (Proc. Sympos., Argonne
                 Nat. Lab., Lemont, Ill., 1975)",
  title =        "How far should you go with the {Lanczos} process?",
  publisher =    pub-AP,
  address =      pub-AP:adr,
  pages =        "131--144",
  year =         "1976",
  MRclass =      "65F15",
  MRnumber =     "MR0458836 (56 \#17036)",
  MRreviewer =   "Michael S. Martin",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Kahan:1976:HFSb,
  author =       "W. Kahan and B. N. Parlett",
  editor =       "J. Bunch and D. Rose",
  booktitle =    "Sparse Matrix Computations",
  title =        "How Far Should You Go with the {Lanczos} Process?",
  publisher =    pub-AP,
  address =      pub-AP:adr,
  pages =        "131--144",
  year =         "1976",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/gvl.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.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 =  "Electronics Research Laboratory, College of
                 Engineering, University of California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "ii + 28",
  day =          "6",
  month =        apr,
  year =         "1977",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.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 =          "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-jr,
}

@TechReport{Kahan:1977:NSC,
  author =       "W. Kahan",
  title =        "And now for something completely different: {The Texas
                 Instruments SR-52}",
  type =         "Memorandum",
  number =       "No. UCB/ERL M77/23",
  institution =  "Electronics Research Laboratory, College of
                 Engineering, University of California",
  address =      "Berkeley",
  pages =        "????",
  month =        apr,
  year =         "1977",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Article{Lauer:1977:SKP,
  author =       "Markus Lauer",
  title =        "A solution to {Kahan}'s problem ({SIGSAM} problem No.
                 9)",
  journal =      j-SIGSAM,
  volume =       "11",
  number =       "2",
  pages =        "16--20",
  month =        "????",
  year =         "1977",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Fri Sep 06 06:46:33 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/sigsam.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@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 =  "Electronics Research Laboratory, College of
                 Engineering, University of California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "16",
  year =         "1978",
  bibdate =      "Fri Nov 11 05:15:08 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.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 =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
  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",
  ZMnumber =     "0397.65081",
}

@Article{Coonen:1979:PSB,
  author =       "Jerome Coonen and William Kahan and John Palmer and
                 Tom Pittman and David Stevenson",
  title =        "A Proposed Standard for Binary Floating Point
                 Arithmetic: Draft 5.11",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "3S (Special issue)",
  pages =        "4--12",
  month =        oct,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:07 MDT 2005",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/signum.bib;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://portal.acm.org/;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  keywords =     "arithmetic; binary; digital arithmetic; floating
                 point; IEEE Computer Society; Microprocessor; standard;
                 standards; Standards Subcommittee",
  treatment =    "P Practical",
  xxnumber =     "si-2",
}

@Article{Kahan:1979:PCK,
  author =       "William M. Kahan",
  title =        "Personal Calculator Has Key to Solve Any Equation
                 {$f(x)=0$}",
  journal =      j-HEWLETT-PACKARD-J,
  volume =       "30",
  number =       "12",
  pages =        "20--26",
  month =        dec,
  year =         "1979",
  CODEN =        "HPJOAX",
  ISSN =         "0018-1153",
  MRclass =      "65-01 (65G05 65H05)",
  MRnumber =     "MR574853 (81k:65002)",
  MRreviewer =   "R. P. Brent",
  bibdate =      "Tue Mar 25 14:12:15 MST 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/hpj.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/SOLVEkey.pdf",
  acknowledgement = ack-nhfb,
  classcodes =   "C5420 (Mainframes and minicomputers); C7310
                 (Mathematics computing)",
  corpsource =   "Univ. of California, Berkeley, CA, USA",
  fjournal =     "Hewlett--Packard Journal",
  keywords =     "electronic calculators; equation solving; finding;
                 handheld calculator; HP 34C; linear algebra; personal
                 calculator; root; SOLVE",
  reviewer =     "R. P. Brent",
  treatment =    "P Practical",
}

@InProceedings{Kahan:1979:PIC,
  author =       "W. Kahan and J. Palmer and J. Coonen",
  title =        "Proposed {IEEE-CS Standard for Binary Floating Point
                 Arithmetic}",
  crossref =     "Gentleman:1979:PCS",
  pages =        "32--36",
  year =         "1979",
  bibdate =      "Tue Apr 26 07:05:24 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1979:PFP,
  author =       "W. Kahan and J. Palmer",
  title =        "On a Proposed Floating-Point Standard",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "3S (Special issue)",
  pages =        "13--21",
  month =        oct,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:07 MDT 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/signum.bib;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://portal.acm.org/",
  abstract =     "A standard for binary floating-point arithmetic is
                 being proposed and there is a very real possibility
                 that it will be adopted by many manufacturers and
                 implemented on a wide range of computers. This
                 development matters to all of us concerned with
                 numerical software. One of the principal motivations
                 for the standard is to distribute more evenly the
                 burden of portability between hardware and software. At
                 present, any program intended to be portable must be
                 designed for a mythical computer that enjoys no
                 capability not supported by every computer on which the
                 program will be run. That mythical computer is so much
                 grubbier than almost any real computer that a portable
                 program will frequently be denigrated as ``suboptimal''
                 and then supplanted by another program supposedly
                 ``optimal'' for the real computer in question but often
                 inferior in critical respects like reliability. A
                 standard --- almost any reasonable standard --- will
                 surely improve the situation. A standard environment
                 for numerical programs will promote fair comparisons
                 and sharing of numerical codes, thereby lowering costs
                 and prices. Furthermore, we have chosen repeatedly to
                 enrich that environment in order that applications
                 programs be simpler and more reliable. Thus will the
                 onus of portability be shared among hardware
                 manufacturers and software producers.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Univ. of California, Berkeley, CA, USA",
  keywords =     "arithmetic; digital arithmetic; floating point;
                 proposal; standard; standards",
  treatment =    "P Practical",
  xxnumber =     "si-2",
}

@Misc{Kahan:1980:AEG,
  author =       "W. Kahan",
  title =        "{Aitken}'s Extrapolation and {Gaussian} Quadrature",
  howpublished = "IEEE Floating-Point Subcommittee Working Document
                 P754/80-1.19",
  year =         "1980",
  bibdate =      "Wed Oct 13 08:50:00 2010",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1980:HCE,
  author =       "William M. Kahan",
  title =        "Handheld Calculator Evaluates Integrals",
  journal =      j-HEWLETT-PACKARD-J,
  volume =       "31",
  number =       "8",
  pages =        "23--32",
  month =        aug,
  year =         "1980",
  CODEN =        "HPJOAX",
  ISSN =         "0018-1153",
  MRclass =      "65-04 (65D30)",
  MRnumber =     "MR590837 (82d:65001)",
  MRreviewer =   "S. Dubuc",
  bibdate =      "Tue Mar 25 14:12:15 MST 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/hpj.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/INTGTkey.pdf",
  acknowledgement = ack-nhfb,
  classcodes =   "C4160 (Numerical integration and differentiation);
                 C5230 (Digital arithmetic methods)",
  corpsource =   "Hewlett--Packard Co., Palo Alto, CA, USA",
  fjournal =     "Hewlett--Packard Journal",
  keywords =     "34C; digital arithmetic; handheld calculator; HP;
                 integrals; integration; numerical integration;
                 numerical methods",
  reviewer =     "S. Dubuc",
  treatment =    "G General Review; P Practical",
}

@InProceedings{Kahan:1980:IAO,
  author =       "William M. Kahan",
  title =        "Interval Arithmetic Options in the Proposed {IEEE
                 Floating Point Arithmetic Standard}",
  crossref =     "Nickel:1980:IMP",
  pages =        "99--128",
  year =         "1980",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-jr,
}

@Unpublished{Kahan:1980:SPI,
  author =       "W. Kahan",
  title =        "Software {$\sqrt{x}$} for the Proposed {IEEE}
                 Floating-Point Standard",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  day =          "25",
  month =        aug,
  year =         "1980",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Book{Laveuve:1980:DKA,
  author =       "S. E. Laveuve",
  title =        "{Definition Einer Kahan-Arithmetik Und Ihre
                 Implementierung In Tripleo}. ({German}) [{Definition} of
                 a {Kahan} Arithmetic and its implementation in
                 {Tripleo}]",
  publisher =    pub-AP,
  address =      pub-AP:adr,
  pages =        "355--366",
  year =         "1980",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-jr,
}

@Article{Kahan:1981:PEC,
  author =       "W. Kahan",
  title =        "The Programming Environment's Contribution to Program
                 Robustness",
  journal =      j-SIGNUM,
  volume =       "16",
  number =       "4",
  pages =        "10--??",
  month =        oct,
  year =         "1981",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Mon Apr 25 06:38:05 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Kahan:1981:WDW,
  author =       "W. Kahan",
  title =        "Why Do We Need a Floating-Point Arithmetic Standard?",
  type =         "Technical Report",
  institution =  inst-BERKELEY,
  address =      inst-BERKELEY:adr,
  pages =        "41",
  day =          "12",
  month =        feb,
  year =         "1981",
  bibdate =      "Fri Apr 7 12:22:17 GMT 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  remark =       "Available in a retypeset version
                 \cite{Kahan:2001:WDW}.",
}

@Article{Neumann:1981:KRC,
  author =       "M. Neumann",
  title =        "The {Kahan S.O.R.} convergence bound for nonsingular
                 and irreducible ${M}$-matrices",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "39",
  pages =        "205--222",
  year =         "1981",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "65F10 (15A06)",
  MRnumber =     "82j:65021",
  MRreviewer =   "R. J. Plemmons",
  bibdate =      "Thu Jan 23 11:18:08 MST 1997",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/linala1980.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  remark =       "Refers to Kahan's 1958 Ph.D. thesis.",
}

@Article{Davis:1982:NPD,
  author =       "Chandler Davis and W. M. Kahan and H. F. Weinberger",
  title =        "Norm-Preserving Dilations and their Applications to
                 Optimal Error Bounds",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "19",
  number =       "3",
  pages =        "445--469",
  month =        jun,
  year =         "1982",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "47A20 (65J10)",
  MRnumber =     "MR656462 (84b:47010)",
  MRreviewer =   "Peter Lancaster",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "See \cite{Meinguet:1986:DKW}.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
}

@TechReport{Kahan:1982:BCC,
  author =       "W. Kahan",
  title =        "Branch Cuts for Complex Elementary Functions",
  type =         "Technical Report",
  number =       "PAM-105",
  institution =  inst-BERKELEY-CPAM,
  address =      inst-BERKELEY-CPAM:adr,
  month =        oct,
  year =         "1982",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Math/Matrix.bib.gz;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  keywords =     "na, elementary function",
}

@InProceedings{Kahan:1982:NOS,
  author =       "W. Kahan and Jerome T. Coonen",
  title =        "The Near Orthogonality of Syntax, Semantics, and
                 Diagnostics in Numerical Programming Environments",
  crossref =     "Reid:1982:RBN",
  pages =        "103--115",
  year =         "1982",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  catcode =      "D.3; G.1.0; F.3.2; D.2.5; D.2; D.3",
  content =      "Programmers of early computers had to content
                 themselves with what the machine designers offered and
                 be glad that the hardware worked at all. Later, with
                 the introduction of higher-level languages, the
                 computing environment was modified by the language
                 designers who attempted to resolve a three-cornered
                 tug-of-war among implementation efficiency, program
                 portability, and usefulness to the programmer. The
                 conflict between the first two resulted in languages
                 that reflected the least common denominator of
                 available hardware, since language designers were
                 disinclined to mention any capability not available on
                 all computers. A case in point is floating-point
                 arithmetic, where the subtleties of overflow,
                 underflow, and rounding are generally well beyond the
                 control of the programmer in a high-level language. The
                 new standard for binary floating-point arithmetic that
                 has been proposed by IEEE Computer Society's
                 Floating-Point Committee, Task P754 [1], makes an
                 attempt to escape from this situation. It represents
                 the Committee's view of the floating-point requirements
                 of the \ldots{}",
  CRclass =      "D.3.1 Formal Definitions and Theory; G.1.0 General;
                 G.1.0 Computer arithmetic; F.3.2 Semantics of
                 Programming Languages; F.3.2 Algebraic approaches to
                 semantics; D.2.5 Testing and Debugging; D.2.5
                 Diagnostics; D.2.6 Programming Environments; D.3.3
                 Language Constructs",
  CRnumber =     "8401-0021",
  descriptor =   "Software, PROGRAMMING LANGUAGES, Formal Definitions
                 and Theory; Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic; Theory of
                 Computation, LOGICS AND MEANINGS OF PROGRAMS, Semantics
                 of Programming Languages, Algebraic approaches to
                 semantics; Software, SOFTWARE ENGINEERING, Testing and
                 Debugging, Diagnostics; Software, SOFTWARE ENGINEERING,
                 Programming Environments; Software, PROGRAMMING
                 LANGUAGES, Language Constructs",
  genterm =      "LANGUAGES; STANDARDIZATION",
  keywords =     "floating-point arithmetic; rounding errors",
  reviewer =     "M. Marcotty; Marcotty, M",
  source =       "in the relationship between numerical computation and
                 programming languages. Proc. IFIP TC2 working
                 conference (Boulder, CO, Aug. 3-7, 1981) J. K. Reid
                 (Ed.) Elsevier North-Holland, Inc., New York, 1982",
  subject =      "D. Software; D.3 PROGRAMMING LANGUAGES; G. Mathematics
                 of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of
                 Computation; F.3 LOGICS AND MEANINGS OF PROGRAMS; D.
                 Software; D.2 SOFTWARE ENGINEERING; D. Software; D.2
                 SOFTWARE ENGINEERING; D. Software; D.3 PROGRAMMING
                 LANGUAGES",
}

@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",
  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 =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/gvl.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
}

@Book{Waser:1982:IAD,
  author =       "Shlomo Waser and Michael J. Flynn",
  title =        "Introduction to Arithmetic for Digital Systems
                 Designers",
  publisher =    pub-HRW,
  address =      pub-HRW:adr,
  pages =        "xvii + 308",
  year =         "1982",
  ISBN =         "0-03-060571-7",
  ISBN-13 =      "978-0-03-060571-0",
  LCCN =         "TK7895.A65 W37 1982",
  bibdate =      "Sat Apr 8 10:43:33 GMT 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  mynote =       "Nothing of particular note. Discusses (a non-final)
                 `Kahan proposal' for the IEEE standard and criticisms
                 of it, but this part now obsolete.",
}

@TechReport{Kahan:1983:M,
  author =       "W. Kahan",
  title =        "Minimizing $q \times m - n$",
  institution =  inst-BERKELEY-MATH-EECS,
  address =      inst-BERKELEY-MATH-EECS:adr,
  month =        mar,
  year =         "1983",
  bibdate =      "Fri May 03 12:26:29 2002",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/testpi/nearpi.c",
  acknowledgement = ack-nhfb,
  remark =       "Nearpi, a C program to exhibit large floating-point
                 numbers $Z = m * 2 ^ L$ very close to integer multiples
                 of $\pi/2$.",
}

@InProceedings{Kahan:1983:MWS,
  author =       "W. Kahan",
  title =        "Mathematics Written in Sand --- The {HP-15C}, {Intel
                 8087}, etc.",
  crossref =     "Anonymous:1983:PSC",
  pages =        "12--26",
  year =         "1983",
  bibdate =      "Fri May 03 12:02:15 2002",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathSand.pdf",
  acknowledgement = ack-nhfb,
  bookpages =    "vi + 344",
  remark =       "The original published version was a photoreduction of
                 dot-matrix printer output; the URL points to a cleaner
                 version.",
}

@Unpublished{Kahan:1983:PISa,
  author =       "W. Kahan",
  title =        "The Proposed {IEEE Standard p754 for Floating-Point
                 Arithmetic}: {What} Good is it?",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "6",
  year =         "1983",
  bibdate =      "Sun Dec 18 15:08:57 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
  mynote =       "Date deduced from info in the paper.",
}

@InProceedings{Kahan:1983:PISb,
  author =       "W. Kahan",
  title =        "The Proposed {IEEE Standard p754 for Floating-Point
                 Arithmetic}: {What} Good is it?",
  crossref =     "IEEE:1983:MMW",
  pages =        "??--??",
  year =         "1983",
  bibdate =      "Tue Apr 26 07:17:11 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Article{Ozawa:1983:AIK,
  author =       "K. Ozawa",
  title =        "Analysis and Improvement of {Kahan}'s Summation
                 Algorithm",
  journal =      j-INFO-PROC,
  volume =       "6",
  number =       "4",
  pages =        "226--230",
  year =         "1983",
  bibdate =      "Mon Sep 12 08:06:17 1994",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nj,
}

@Article{Cody:1984:PRW,
  author =       "William J. {Cody, Jr.} and Jerome T. Coonen and David
                 M. Gay and K. Hanson and David Hough and W. Kahan and
                 R. Karpinski and John F. Palmer and F. N. Ris and D.
                 Stevenson",
  title =        "A Proposed Radix- and Word-length-independent Standard
                 for Floating-Point Arithmetic",
  journal =      j-IEEE-MICRO,
  volume =       "4",
  number =       "4",
  pages =        "86--100",
  month =        aug,
  year =         "1984",
  CODEN =        "IEMIDZ",
  DOI =          "http://dx.doi.org/10.1109/MM.1984.291224",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "Compendex database;
                 http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/g/gay-david-m.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib;
                 http://www.math.utah.edu/pub/tex/bib/standard.bib;
                 Science Citation Index database (1980--2000);
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "723; 902; 921",
  corpsource =   "Argonne Nat. Lab., IL, USA",
  keywords =     "computer software; digital arithmetic; exceptions;
                 floating-point arithmetic; IEEE P854; independent
                 standard; infinity; mathematical techniques --- Digital
                 Arithmetic; NaNs; operations; precision; proposed
                 radix- and word-length-independent standard; radix
                 independent standard; rounding errors; standardization;
                 standards; traps; word-length-",
  mynote =       "IEEE P854 draft 1.0",
  subject =      "K.1 Computing Milieux, THE COMPUTER INDUSTRY,
                 Suppliers \\ G.1.0 Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic",
  treatment =    "P Practical",
  xxtitle =      "A Proposed Radix-Independent and
                 Word-Length-Independent Standard for Floating-Point
                 Arithmetic",
}

@Article{Cody:1985:PRW,
  author =       "W. J. Cody and J. T. Coonen and D. M. Gay and K.
                 Hanson and D. Hough and W. Kahan and R. Karpinski and
                 J. Palmer and F. N. Ris and D. Stevenson",
  title =        "A Proposed Radix- and Word-length-independent Standard
                 for Floating-point Arithmetic",
  journal =      j-SIGNUM,
  volume =       "20",
  number =       "1",
  pages =        "37--51",
  month =        jan,
  year =         "1985",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:14:17 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/signum.bib;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Kahan:1985:AIA,
  author =       "W. Kahan and E. LeBlanc",
  title =        "Anomalies in the {IBM ACRITH} Package",
  crossref =     "Hwang:1985:PSC",
  pages =        "322--331",
  year =         "1985",
  DOI =          "http://dx.doi.org/10.1109/ARITH.1985.6158956",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Kahan_LeBlanc.pdf",
  abstract =     "The IBM ACRITH package of numerical software is
                 advertised as reliable and easy to use; but sometimes
                 its results must astonish or confuse a naive user, This
                 report exhibits a few of the surprises. For instance, a
                 finite continued fraction, easy to evaluate in two
                 dozen keystrokes on a handheld calculator, causes
                 ACRITH to overflow either exponent range or 15
                 Megabytes of virtual memory. Lacking access to source
                 code, we must speculate to explain the anomalies. Some
                 seem attributable to small bugs in the code; some to
                 optimistic claims or oversimplifications in the code's
                 documentation; some to flaws in the doctrine underlying
                 the code. We conclude that different techniques than
                 used by ACRITH might have been about as accurate and
                 yet more economical, robust and perspicuous.",
  acknowledgement = ack-jr # " and " # ack-nj,
  keywords =     "ARITH-7",
}

@TechReport{Kahan:1985:MSC,
  author =       "W. Kahan",
  title =        "On the monotonicity of some computed functions",
  type =         "Technical Report",
  number =       "PAM-261",
  institution =  inst-BERKELEY-CPAM,
  address =      inst-BERKELEY-CPAM:adr,
  month =        jan,
  year =         "1985",
  bibdate =      "Fri Nov 11 17:10:00 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1986:DVB,
  author =       "W. Kahan",
  title =        "Decimal Versus Binary Floating-Point Arithmetic",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "4",
  day =          "12",
  month =        nov,
  year =         "1986",
  bibdate =      "Mon Dec 26 21:15:58 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@TechReport{Kahan:1986:RAF,
  author =       "W. Kahan",
  title =        "Rational Arithmetic in Floating-Point",
  type =         "Technical Report",
  number =       "PAM-343",
  institution =  inst-BERKELEY-CPAM,
  address =      inst-BERKELEY-CPAM:adr,
  pages =        "8",
  month =        sep,
  year =         "1986",
  bibdate =      "Sun Dec 18 15:33:08 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1986:RPE,
  author =       "W. Kahan",
  title =        "Roundoff in Polynomial Evaluation",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "7",
  day =          "16",
  month =        nov,
  year =         "1986",
  bibdate =      "Sun Dec 18 15:11:41 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; rounding errors",
}

@TechReport{Kahan:1986:SRC,
  author =       "W. Kahan",
  title =        "To Solve a Real Cubic Equation",
  type =         "Technical Report",
  number =       "PAM-352",
  institution =  inst-BERKELEY-CPAM,
  address =      inst-BERKELEY-CPAM:adr,
  pages =        "20",
  month =        nov,
  year =         "1986",
  bibdate =      "Tue Feb 7 15:14:37 GMT 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  mynote =       "Plus Oct 11 1991 updated version of which I have a few
                 pages.",
}

@Article{Meinguet:1986:DKW,
  author =       "Jean Meinguet",
  title =        "On the {Davis-Kahan-Weinberger} solution of the
                 norm-preserving dilation problem",
  journal =      j-NUM-MATH,
  volume =       "49",
  number =       "2/3",
  pages =        "331--341",
  month =        jul,
  year =         "1986",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "47A20 (15A09 47A62 65F05)",
  MRnumber =     "87i:47008",
  MRreviewer =   "T. Ando",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/nummath.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Refers to the work \cite{Davis:1982:NPD}.",
  acknowledgement = ack-nhfb,
  classification = "B0210 (Algebra); C1110 (Algebra)",
  corpsource =   "Inst. de Math. pure et Appl., Louvain Univ., Belgium",
  keywords =     "Davis-Kahan-Weinberger solution; finite-dimensional
                 dilations; Hilbert spaces; matrix algebra; matrix
                 theory; norm-preserving dilation problem",
  treatment =    "T Theoretical or Mathematical",
}

@TechReport{Fateman:1987:IEI,
  author =       "Richard J. Fateman and W. Kahan",
  title =        "Improving exact integrals from symbolic algebra
                 systems",
  type =         "Technical Report",
  number =       "PAM-261",
  institution =  inst-BERKELEY-CPAM,
  address =      inst-BERKELEY-CPAM:adr,
  month =        aug,
  year =         "1987",
  bibdate =      "Fri Nov 11 17:10:00 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cybertester.com/data/iintegr.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kahan:1987:BCC,
  author =       "W. Kahan",
  title =        "Branch Cuts for Complex Elementary Functions or Much
                 Ado About Nothing's Sign Bit",
  crossref =     "Iserles:1987:SAN",
  volume =       "9",
  pages =        "165--211",
  year =         "1987",
  MRclass =      "65E05",
  MRnumber =     "88k:65027",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  series =       "Inst. Math. Appl. Conf. Ser. New Ser.",
  URL =          "http://www.cs.berkeley.edu/~dbindel/class/cs279/",
  acknowledgement = ack-nhfb # " and " # ack-nj,
}

@Unpublished{Kahan:1987:CWF,
  author =       "W. Kahan",
  title =        "Checking whether floating-point division is correctly
                 rounded",
  year =         "1987",
  bibdate =      "Mon Apr 25 05:40:03 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; rounding errors",
}

@Unpublished{Kahan:1987:DPI,
  author =       "W. Kahan",
  title =        "Doubled-Precision {IEEE} Standard 754 Floating-Point
                 Arithmetic",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "14",
  day =          "26",
  month =        feb,
  year =         "1987",
  bibdate =      "Fri Dec 16 09:06:09 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Higham:1993:AFP}.",
}

@Unpublished{Kahan:1987:HSM,
  author =       "W. Kahan",
  title =        "How Should {Max} and {Min} be Defined?",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "3",
  day =          "19",
  month =        aug,
  year =         "1987",
  bibdate =      "Thu Dec 15 11:52:20 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1987:PCF,
  author =       "W. Kahan",
  title =        "Presubstitution and Continued Fractions",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "8",
  day =          "17",
  month =        mar,
  year =         "1987",
  bibdate =      "Thu Dec 15 11:52:20 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
  xxnote =       "Found cited as 1995??",
}

@TechReport{Demmel:1988:CSS,
  author =       "J. Demmel and W. Kahan",
  title =        "Computing Small Singular Values of Bidiagonal Matrices
                 with Guaranteed High Relative Accuracy",
  type =         "LAPACK Working Note",
  number =       "03",
  institution =  inst-ANL-MCS,
  address =      inst-ANL-MCS:adr,
  month =        feb,
  year =         "1988",
  bibdate =      "Fri Apr 22 17:06:37 2005",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/lawn.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "ANL, MCS-TM-110, February 1988.",
  URL =          "http://www.netlib.org/lapack/lawns/lawn03.ps;
                 http://www.netlib.org/lapack/lawnspdf/lawn03.pdf",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1988:CPA,
  author =       "W. Kahan",
  title =        "A Computer Program with Almost No Significance",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  day =          "9",
  month =        nov,
  year =         "1988",
  bibdate =      "Thu Dec 15 14:07:12 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Misc{Lenstra:1988:PT,
  author =       "H. W. {Lenstra, Jr.}",
  title =        "Probability theory",
  howpublished = "World-Wide Web document",
  pages =        "1",
  month =        nov,
  year =         "1988",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/Lenstra.pdf",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1989:CAA,
  author =       "W. Kahan",
  title =        "Calculating Area and Angle of a Needle-Like Triangle",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "5",
  day =          "26",
  month =        jan,
  year =         "1989",
  bibdate =      "Thu Dec 15 14:03:57 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1989:OFH,
  author =       "W. Kahan",
  title =        "The Occasional Futility of Higher-Precision
                 Arithmetic",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "3",
  day =          "28",
  month =        sep,
  year =         "1989",
  bibdate =      "Fri Dec 16 09:07:41 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1989:PCA,
  author =       "W. Kahan",
  title =        "Paradoxes in Concepts of Accuracy",
  howpublished = "Lecture notes from Joint Seminar on Issues and
                 Directions in Scientific Computation, Berkeley",
  year =         "1989",
  bibdate =      "Sat Sep 17 18:40:08 1994",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1989:SRN,
  author =       "W. Kahan",
  title =        "A Singularity Removable Numerically when Arithmetic is
                 Clean",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "2",
  day =          "17",
  month =        may,
  year =         "1989",
  bibdate =      "Thu Dec 15 12:50:47 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@TechReport{Anderson:1990:PEL,
  author =       "E. Anderson and C. Bischof and J. Demmel and J.
                 Dongarra and J. {Du Croz} and S. Hammarling and W.
                 Kahan",
  title =        "Prospectus for an Extension to {LAPACK}: {A} Portable
                 Linear Algebra Library for High-Performance Computers",
  type =         "LAPACK Working Note" # " and " # type-CSDTR,
  number =       "26 and CS-90-118",
  institution =  inst-UTK-CS,
  address =      inst-UTK-CS:adr,
  pages =        "10",
  month =        nov,
  year =         "1990",
  bibdate =      "Fri Apr 22 17:06:37 2005",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/par.lin.alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/lawn.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "LAPACK Working Note \#26. UT-CS-90-118, November
                 1990.",
  URL =          "http://www.netlib.org/lapack/lawns/lawn26.ps;
                 http://www.netlib.org/lapack/lawnspdf/lawn26.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Demmel:1990:ASV,
  author =       "James W. Demmel and W. Kahan",
  title =        "Accurate Singular Values of Bidiagonal Matrices",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "11",
  number =       "5",
  pages =        "873--912",
  month =        sep,
  year =         "1990",
  CODEN =        "SIJCD4",
  ISSN =         "0196-5204",
  MRclass =      "65F15",
  MRnumber =     "MR1057146 (91i:65072)",
  MRreviewer =   "J. Segethov{\'a}",
  bibdate =      "Tue Apr 29 19:18:28 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib;
                 Parallel/par.lin.alg.bib; Theory/Matrix.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 B0290H (Linear algebra); C4130 (Interpolation and
                 function approximation); C4140 (Linear algebra)",
  corpsource =   "Courant Inst. of Math. Sci., New York Univ., NY, USA",
  fjournal =     "Society for Industrial and Applied Mathematics.
                 Journal on Scientific and Statistical Computing",
  keywords =     "bidiagonal matrices; floating-point arithmetic;
                 iterative methods; matrix algebra; rounding errors;
                 singular value decomposition",
  mynote =       "LAPACK Working Note \#3, Tech. Memo. 110, Argonne, Feb
                 1988",
  treatment =    "T Theoretical or Mathematical",
}

@TechReport{Kahan:1990:BPA,
  author =       "W. Kahan",
  title =        "Better to prescribe arithmetic than describe it",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  day =          "21",
  month =        feb,
  year =         "1990",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Turing Award Lecture presented at ACM Conference,
                 Washington",
  acknowledgement = ack-nhfb,
  mynote =       "Same talk given at Toronto 10 April 1990.",
}

@InProceedings{Kahan:1990:HCA,
  author =       "W. Kahan",
  title =        "How {Cray}'s arithmetic hurts scientific computation
                 (and what might be done about it)",
  crossref =     "CUG:1990:PSC",
  pages =        "42",
  day =          "14",
  month =        jun,
  year =         "1990",
  bibdate =      "Tue Jan 03 18:17:16 2006",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript prepared for the Cray User Group meeting in
                 Toronto, Canada, April 10, 1990.",
  URL =          "http://754r.ucbtest.org/issues/cray-hurts-uk.pdf;
                 http://754r.ucbtest.org/issues/cray-hurts-ut.pdf;
                 http://754r.ucbtest.org/issues/cray-hurts.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1990:PCA,
  author =       "William Kahan",
  title =        "Paradoxes in concepts of accuracy",
  publisher =    "Carnegie Mellon University",
  address =      "Pittsburgh, PA, USA",
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "1 videocassette (60 min.)",
  series =       "Distinguished lecture series",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic.; Floating-point arithmetic ---
                 Data processing.",
  remark =       "Lecture given February 15, 1990. VHS format. Lecturer,
                 William Kahan. Paradoxes expose errors in conventional
                 wisdom about floating-point arithmetic.",
}

@Unpublished{Kahan:1990:POC,
  author =       "W. Kahan",
  title =        "Paradoxes in Our Concepts of Computational Accuracy",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "1",
  day =          "1",
  month =        oct,
  year =         "1990",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1990:TCC,
  author =       "W. Kahan",
  title =        "Twenty Challenges for Computerized Symbolic Algebra
                 Systems",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "3",
  day =          "16",
  month =        aug,
  year =         "1990",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@TechReport{Demmel:1991:DPHa,
  author =       "James Demmel and Jack Dongarra and W. Kahan",
  title =        "On Designing Portable High Performance Numerical
                 Libraries",
  type =         "LAPACK Working Note",
  number =       "39",
  institution =  inst-UTK-CS,
  address =      inst-UTK-CS:adr,
  month =        jul,
  year =         "1991",
  bibdate =      "Fri Apr 22 17:06:37 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 http://www.math.utah.edu/pub/tex/bib/lawn.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "UT-CS-91-141, July, 1991.",
  URL =          "http://www.netlib.org/lapack/lawns/lawn39.ps;
                 http://www.netlib.org/lapack/lawnspdf/lawn39.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Demmel:1991:DPHb,
  author =       "J. Demmel and J. Dongarra and W. Kahan",
  title =        "On Designing Portable High Performance Numerical
                 Libraries",
  crossref =     "Griffiths:1991:NAP",
  pages =        "??--??",
  month =        jun,
  year =         "1991",
  bibdate =      "Tue Feb 26 10:10:44 2002",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/par.lin.alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Kahan:1991:APL,
  author =       "William Kahan and J. W. Thomas",
  title =        "Augmenting a Programming Language with Complex
                 Arithmetic",
  number =       "NCEG/91-039, UCB/CSD 91/667",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "8",
  day =          "15",
  month =        nov,
  year =         "1991",
  bibdate =      "Mon Dec 26 21:13:51 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1991:ARL,
  author =       "W. Kahan",
  title =        "Analysis and Refutation of the {LCAS}",
  journal =      j-SIGNUM,
  volume =       "26",
  number =       "3",
  pages =        "2--15",
  month =        jul,
  year =         "1991",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:20 MDT 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/signum.bib;
                 http://portal.acm.org/;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  keywords =     "LCAS (Language Compatible Arithmetic Standard)",
}

@Unpublished{Kahan:1991:CMA,
  author =       "W. Kahan",
  title =        "Contracted Multiply-Adds",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "3",
  day =          "20",
  month =        sep,
  year =         "1991",
  bibdate =      "Sun Dec 18 15:17:20 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1991:VTC,
  author =       "W. Kahan",
  title =        "Validating\slash Testing\slash Confirming\slash
                 Checking\slash Correcting Numerical Software",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "2",
  day =          "26",
  month =        nov,
  year =         "1991",
  bibdate =      "Sun Dec 18 15:16:37 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Misc{Paxson:1991:PTI,
  author =       "Vern Paxson and W. Kahan",
  title =        "A Program for Testing {IEEE} Binary--Decimal
                 Conversion",
  howpublished = "World-Wide Web document",
  month =        may,
  year =         "1991",
  bibdate =      "Wed Jan 29 17:59:29 2003",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "ftp://ftp.ee.lbl.gov/testbase-report.ps.Z;
                 ftp://ftp.ee.lbl.gov/testbase.tar.Z",
  acknowledgement = ack-nhfb,
}

@InProceedings{Demmel:1992:DPH,
  author =       "James W. Demmel and J. J. Dongarra and W. Kahan",
  editor =       "D. F. Griffiths and G. A. Watson",
  booktitle =    "Numerical Analysis 1991, Proceedings of the 14th
                 Dundee Conference",
  title =        "On Designing Portable High Performance Numerical
                 Libraries",
  volume =       "260",
  publisher =    pub-LONGMAN-ST,
  address =      pub-LONGMAN-ST:adr,
  pages =        "69--84",
  year =         "1992",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  series =       "Pitman Research Notes in Mathematics",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1992:ARL,
  author =       "W. Kahan",
  title =        "Analysis and Refutation of the {LCAS}",
  journal =      j-SIGPLAN,
  volume =       "27",
  number =       "1",
  pages =        "61--74",
  month =        jan,
  year =         "1992",
  CODEN =        "SINODQ",
  DOI =          "http://doi.acm.org/10.1145/130722.130727",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:16:16 MST 2003",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib;
                 http://www.math.utah.edu/pub/tex/bib/sigplan1990.bib;
                 http://portal.acm.org/",
  abstract =     "A Language Compatible Arithmetic Standard (LCAS) has
                 been proposed as International Standard ISO/IEC
                 10967:1991 for Language Compatible Arithmetic, Project
                 JTC. 22.28, Version 3.1 (1 March 1991), by Drs. Mary
                 Payne and Brian Wichmann. An earlier version appeared
                 in both ACM SIGNUM and ACM SIGPLAN 25 1 (Jan. 1990).
                 The following remonstrance has been sent to ANSI X3-T2,
                 the American committee in charge of the proposal: This
                 proposed Language Compatible Arithmetic Standard is so
                 severely flawed that the computing world must reject
                 it.",
  acknowledgement = ack-nhfb,
  keywords =     "LCAS (Language Compatible Arithmetic Standard)",
}

@Misc{Kahan:1992:DCD,
  author =       "W. Kahan",
  title =        "{DAYDATE}: Computing Days between Dates, the Day of
                 the Week, etc.",
  howpublished = "World-Wide Web document",
  day =          "16",
  month =        sep,
  year =         "1992",
  bibdate =      "Mon Apr 25 17:29:28 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/daydate/",
  acknowledgement = ack-nhfb,
  keywords =     "Gregorian calendar",
}

@Unpublished{Kahan:1992:FPE,
  author =       "W. Kahan",
  title =        "Floating-Point Exception-Handling",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "2",
  day =          "31",
  month =        jul,
  year =         "1992",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1992:NLI,
  author =       "W. Kahan",
  title =        "Notes on {Laguerre}'s Iteration",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  day =          "4",
  month =        dec,
  year =         "1992",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1992:RCM,
  author =       "W. Kahan",
  title =        "Roundoff in Complex Multiplication",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "1",
  day =          "11",
  month =        nov,
  year =         "1992",
  bibdate =      "Sun Dec 18 15:12:30 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; rounding errors",
}

@Unpublished{Kahan:1992:WN,
  author =       "W. Kahan",
  title =        "What Numbers?",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  day =          "9",
  month =        sep,
  year =         "1992",
  bibdate =      "Thu Dec 15 14:06:14 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
  mynote =       "Math 128 A notes, 13",
}

@Unpublished{Kahan:1993:AAS,
  author =       "W. Kahan",
  title =        "Analysis and Application of Simply Compensated
                 Summation",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "13",
  day =          "7",
  month =        sep,
  year =         "1993",
  bibdate =      "Fri Dec 16 09:44:55 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1993:TIE,
  author =       "W. Kahan",
  title =        "A Tridiagonal Inverse Eigenproblem and the Travails of
                 a Would-be Portable Programmer",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  day =          "1",
  month =        jun,
  year =         "1993",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Article{Ozawa:1993:SAE,
  author =       "K. Ozawa and M. Miyazaki",
  title =        "A summation algorithm with error correction for
                 parallel computers",
  journal =      j-SYS-COMP-JAPAN,
  volume =       "24",
  number =       "7",
  pages =        "62--68",
  month =        "????",
  year =         "1993",
  CODEN =        "SCJAEP",
  ISSN =         "0882-1666 (print), 1520-684X (electronic)",
  ISSN-L =       "0882-1666",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "See \cite{Kahan:1965:FRR}.",
  abstract =     "Proposes an algorithm to accurately compute the sum of
                 floating-point numbers on parallel computers. This
                 algorithm is an extension of the well-known recursive
                 doubling technique which computes the sum of n
                 floating-point number in log/sub 2/n parallel steps.
                 The time complexity of the present algorithm also is
                 O(logn), and the space complexity is O(n). This
                 algorithm enables a highly accurate result to be
                 obtained with guarantee. The theoretical analysis and
                 the numerical experiments on a parallel computer show
                 that this algorithm is as accurate as Kahan's, which is
                 the fastest and an accurate serial algorithm for the
                 summation of the numbers, and also that the present
                 algorithm is faster than Kahan's provided that two or
                 more processors are available.",
  acknowledgement = ack-nhfb,
  affiliation =  "Coll. of Gen. Educ., Tohoku Univ., Sendai, Japan",
  classification = "C4110 (Error analysis in numerical methods); C4240P
                 (Parallel programming and algorithm theory)",
  keywords =     "Error correction; Floating-point numbers; Guaranteed
                 accuracy; Parallel computation; Parallel computers;
                 Recursive doubling; Recursive doubling technique;
                 Round-off error analysis; rounding errors; Space
                 complexity; Summation; Summation algorithm; Time
                 complexity",
  language =     "English",
  pubcountry =   "USA",
  thesaurus =    "Computational complexity; Error correction; Parallel
                 algorithms",
}

@Misc{Axler:1994:DD,
  author =       "Sheldon Axler",
  title =        "Down with Determinants!",
  howpublished = "World-Wide Web document",
  pages =        "18",
  day =          "21",
  month =        dec,
  year =         "1994",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/DownDets.pdf",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1994:AS,
  author =       "W. Kahan",
  title =        "On the Advantages of the 8087's Stack",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "4 + 9",
  day =          "23",
  month =        aug,
  year =         "1994",
  bibdate =      "Sun Dec 18 15:10:30 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1994:CBV,
  author =       "W. Kahan",
  title =        "Computer Benchmarks Versus Accuracy",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  month =        jun,
  year =         "1994",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Draft manuscript",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1994:W,
  author =       "W. Kahan",
  title =        "When is {$x*[1/x] < x/x = 1$}?",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "12",
  day =          "1",
  month =        jan,
  year =         "1994",
  bibdate =      "Sun Dec 18 15:10:30 GMT 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Article{Sanz-Serna:1994:USI,
  author =       "J. M. Sanz-Serna",
  title =        "An unconventional symplectic integrator of {W.
                 Kahan}",
  journal =      j-APPL-NUM-MATH,
  volume =       "16",
  number =       "1--2",
  pages =        "245--250",
  day =          "1",
  month =        dec,
  year =         "1994",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "65L08",
  MRnumber =     "95k:65071",
  bibdate =      "Wed Jul 28 14:35:54 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1994&volume=16&issue=1-2;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "A Festschrift to honor Professor Robert Vichnevetsky
                 on his 65th birthday.",
  URL =          "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1994&volume=16&issue=1-2&aid=506",
  acknowledgement = ack-nhfb,
}

@Article{Woehr:1994:LVP,
  author =       "Jack Woehr",
  title =        "{Lotfi} Visions, Part 2",
  journal =      j-DDJ,
  volume =       "19",
  number =       "8",
  pages =        "52--??",
  month =        aug,
  year =         "1994",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Sep 03 09:15:51 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/dr-dobbs-1990.bib;
                 http://www.ddj.com/index/author/index.htm; UnCover
                 database;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  abstract =     "Lotfi Zadeh discusses Japan's Senai train and verbally
                 spars with William Kahan, who shares his two cents
                 worth on fuzzy logic.",
  acknowledgement = ack-nhfb,
}

%%% To find: Special issue of Numerical Linear Algebra with Applications
%%% (ISSN 1070-5325 (print), 1099-1506 (electronic), CODEN NLAAEM),
%%% pp. 85--190, volume 2, numbers 2 and 3, edited by James R. Bunch and
%%% dedicated to Beresford Parlett and William Kahan on the occasion of
%%% their 60th birthdays.  Publisher Web site coverage starts only with
%%% 1996 issues.

@Unpublished{Kahan:1995:LNS,
  author =       "W. Kahan",
  title =        "Lecture Notes on the Status of {IEEE Standard} 754 for
                 Binary Floating-Point Arithmetic",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "29",
  day =          "23",
  month =        may,
  year =         "1995",
  bibdate =      "Tue Jun 6 11:09:38 GMT 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1995:TSD,
  author =       "W. Kahan",
  title =        "A Test for {SRT} Division",
  year =         "1995",
  bibdate =      "Mon Apr 25 05:50:41 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes",
  URL =          "http://www.cs.berkeley.edu/~wkahan/srtest",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1995:USP,
  author =       "{Students of Prof. W. Kahan}",
  title =        "{UCBTEST}: a suite of programs for testing certain
                 difficult cases of {IEEE 754} floating-point
                 arithmetic",
  howpublished = "World-Wide Web document",
  day =          "12",
  month =        mar,
  year =         "1995",
  bibdate =      "Wed May 26 07:29:55 2004",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.netlib.org/fp/ucbtest.tgz",
  acknowledgement = ack-nhfb,
  remark =       "From the source code, students and authors credited
                 are (in alphabetical order) M. Alemi, D. Feenberg,
                 Warren Ferguson David G. Hough, David Gay, W. J. Cody,
                 R. Karpinski, Z. A. Liu, S. Ma, Stephen Moshier, M.
                 Mueller, K. C. Ng, D. Priest, T. Quarles, T. Sumner, G.
                 Taylor, B. Toy, W. Waite, and B. Wichmann.",
}

@Article{Cao:1996:SVK,
  author =       "Zhi-hao Cao and Jin-jun Xie and Ren-Cang Li",
  title =        "A Sharp Version of {Kahan}'s Theorem on Clustered
                 Eigenvalues",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "245",
  number =       "1--3",
  pages =        "147--155",
  day =          "15",
  month =        sep,
  year =         "1996",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A18",
  MRnumber =     "1 404 174",
  bibdate =      "Sat May 29 08:35:43 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/linala1990.bib;
                 http://www.elsevier.com/locate/laa;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/browse.cgi?year=1996&volume=245&issue=1-3&aid=9400226",
  acknowledgement = ack-nhfb,
}

@Article{Goldreich:1996:HCC,
  author =       "Oded Goldreich and Ariel Kahan",
  title =        "How To Construct Constant-Round Zero-Knowledge Proof
                 Systems for {NP}",
  journal =      j-J-CRYPTOLOGY,
  volume =       "9",
  number =       "3",
  pages =        "167--189",
  month =        "Summer",
  year =         "1996",
  CODEN =        "JOCREQ",
  ISSN =         "0933-2790 (print), 1432-1378 (electronic)",
  ISSN-L =       "0933-2790",
  MRclass =      "94A60",
  MRnumber =     "97f:94008",
  bibdate =      "Sat Nov 21 16:36:38 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/jcryptology.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://link.springer.de/link/service/journals/00145/bibs/9n3p167.html;
                 http://link.springer.de/link/service/journals/00145/bibs/9n3p167.pdf;
                 http://link.springer.de/link/service/journals/00145/bibs/9n3p167.tex;
                 http://link.springer.de/link/service/journals/00145/tocs/00903.html",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1996:BEC,
  author =       "W. Kahan",
  title =        "The baleful effect of computer benchmarks upon applied
                 mathematics, physics, and chemistry",
  howpublished = "World-Wide Web document.",
  year =         "1996",
  bibdate =      "Sat Apr 28 18:52:17 2001",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/baleful.ps",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1996:BN,
  author =       "W. Kahan",
  title =        "Beastly Numbers",
  howpublished = "World-Wide Web document.",
  pages =        "3",
  day =          "13",
  month =        jan,
  year =         "1996",
  bibdate =      "Mon Apr 25 17:26:40 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/tests/numbeast.ps;
                 http://www.cs.berkeley.edu/~wkahan/tests/",
  abstract =     "It seems unlikely that two computers, designed by
                 different people 1800 miles apart, would be upset in
                 the same way by the same two floating-point numbers
                 $65535.\cdots$ and $4294967295.\cdots$, but it has
                 happened.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1996:IPE,
  author =       "W. Kahan",
  title =        "The Improbability of Probabilistic Error Analyses for
                 Numerical Computations",
  pages =        "34",
  day =          "28",
  month =        feb,
  year =         "1996",
  bibdate =      "Mon Apr 25 06:40:29 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript. This is an extended version of
                 transparencies titled ``The Improbability of
                 Probabilistic Error Analysis'', first presented in
                 Hamburg at the third ICIAM Congress, 3--7 July, 1995.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/improber.ps",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1996:LNS,
  author =       "W. Kahan",
  title =        "Lecture notes on the status of {IEEE Standard 754} for
                 binary floating-point arithmetic",
  howpublished = "World-Wide Web document.",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "30",
  month =        may,
  year =         "1996",
  bibdate =      "Sat Apr 28 18:52:17 2001",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/ieee754.ps",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1996:TCR,
  author =       "W. Kahan",
  title =        "A Test for Correctly Rounded {SQRT}",
  pages =        "4",
  year =         "1996",
  bibdate =      "Mon Apr 25 05:47:38 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/SQRTest.ps",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; rounding errors",
}

@Unpublished{Kahan:1996:WCY,
  author =       "W. Kahan",
  key =          "Kah96a",
  title =        "What can you learn about floating-point arithmetic in
                 one hour?",
  institution =  inst-BERKELEY-EECS,
  address =      inst-BERKELEY-EECS:adr,
  pages =        "23",
  year =         "1996",
  bibdate =      "Mon Apr 25 17:58:22 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Postscript version accessible electronically at
                 \path=http://http.cs.berkeley.edu/~wkahan/ieee754status=.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/cs267fp.ps",
  acknowledgement = ack-nhfb,
}

@Article{Zheng:1996:FSG,
  author =       "Dao-Sheng Zheng",
  title =        "Further Study and Generalization of {Kahan}'s Matrix
                 Extension Theorem",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "17",
  number =       "3",
  pages =        "621--631",
  month =        jul,
  year =         "1996",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "15A09",
  MRnumber =     "1 397 249",
  bibdate =      "Tue Jan 21 08:54:30 MST 1997",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "See note \cite{Zheng:1998:NFS}.",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1997:CCR,
  author =       "William Kahan and Ren-Cang Li",
  title =        "Composition constants for raising the orders of
                 unconventional schemes for ordinary differential
                 equations",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "219",
  pages =        "1089--1099",
  month =        jul,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65L05",
  MRnumber =     "MR1423077 (97m:65120)",
  bibdate =      "Fri Jul 16 10:38:45 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib;
                 http://www.ams.org/mcom/1997-66-219;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00873-9&u=/mcom/1997-66-219/",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
}

@Misc{Kahan:1997:JNL,
  author =       "W. Kahan",
  title =        "The {John von Neumann} Lecture on The Baleful Effect
                 of Computer Languages and Benchmarks upon Applied
                 Mathematics, Physics and Chemistry",
  howpublished = "World-Wide Web document.",
  institution =  inst-BERKELEY-MATH-EECS,
  address =      inst-BERKELEY-MATH-EECS:adr,
  pages =        "37",
  day =          "15",
  month =        jul,
  year =         "1997",
  bibdate =      "Sat Apr 28 18:52:17 2001",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Presented at the {SIAM} 45th annual meeting, Stanford
                 University",
  URL =          "http://www.cs.berkeley.edu/~wkahan/SIAMjvnl.ps",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1997:LNS,
  author =       "W. Kahan",
  title =        "Lecture Notes on the Status of {IEEE Standard 754 for
                 Binary Floating-Point Arithmetic}",
  howpublished = "World-Wide Web document",
  pages =        "30",
  day =          "1",
  month =        oct,
  year =         "1997",
  bibdate =      "Mon Apr 25 17:54:35 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1997:MAA,
  author =       "W. Kahan",
  title =        "Miscalculating Area and Angles of a Needle-Like
                 Triangle",
  pages =        "20",
  month =        jul,
  year =         "1997",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@TechReport{Kahan:1997:RDI,
  author =       "W. Kahan and Melody Y. Ivory",
  title =        "Roundoff Degrades an Idealized Cantilever",
  type =         "Technical report",
  institution =  inst-BERKELEY-MATH-EECS,
  address =      inst-BERKELEY-MATH-EECS:adr,
  pages =        "11",
  day =          "3",
  month =        jul,
  year =         "1997",
  bibdate =      "Mon Apr 25 05:56:54 2005",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Cantilever.pdf;
                 http://www.cs.berkeley.edu/~wkahan/Cantilever.ps",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; rounding errors",
}

@Article{Kahan:1997:USC,
  author =       "William Kahan and Ren-Chang Li",
  title =        "Unconventional schemes for a class of ordinary
                 differential equations---with applications to the
                 {Korteweg--de Vries} equation",
  journal =      j-J-COMPUT-PHYS,
  volume =       "134",
  number =       "2",
  pages =        "316--331",
  year =         "1997",
  CODEN =        "JCTPAH",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  MRclass =      "65L05 (65M99)",
  MRnumber =     "MR1458831 (98b:65078)",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
}

@Article{Woehr:1997:CWK,
  author =       "Jack Woehr",
  title =        "A Conversation with {William Kahan}: How important is
                 numerical accuracy?",
  journal =      j-DDJ,
  volume =       "22",
  number =       "11",
  pages =        "18--20, 22, 24, 26, 30, 32",
  month =        nov,
  year =         "1997",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Fri Nov 28 17:28:03 MST 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/tex/bib/dr-dobbs-1990.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/java.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Kahan, the father of the IEEE 754 floating-point
                 standard, talks about floating-point arithmetic issues,
                 and numerical deficiencies in Java.",
  abstract =     "Noted mathematician and computer scientist William
                 Kahan has played a central role in everything from the
                 design of the 8087 math coprocessor to defining the
                 ANSI\slash IEEE Standard for binary floating-point
                 arithmetic. He takes time out of his schedule to talk
                 with us about the current state of numeric computing.",
  acknowledgement = ack-nhfb,
}

@Article{Xie:1997:NDK,
  author =       "Jianjun Xie",
  title =        "A note on the {Davis-Kahan} {$\sin\Theta$} theorem",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "258",
  number =       "1--3",
  pages =        "129--135",
  day =          "??",
  month =        jun,
  year =         "1997",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A18; 15-XX",
  MRnumber =     "98a:15022; 1 444 097",
  MRreviewer =   "Hongyuan Zha",
  bibdate =      "Fri May 28 11:36:44 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/linala1990.bib;
                 http://www.elsevier.com/locate/laa;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.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=9600207",
  acknowledgement = ack-nhfb,
}

@TechReport{Darcy:1998:APE,
  author =       "Joseph D. Darcy and William Kahan",
  title =        "Analysis of {{\em Proposal for Extension to Java
                 Floating Point Semantics, Revision 1}}",
  institution =  "{Java Grande Numerics Working Group}",
  pages =        "18",
  day =          "7",
  month =        aug,
  year =         "1998",
  bibdate =      "Mon May 06 09:08:27 2002",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/java.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.sonic.net/~jddarcy/Research/jgrande.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1998:AFE,
  author =       "W. Kahan",
  title =        "Answers for Final Examination",
  howpublished = "World-Wide Web document",
  pages =        "4",
  day =          "19",
  month =        dec,
  year =         "1998",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/finexms.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1998:CTL,
  author =       "W. Kahan",
  title =        "{Chi{\'o}}'s Trick for Linear Equations with Integer
                 Coefficients",
  howpublished = "World-Wide Web document",
  pages =        "3",
  day =          "24",
  month =        oct,
  year =         "1998",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/chio.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1998:DP,
  author =       "W. Kahan",
  title =        "Diagonal Prominence",
  howpublished = "World-Wide Web document",
  pages =        "1",
  day =          "25",
  month =        oct,
  year =         "1998",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/diagprom.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1998:GEO,
  author =       "W. Kahan",
  title =        "Geometry of Elementary Operations",
  howpublished = "World-Wide Web document",
  pages =        "22",
  day =          "22",
  month =        sep,
  year =         "1998",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/geo.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1998:GJI,
  author =       "W. Kahan",
  title =        "{Gauss--Jordan} Inversion of a Matrix",
  howpublished = "World-Wide Web document",
  pages =        "4",
  day =          "16",
  month =        oct,
  year =         "1998",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/gji.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Kahan:1998:HJFa,
  author =       "W. Kahan and Joseph D. Darcy",
  title =        "How {Java}'s Floating-Point Hurts Everyone
                 Everywhere",
  type =         "Technical Report",
  institution =  inst-BERKELEY-MATH-EECS,
  address =      inst-BERKELEY-MATH-EECS:adr,
  pages =        "80",
  day =          "18",
  month =        jun,
  year =         "1998",
  bibdate =      "Sat Sep 12 18:53:11 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/java.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/JAVAhurt.pdf;
                 http://www.cs.berkeley.edu/~wkahan/JAVAhurt.ps",
  acknowledgement = ack-nhfb,
  remark =       "The authors deliver a biting criticism of Java for its
                 failure to use the 80-bit temporary real format on
                 Intel x86 architectures, failure to use multiply-add
                 instructions when available, and failure to compute
                 float subexpressions in double precision.",
}

@InProceedings{Kahan:1998:HJFb,
  author =       "William Kahan",
  title =        "How {Java}'s Floating-Point Hurts Everyone
                 Everywhere",
  crossref =     "ACM:1998:AWJ",
  pages =        "??--??",
  year =         "1998",
  bibdate =      "Sat Dec 01 07:55:27 2001",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.ucsb.edu/conferences/java98/papers/javahurt.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Kahan:1998:IPE,
  author =       "W. Kahan",
  title =        "The Improbability of Probabilistic Error Analyses for
                 Numerical Computations",
  institution =  inst-BERKELEY-MATH-EECS,
  address =      inst-BERKELEY-MATH-EECS:adr,
  pages =        "34",
  day =          "10",
  month =        jun,
  year =         "1998",
  bibdate =      "Fri May 03 12:30:29 2002",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/improber.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1998:JFD,
  author =       "W. Kahan",
  title =        "{Jacobi}'s Formula for the Derivative of a
                 Determinant",
  howpublished = "World-Wide Web document",
  pages =        "4",
  day =          "14",
  month =        oct,
  year =         "1998",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/jacobi.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1998:LNR,
  author =       "W. Kahan",
  title =        "Lecture Notes on Real Root-Finding",
  howpublished = "World-Wide Web document",
  pages =        "4",
  day =          "4",
  month =        mar,
  year =         "1998",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/LNRRabst.txt",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1998:LRR,
  author =       "W. Kahan",
  title =        "A Lecture on Real Root-Finding",
  howpublished = "World-Wide Web document",
  pages =        "14",
  day =          "6",
  month =        apr,
  year =         "1998",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128. Extracted from ``Lecture
                 Notes on Real Root-Finding'' \cite{Kahan:1998:LNR}.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/LecRlRtF.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1998:LSA,
  author =       "W. Kahan",
  title =        "Least-Squares Approximation and Bilinear Forms",
  howpublished = "World-Wide Web document",
  pages =        "4",
  day =          "20",
  month =        sep,
  year =         "1998",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/lstsqrs.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Kahan:1998:MLN,
  author =       "W. Kahan",
  title =        "{Matlab}'s Loss is Nobody's Gain",
  type =         "Technical Report",
  institution =  inst-BERKELEY-MATH-EECS,
  address =      inst-BERKELEY-MATH-EECS:adr,
  pages =        "35",
  day =          "23",
  month =        aug,
  year =         "1998",
  bibdate =      "Sat Sep 12 18:47:22 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MxMulEps.pdf;
                 http://www.cs.berkeley.edu/~wkahan/MxMulEps.ps",
  acknowledgement = ack-nhfb,
  annote =       "The author delivers a strong criticism of Matlab 5 for
                 its failure to use the 80-bit temporary real format on
                 Intel x86 architectures, with several examples that
                 illustrate the benefit to be gained from the extra 16
                 bits (11 bits of significand, 5 of exponent).",
}

@Misc{Kahan:1998:NDS,
  author =       "W. Kahan",
  title =        "Notes on 2-Dimensional Spaces",
  howpublished = "World-Wide Web document",
  day =          "4",
  month =        oct,
  year =         "1998",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/2dspaces.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1998:PSP,
  author =       "W. Kahan",
  title =        "Problem Set 1: Problems about our Axioms for a Vector
                 Space",
  howpublished = "World-Wide Web document",
  pages =        "1",
  day =          "16",
  month =        sep,
  year =         "1998",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/prblms1.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1998:RRE,
  author =       "W. Kahan",
  title =        "The Reduced Row-Echelon Form is Unique",
  howpublished = "World-Wide Web document",
  pages =        "3",
  day =          "12",
  month =        sep,
  year =         "1998",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/RREF1.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1998:SPS,
  author =       "W. Kahan",
  title =        "Solutions for Problem Set 2",
  howpublished = "World-Wide Web document",
  pages =        "1",
  day =          "1",
  month =        oct,
  year =         "1998",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/prblms2.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1998:THT,
  author =       "W. Kahan",
  title =        "Take-Home Test's Solutions",
  howpublished = "World-Wide Web document",
  pages =        "3",
  day =          "5",
  month =        oct,
  year =         "1998",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/tkhms.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1998:TPS,
  author =       "W. Kahan",
  title =        "Test Problems and Solutions",
  howpublished = "World-Wide Web document",
  pages =        "4",
  day =          "4",
  month =        dec,
  year =         "1998",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/testexam.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1998:VSB,
  author =       "W. Kahan",
  title =        "Vector Spaces, Bases, and Dual Spaces",
  howpublished = "World-Wide Web document",
  pages =        "9",
  day =          "4",
  month =        nov,
  year =         "1998",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/pts.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Severance:1998:IOM,
  author =       "Charles Severance",
  title =        "An Interview with the Old Man of Floating-Point.
                 {Reminiscences} Elicited from {William Kahan}",
  howpublished = "World-Wide Web document.",
  month =        feb,
  year =         "1998",
  bibdate =      "Sat Apr 28 19:05:42 2001",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "A shortened version appears in
                 \cite{Severance:1998:SII}.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/754story.html",
  acknowledgement = ack-nhfb,
}

@Article{Severance:1998:SII,
  author =       "Charles Severance",
  title =        "Standards: {IEEE 754}: An Interview with {William
                 Kahan}",
  journal =      j-COMPUTER,
  volume =       "31",
  number =       "3",
  pages =        "114--115",
  month =        mar,
  year =         "1998",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Wed Mar 4 10:07:59 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/computer1990.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://pdf.computer.org/co/books/co1998/pdf/r3114.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Zheng:1998:NFS,
  author =       "Dao-Sheng Zheng",
  title =        "Note On {``Further Study and Generalization of Kahan's
                 Matrix Extension Theorem''}",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "19",
  number =       "1",
  pages =        "277--278",
  month =        jan,
  year =         "1998",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Fri Dec 4 12:14:09 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib;
                 http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/19/1;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "See \cite{Zheng:1996:FSG}.",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/31443",
  acknowledgement = ack-nhfb,
}

@Misc{Anonymous:1999:AAM,
  author =       "Anonymous",
  title =        "{ACM Alan M. Turing Award: William V. Kahan}",
  howpublished = "World Wide Web document",
  day =          "8",
  month =        feb,
  year =         "1999",
  bibdate =      "Mon Apr 25 08:13:18 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.acm.org/awards/turing_citations/kahan.html",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:C,
  author =       "W. Kahan",
  title =        "Computing $x^n$",
  howpublished = "World-Wide Web document",
  pages =        "2",
  day =          "20",
  month =        mar,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/npower.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:CS,
  author =       "W. Kahan",
  title =        "Coins and Stamps",
  howpublished = "World-Wide Web document",
  pages =        "2",
  day =          "1",
  month =        may,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/coins.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:CSC,
  author =       "W. Kahan",
  title =        "Conic Sections in the Complex $z$-plane",
  howpublished = "World-Wide Web document",
  day =          "4",
  month =        sep,
  year =         "1999",
  bibdate =      "Mon Apr 25 17:45:58 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 185.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math185/conics.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:CSL,
  author =       "W. Kahan",
  title =        "{California} Super Lottery",
  howpublished = "World-Wide Web document",
  pages =        "3",
  day =          "13",
  month =        apr,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/lotto.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:CVC,
  author =       "W. Kahan",
  title =        "Complexity vs. Cost",
  howpublished = "World-Wide Web document",
  pages =        "10",
  day =          "24",
  month =        aug,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/cmplxty.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:D,
  author =       "W. Kahan",
  title =        "Derangements",
  howpublished = "World-Wide Web document",
  pages =        "1",
  day =          "9",
  month =        jun,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/derange.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:DTP,
  author =       "W. Kahan",
  title =        "Discussion of two problems in the text",
  howpublished = "World-Wide Web document",
  pages =        "2",
  day =          "3",
  month =        feb,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/m55jan28.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:EGA,
  author =       "W. Kahan",
  title =        "{Euclid}'s {GCD} Algorithm",
  howpublished = "World-Wide Web document",
  pages =        "3",
  day =          "10",
  month =        may,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/gcd.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:EMSa,
  author =       "W. Kahan",
  title =        "Exam Model Solutions",
  howpublished = "World-Wide Web document",
  pages =        "1",
  day =          "10",
  month =        feb,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/feb10s.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:EMSb,
  author =       "W. Kahan",
  title =        "Exam: Model Solutions",
  howpublished = "World-Wide Web document",
  pages =        "3",
  day =          "3",
  month =        mar,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/m55mar3s.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:EMSc,
  author =       "W. Kahan",
  title =        "Exam: Model Solutions",
  howpublished = "World-Wide Web document",
  pages =        "4",
  day =          "18",
  month =        mar,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/m55mr18s.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:EMSd,
  author =       "W. Kahan",
  title =        "Exam: Model Solutions",
  howpublished = "World-Wide Web document",
  pages =        "2",
  day =          "11",
  month =        may,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/m55my11s.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:EPI,
  author =       "W. Kahan",
  title =        "Enumerating Pairs of Integers",
  howpublished = "World-Wide Web document",
  pages =        "2",
  day =          "30",
  month =        apr,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/pairs.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:FEM,
  author =       "W. Kahan",
  title =        "Final Exam: Model Solutions",
  howpublished = "World-Wide Web document",
  pages =        "4",
  day =          "14",
  month =        may,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/m55finls.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:FI,
  author =       "W. Kahan",
  title =        "The Fragility of Improbability",
  howpublished = "World-Wide Web document",
  pages =        "7",
  day =          "9",
  month =        jun,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/correln.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:FLT,
  author =       "W. Kahan",
  title =        "{Fermat}'s Little Theorem",
  howpublished = "World-Wide Web document",
  pages =        "1",
  day =          "1",
  month =        mar,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/fermat.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:HP,
  author =       "W. Kahan",
  title =        "The Halting Problem",
  howpublished = "World-Wide Web document",
  pages =        "2",
  day =          "13",
  month =        mar,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/halting.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:LLN,
  author =       "W. Kahan",
  title =        "The {Law of Large Numbers}",
  howpublished = "World-Wide Web document",
  pages =        "10",
  day =          "29",
  month =        may,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/largenos.pdf",
  acknowledgement = ack-nhfb,
  remark =       "The {\em Law of Large Numbers\/} says roughly this:
                 ``The probability distribution of practically any
                 random variable can be determined to any desired degree
                 of accuracy as nearly certainly as desired by sampling
                 that random variable independently and often
                 enough.''",
}

@Misc{Kahan:1999:MS,
  author =       "W. Kahan",
  title =        "{Math 55} Syllabus",
  howpublished = "World-Wide Web document",
  pages =        "3",
  day =          "20",
  month =        jun,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/syllabus.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:MSS,
  author =       "W. Kahan",
  title =        "{Math 55 Spring 1999} Syllabus",
  howpublished = "World-Wide Web document",
  pages =        "2",
  day =          "6",
  month =        may,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/math55.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:OCT,
  author =       "W. Kahan",
  title =        "Only Commutators Have Trace Zero",
  howpublished = "World-Wide Web document",
  pages =        "3",
  day =          "10",
  month =        jun,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/trace0.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:PS,
  author =       "W. Kahan",
  title =        "Problems' Solutions",
  howpublished = "World-Wide Web document",
  day =          "15",
  month =        dec,
  year =         "1999",
  bibdate =      "Mon Apr 25 17:45:58 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 185.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math185/probsoln.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:RAI,
  author =       "W. Kahan",
  title =        "Rational Approximations of Irrationals",
  howpublished = "World-Wide Web document",
  pages =        "2",
  day =          "8",
  month =        apr,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/p249n17.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1999:SCD,
  author =       "W. Kahan and Richard J. Fateman",
  title =        "Symbolic Computation of Divided Differences",
  journal =      j-SIGSAM,
  volume =       "33",
  number =       "2",
  pages =        "7--28",
  month =        jun,
  year =         "1999",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Fri Feb 8 18:27:06 MST 2002",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/sigsam.bib;
                 http://portal.acm.org/;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  issue =        "128",
}

@Misc{Kahan:1999:SFE,
  author =       "W. Kahan",
  title =        "Solutions for Final Exam",
  howpublished = "World-Wide Web document",
  day =          "11",
  month =        dec,
  year =         "1999",
  bibdate =      "Mon Apr 25 17:45:58 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 185.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math185/xm11decs.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:SI,
  author =       "W. Kahan",
  title =        "Some Inequalities",
  howpublished = "World-Wide Web document",
  pages =        "5",
  day =          "9",
  month =        may,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/ineq.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:SP,
  author =       "W. Kahan",
  title =        "Solutions to Problems",
  howpublished = "World-Wide Web document",
  day =          "12",
  month =        dec,
  year =         "1999",
  bibdate =      "Mon Apr 25 17:45:58 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 185.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math185/31aug99s.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:SPH,
  author =       "W. Kahan",
  title =        "Solutions to Problems in {H. W. Lenstra}'s Notes",
  howpublished = "World-Wide Web document",
  pages =        "9",
  day =          "9",
  month =        jul,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/lenstras.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:SRD,
  author =       "W. Kahan",
  title =        "Square Root Without Division",
  howpublished = "World-Wide Web document",
  pages =        "3",
  day =          "23",
  month =        feb,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:01:49 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/reciprt.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:SSE,
  author =       "W. Kahan",
  title =        "{SOLVEzag}: Solve the equation $z = (1
                 -exp(-pz))/(pz)$ for $z \geq 0$ as a function of $p
                 \geq 0$",
  howpublished = "World-Wide Web document",
  pages =        "3",
  day =          "1",
  month =        aug,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/SOLVEzag.pdf;
                 http://www.cs.berkeley.edu/~wkahan/Math128/SOLVEzag.ps",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:T,
  author =       "W. Kahan",
  title =        "Test",
  howpublished = "World-Wide Web document",
  pages =        "2",
  day =          "27",
  month =        jan,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/jan27s.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:TMS,
  author =       "W. Kahan",
  title =        "Test: Model Solutions",
  howpublished = "World-Wide Web document",
  pages =        "5",
  day =          "26",
  month =        apr,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/m55ap26s.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:TPA,
  author =       "W. Kahan",
  title =        "Three Problems about Combinatorial Coefficients",
  howpublished = "World-Wide Web document",
  pages =        "6",
  day =          "26",
  month =        apr,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/ncr.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1999:WB,
  author =       "W. Kahan",
  title =        "Waiting for a Bus",
  howpublished = "World-Wide Web document",
  pages =        "1",
  day =          "12",
  month =        apr,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 55.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math55/bus.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Bhatia:2000:PNS,
  author =       "Rajendra Bhatia and William Kahan and Ren-Cang Li",
  title =        "Pinchings and norms of scaled triangular matrices",
  type =         "Technical Report",
  number =       "2000-23",
  institution =  "Department of Mathematics, University of Kentucky",
  address =      "Lexington, KY, USA",
  year =         "2000",
  bibdate =      "Mon Apr 25 06:22:43 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.uky.edu/~rcli/papers/kablrep.ps",
  acknowledgement = ack-nhfb,
  xxnote =       "URL no longer available, and absent from
                 www.archive.org.",
}

@TechReport{Bindel:2000:CGR,
  author =       "D. Bindel and J. Demmel and W. Kahan and O. Marques",
  title =        "On Computing {Givens} rotations reliably and
                 efficiently",
  type =         "LAPACK Working Note",
  number =       "148",
  institution =  inst-UTK-CS,
  address =      inst-UTK-CS:adr,
  month =        oct,
  year =         "2000",
  bibdate =      "Fri Apr 22 17:06:37 2005",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/lawn.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "UT-CS-00-449, October 2000. Published in
                 \cite{Bindel:2002:CGR}.",
  URL =          "http://www.netlib.org/lapack/lawns/lawn148.ps;
                 http://www.netlib.org/lapack/lawnspdf/lawn148.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{He:2000:PAA,
  author =       "Yun (Helen) He and Chris H. Q. Ding",
  title =        "Platforms: An Accurate Arithmetics Approach",
  crossref =     "ACM:2000:SHP",
  pages =        "150--150",
  year =         "2000",
  bibdate =      "Sat Feb 10 14:28:55 2001",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/supercomputing2000.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  abstract =     "Numerical reproducibility of large-scale scientific
                 simulations, especially climate modeling, on
                 distributed memory parallel computers are becoming
                 critical issues. In particular, global summation and
                 dot products of distributed arrays are very susceptible
                 to rounding errors. We analyzed several accurate
                 summation methods and found that two methods are
                 particularly effective to improve (ensure)
                 reproducibility: Kahan's self-compensated summation and
                 Bailey's double-double precision summation. We provide
                 an MPI operator MPI\_SUMDD to work with MPI collective
                 operations to ensure a scalable implementation on large
                 number of processors. The final methods are
                 particularly simple to adopt in practical codes.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; rounding errors",
}

@Misc{Kahan:2000:AFE,
  author =       "W. Kahan",
  title =        "Answers for Final Examination",
  howpublished = "World-Wide Web document",
  pages =        "5",
  day =          "21",
  month =        dec,
  year =         "2000",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/finals.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2000:AFV,
  author =       "W. Kahan",
  title =        "Axioms for Fields and Vector Spaces",
  howpublished = "World-Wide Web document",
  pages =        "2",
  day =          "17",
  month =        may,
  year =         "2000",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/Axioms.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2000:CPR,
  author =       "W. Kahan",
  title =        "Cross-Products and Rotations in $2$- and
                 $3$-Dimensional {Euclidean} Spaces: Notes for Math.
                 {H110}",
  howpublished = "World-Wide Web document",
  pages =        "10",
  day =          "11",
  month =        oct,
  year =         "2000",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/Cross.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2000:EGA,
  author =       "W. Kahan",
  title =        "{Euclid}'s {GCD} Algorithm",
  howpublished = "World-Wide Web document",
  pages =        "4",
  day =          "5",
  month =        oct,
  year =         "2000",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/gcd5.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2000:GEO,
  author =       "W. Kahan",
  title =        "Geometry of Elementary Operations and Subspaces: {A}
                 continuation of notes titled ``Geometry of Elementary
                 Operations''",
  howpublished = "World-Wide Web document",
  pages =        "6",
  day =          "14",
  month =        dec,
  year =         "2000",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/geos.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2000:GMH,
  author =       "W. Kahan",
  title =        "Grades for {Math. H110}",
  howpublished = "World-Wide Web document",
  pages =        "1",
  year =         "2000",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/h110_00.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2000:HRQ,
  author =       "W. Kahan",
  title =        "How to Recognize a Quadratic Form",
  howpublished = "World-Wide Web document",
  pages =        "2",
  day =          "31",
  month =        oct,
  year =         "2000",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/qf.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2000:JNF,
  author =       "W. Kahan",
  title =        "{Jordan}'s Normal Form",
  howpublished = "World-Wide Web document",
  pages =        "18",
  day =          "7",
  month =        dec,
  year =         "2000",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/jordan.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2000:LAM,
  author =       "W. Kahan",
  title =        "Linear Algebra and Matrix Theory",
  howpublished = "World-Wide Web document",
  pages =        "1",
  month =        "Fall",
  year =         "2000",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/Topics.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2000:MAA,
  author =       "W. Kahan",
  title =        "Miscalculating Area and Angles of a Needle-like
                 Triangle",
  howpublished = "World-Wide Web lecture notes for introductory
                 numerical analysis classes.",
  day =          "24",
  month =        mar,
  year =         "2000",
  bibdate =      "Fri Jul 15 12:30:24 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Triangle.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic",
}

@TechReport{Kahan:2000:MVM,
  author =       "W. Kahan",
  title =        "Marketing versus Mathematics and other Ruminations on
                 the design of floating-point arithmetic",
  howpublished = "World-Wide Web document.",
  institution =  "Mathematics Department and Electrical Engineering and
                 Computer Science Department, University of California,
                 Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "48",
  day =          "27",
  month =        aug,
  year =         "2000",
  bibdate =      "Fri May 03 12:19:56 2002",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MktgMath.pdf;
                 http://www.cs.nyu.edu/cs/faculty/overton/book/docs/KahanTalk.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2000:NJI,
  author =       "W. Kahan",
  title =        "Notes on {Jensen}'s Inequality for {Math. H90}",
  howpublished = "World-Wide Web document",
  pages =        "3",
  day =          "27",
  month =        sep,
  year =         "2000",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/jensen.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2000:NVN,
  author =       "W. Kahan",
  title =        "Notes on Vector Norms",
  howpublished = "World-Wide Web document",
  pages =        "10",
  day =          "6",
  month =        dec,
  year =         "2000",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/normlite.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2000:PSa,
  author =       "W. Kahan",
  title =        "Problems' Solutions",
  howpublished = "World-Wide Web document",
  pages =        "19",
  day =          "19",
  month =        oct,
  year =         "2000",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/s10oct.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2000:PSb,
  author =       "W. Kahan",
  title =        "Problems' Solutions",
  howpublished = "World-Wide Web document",
  pages =        "2",
  day =          "27",
  month =        nov,
  year =         "2000",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/s21nov.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2000:RDFa,
  author =       "W. Kahan",
  title =        "Ruminations on the Design of Floating-Point
                 Arithmetic",
  howpublished = "World-Wide Web document",
  pages =        "29",
  day =          "25",
  month =        apr,
  year =         "2000",
  bibdate =      "Sat Mar 03 18:19:26 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://cs.nyu.edu/cs/faculty/overton/book/docs/KahanTalk.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Kahan:2000:RDFb,
  author =       "W. Kahan",
  title =        "Marketing versus Mathematics and other Ruminations on
                 the design of floating-point arithmetic",
  howpublished = "World-Wide Web document.",
  institution =  "Mathematics Department and Electrical Engineering and
                 Computer Science Department, University of California,
                 Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "48",
  day =          "27",
  month =        aug,
  year =         "2000",
  bibdate =      "Fri May 03 12:19:56 2002",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/%7Ewkahan/MktgMath.pdf;
                 http://www.cs.nyu.edu/cs/faculty/overton/book/docs/KahanTalk.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2000:TCE,
  author =       "W. Kahan",
  title =        "Topics Covered For Exam Purposes",
  howpublished = "World-Wide Web document",
  pages =        "2",
  day =          "12",
  month =        dec,
  year =         "2000",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/covered.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Li:2000:DIT,
  author =       "X. S. Li and J. W. Demmel and D. H. Bailey and G.
                 Henry and Y. Hida and J. Iskandar and W. Kahan and A.
                 Kapur and M. C. Martin and T. Tung and D. J. Yoo",
  title =        "Design, Implementation and Testing of Extended and
                 Mixed Precision {BLAS}",
  type =         "{LAPACK} Working Note and {University of Tennessee}
                 report",
  number =       "149 and CS-00-451",
  institution =  inst-UTK-CS,
  address =      inst-UTK-CS:adr,
  pages =        "61",
  month =        oct,
  year =         "2000",
  bibdate =      "Fri Apr 22 17:06:37 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/tex/bib/lawn.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.netlib.org/lapack/lawns/lawn149.ps;
                 http://www.netlib.org/lapack/lawnspdf/lawn149.pdf",
  acknowledgement = ack-nhfb,
}

@Unpublished{Demmel:2001:CAF,
  author =       "J. Demmel and Ben Diament and W. Kahan and Plamen Koev
                 and Ming Gu and Stan Eisenstat and Ivan Slapni{\v{c}}ar
                 and Kresimir Veseli{\'c} and Zlatko Drma{\v{c}}",
  title =        "The Complexity of Accurate Floating Point Computation
                 and Symbolic Computing, or, Can we do Numerical Linear
                 Algebra In Polynomial Time?",
  pages =        "31",
  year =         "2001",
  bibdate =      "Mon Apr 25 06:47:21 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture slides",
  URL =          "http://www.cs.berkeley.edu/~demmel/ISSAC2001_2.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2001:ATA,
  author =       "W. Kahan",
  title =        "Approximate Trisection of an Angle",
  howpublished = "World-Wide Web document",
  day =          "31",
  month =        jan,
  year =         "2001",
  bibdate =      "Mon Apr 25 17:45:58 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/trisect.pdf;
                 http://www.cs.berkeley.edu/~wkahan/trisect.ps",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2001:HBM,
  author =       "W. Kahan",
  title =        "How Blabber-Mouth {U}-Boats got Sunk in {World War
                 II}",
  howpublished = "World-Wide Web document",
  institution =  inst-BERKELEY-MATH-EECS,
  address =      inst-BERKELEY-MATH-EECS:adr,
  pages =        "25",
  day =          "24",
  month =        nov,
  year =         "2001",
  bibdate =      "Mon Apr 25 17:35:30 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/BlaUboat.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2001:MBR,
  author =       "W. Kahan",
  title =        "{M. Brand}'s 2nd Revised Problem has Infinitely Many
                 Solutions",
  howpublished = "World-Wide Web document",
  pages =        "2",
  day =          "13",
  month =        apr,
  year =         "2001",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/Brand2.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Kahan:2001:NSF,
  author =       "W. Kahan",
  title =        "Names for Standardized Floating-Point Formats",
  institution =  "Mathematics Department and Electrical Engineering and
                 Computer Science Department, University of California,
                 Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "4",
  day =          "17",
  month =        may,
  year =         "2001",
  bibdate =      "Fri May 03 12:23:25 2002",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/Names.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2001:SFP,
  author =       "W. Kahan",
  title =        "{SRTEST}: {A} {Fortran} program to test any {SRT}
                 divider's logic for quotient-digit selection",
  howpublished = "World-Wide Web document",
  day =          "6",
  month =        aug,
  year =         "2001",
  bibdate =      "Mon Apr 25 17:47:53 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/srtest/",
  acknowledgement = ack-nhfb,
}

@TechReport{Kahan:2001:WDW,
  author =       "W. Kahan",
  title =        "Why Do We Need a Floating-Point Arithmetic Standard?",
  type =         "Technical Report",
  institution =  inst-BERKELEY,
  address =      inst-BERKELEY:adr,
  pages =        "49",
  month =        mar,
  year =         "2001",
  bibdate =      "Fri Apr 7 12:22:17 GMT 1995",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/why-ieee.pdf",
  acknowledgement = ack-nhfb,
  remark =       "This is \cite{Kahan:1981:WDW}, retypeset by David
                 Bindel.",
}

@TechReport{Kahan:2001:WVT,
  author =       "W. Kahan",
  title =        "What has the Volume of a Tetrahedron to do with
                 Computer Programming Languages?",
  institution =  inst-BERKELEY-MATH-EECS,
  address =      inst-BERKELEY-MATH-EECS:adr,
  pages =        "31",
  day =          "20",
  month =        apr,
  year =         "2001",
  bibdate =      "Fri May 03 13:36:17 2002",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/VtetLang.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Bhatia:2002:PNS,
  author =       "Rajendra Bhatia and William Kahan and Ren-Cang Li",
  title =        "Pinchings and norms of scaled triangular matrices",
  journal =      j-LIN-MULT-ALGEBRA,
  volume =       "50",
  number =       "1",
  pages =        "15--21",
  year =         "2002",
  CODEN =        "LNMLAZ",
  ISSN =         "0308-1087",
  ISSN-L =       "0308-1087",
  MRclass =      "15A45 (15A60 65F35)",
  MRnumber =     "MR1890985 (2002k:15043)",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear and Multilinear Algebra",
}

@Article{Bindel:2002:CGR,
  author =       "David Bindel and James Demmel and William Kahan and
                 Osni Marques",
  title =        "On computing {Givens} rotations reliably and
                 efficiently",
  journal =      j-TOMS,
  volume =       "28",
  number =       "2",
  pages =        "206--238",
  month =        jun,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/567806.567809",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F15 (65-04)",
  MRnumber =     "MR1928067 (2003h:65046)",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/toms.bib;
                 http://www.acm.org/pubs/contents/journals/toms/;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://doi.acm.org/10.1145/567806.567809",
  abstract =     "We consider the efficient and accurate computation of
                 Givens rotations. When $f$ and $g$ are positive real
                 numbers, this simply amounts to computing the values of
                 $c = f/\sqrt{f^2+g^2}$, $s = g/\sqrt{f^2+g^2}$, and $r
                 = \sqrt{f^2+g^2}$. This apparently trivial computation
                 merits closer consideration for the following three
                 reasons. First, while the definitions of $c$, $s$ and
                 $r$ seem obvious in the case of two nonnegative
                 arguments $f$ and $g$, there is enough freedom of
                 choice when one or more of $f$ and $g$ are negative,
                 zero or complex that LAPACK auxiliary routines SLARTG,
                 CLARTG, SLARGV and CLARGV can compute rather different
                 values of $c$, $s$ and $r$ for mathematically identical
                 values of $f$ and $g$. To eliminate this unnecessary
                 ambiguity, the BLAS Technical Forum chose a single
                 consistent definition of Givens rotations that we will
                 justify here. Second, computing accurate values of $c$,
                 $s$ and $r$ as efficiently as possible and reliably
                 despite over/underflow is surprisingly complicated. For
                 complex Givens rotations, the most efficient formulas
                 require only one real square root and one real divide
                 (as well as several much cheaper additions and
                 multiplications), but a reliable implementation using
                 only working precision has a number of cases. On a Sun
                 Ultra-10, the new implementation is slightly faster
                 than the previous LAPACK implementation in the most
                 common case, and 2.7 to 4.6 times faster than the
                 corresponding vendor, reference or ATLAS routines. It
                 is also more reliable; all previous codes occasionally
                 suffer from large inaccuracies due to over/underflow.
                 For real Givens rotations there are also improvements
                 in speed and accuracy, though not as striking. Third,
                 the design process that led to this reliable
                 implementation is quite systematic, and could be
                 applied to the design of similarly reliable
                 subroutines.",
  acknowledgement = ack-nhfb,
  fjournal =     "Association for Computing Machinery. Transactions on
                 Mathematical Software",
}

@Misc{Kahan:2002:AI,
  author =       "W. Kahan",
  title =        "About Infinity",
  howpublished = "World-Wide Web document",
  pages =        "6",
  day =          "7",
  month =        mar,
  year =         "2002",
  bibdate =      "Mon Apr 25 17:34:16 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Infinity.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2002:ALN,
  author =       "W. Kahan",
  title =        "Abbreviated Lecture Notes on Ellipsoidal Error Bounds
                 for Trajectory Calculations",
  howpublished = "World-Wide Web document",
  pages =        "5",
  day =          "9",
  month =        mar,
  year =         "2002",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/Ellipsoi.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2002:CA,
  author =       "W. Kahan",
  title =        "Computing an Adjugate",
  howpublished = "World-Wide Web document",
  pages =        "",
  day =          "19",
  month =        mar,
  year =         "2002",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/Adjx.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2002:FPC,
  author =       "W. Kahan",
  title =        "{Fclass}: a Proposed Classification of Standard
                 Floating-Point Operands",
  howpublished = "World-Wide Web document",
  pages =        "6",
  day =          "23",
  month =        mar,
  year =         "2002",
  bibdate =      "Mon Apr 25 17:53:00 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/%7Ewkahan/ieee754status/Fclass.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2002:HGI,
  author =       "W. Kahan",
  title =        "Huge Generalized Inverses of Rank-Deficient Matrices",
  howpublished = "World-Wide Web document",
  pages =        "8",
  day =          "2",
  month =        may,
  year =         "2002",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/GIlite.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2002:IBD,
  author =       "W. Kahan",
  title =        "Idempotent Binary $\rightarrow$ Decimal $\rightarrow$
                 Binary Conversion",
  howpublished = "World-Wide Web document",
  pages =        "1",
  day =          "2",
  month =        feb,
  year =         "2002",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/BinDecBin.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2002:MFE,
  author =       "W. Kahan",
  title =        "Math. 110 Final Exam",
  howpublished = "World-Wide Web document",
  pages =        "6",
  day =          "27",
  month =        may,
  year =         "2002",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/Final02.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2002:MIH,
  author =       "W. Kahan",
  title =        "{Matlab}'s Inverses of {Hilbert} Matrices",
  howpublished = "World-Wide Web document",
  pages =        "4",
  day =          "2",
  month =        may,
  year =         "2002",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/HilbMats.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2002:MPI,
  author =       "W. Kahan",
  title =        "{Matlab} programs for Interpolation and
                 Extrapolation",
  howpublished = "World-Wide Web document",
  pages =        "5",
  day =          "11",
  month =        feb,
  year =         "2002",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/XPOLATE",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2002:MTa,
  author =       "W. Kahan",
  title =        "MidTerm Test",
  howpublished = "World-Wide Web document",
  pages =        "5",
  day =          "5",
  month =        mar,
  year =         "2002",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/MidTerm.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2002:MTb,
  author =       "W. Kahan",
  title =        "MidTerm Test",
  howpublished = "World-Wide Web document",
  pages =        "3",
  day =          "29",
  month =        apr,
  year =         "2002",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/MidTerm2.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2002:NAC,
  author =       "W. Kahan",
  title =        "The Numerical Analyst as Computer Science Curmudgeon",
  howpublished = "World-Wide Web document",
  institution =  inst-BERKELEY-MATH-EECS,
  address =      inst-BERKELEY-MATH-EECS:adr,
  day =          "11",
  month =        sep,
  year =         "2002",
  bibdate =      "Mon Apr 25 17:37:33 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Curmudge.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2002:ODE,
  author =       "W. Kahan",
  title =        "An Ordinary Differential Equation in
                 Interval-Arithmetic",
  howpublished = "World-Wide Web document",
  pages =        "1",
  day =          "9",
  month =        mar,
  year =         "2002",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/ODEintvl.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2002:RPR,
  author =       "W. Kahan",
  title =        "{\tt Refineig}: a Program to Refine Eigensystems",
  howpublished = "World-Wide Web document",
  pages =        "20",
  day =          "29",
  month =        may,
  year =         "2002",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128. Work in progress: not for
                 redistribution.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/RefinEig.pdf;
                 http://www.cs.berkeley.edu/~wkahan/Math128/refineig.abs",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2002:SCP,
  author =       "W. Kahan",
  title =        "Separation of Clouds by a Plane",
  howpublished = "World-Wide Web document",
  pages =        "4",
  day =          "17",
  month =        may,
  year =         "2002",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110 and Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/Separate.pdf;
                 http://www.cs.berkeley.edu/~wkahan/Math128/Separate.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2002:TPM,
  author =       "W. Kahan",
  title =        "Two Problems: Must Triangular Matrices have Triangular
                 Inverses? When are Triangular Factorizations Unique?",
  howpublished = "World-Wide Web document",
  pages =        "2",
  day =          "20",
  month =        feb,
  year =         "2002",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/TriFact.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2002:TRD,
  author =       "W. Kahan",
  title =        "{Thiele}'s Reciprocal Differences and Derivatives",
  howpublished = "World-Wide Web document",
  pages =        "5",
  day =          "14",
  month =        feb,
  year =         "2002",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/THIELEDF",
  acknowledgement = ack-nhfb,
}

@Article{Li:2002:DIT,
  author =       "Xiaoye S. Li and James W. Demmel and David H. Bailey
                 and Greg Henry and Yozo Hida and Jimmy Iskandar and
                 William Kahan and Suh Y. Kang and Anil Kapur and
                 Michael C. Martin and Brandon J. Thompson and Teresa
                 Tung and Daniel J. Yoo",
  title =        "Design, implementation and testing of extended and
                 mixed precision {BLAS}",
  journal =      j-TOMS,
  volume =       "28",
  number =       "2",
  pages =        "152--205",
  month =        jun,
  year =         "2002",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/toms.bib;
                 http://www.acm.org/pubs/contents/journals/toms/;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://doi.acm.org/10.1145/567806.567808",
  abstract =     "This paper describes the design rationale, a C
                 implementation, and conformance testing of a subset of
                 the new Standard for the BLAS (Basic Linear Algebra
                 Subroutines): Extended and Mixed Precision BLAS.
                 Permitting higher internal precision and mixed
                 input\slash output types and precisions allows us to
                 implement some algorithms that are simpler, more
                 accurate, and sometimes faster than possible without
                 these features. The new BLAS are challenging to
                 implement and test because there are many more
                 subroutines than in the existing Standard, and because
                 we must be able to assess whether a higher precision is
                 used for internal computations than is used for either
                 input or output variables. We have therefore developed
                 an automated process of generating and systematically
                 testing these routines. Our methodology is applicable
                 to languages besides C. In particular, our algorithms
                 used in the testing code will be valuable to all other
                 BLAS implementors. Our extra precision routines achieve
                 excellent performance---close to half of the machine
                 peak Megaflop rate even for the Level 2 BLAS, when the
                 data access is stride one.",
  acknowledgement = ack-nhfb,
}

@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 =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/Parlett.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Shampine:2002:MOS,
  author =       "Lawrence F. Shampine and Mark W. Reichelt",
  title =        "The {Matlab ODE} Suite",
  howpublished = "World-Wide Web document",
  pages =        "35",
  day =          "27",
  month =        feb,
  year =         "2002",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/ODEsuite.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2003:CPR,
  author =       "W. Kahan",
  title =        "Cross-Products and Rotations in $2$- and
                 $3$-Dimensional {Euclidean} Spaces",
  howpublished = "World-Wide Web document",
  pages =        "12",
  day =          "23",
  month =        nov,
  year =         "2003",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math H110.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathH110/Cross.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Randolph:2003:WKT,
  author =       "Dan W. Randolph",
  title =        "{William Kahan: 1989 Turing Award} Winner",
  type =         "COSC 5000 class report",
  institution =  "Department of Computer Science University of Wyoming",
  address =      "Laramie, WY, USA",
  pages =        "7",
  day =          "16",
  month =        may,
  year =         "2003",
  bibdate =      "Mon Apr 25 06:25:58 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.mapsharecorp.com/kahan.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2004:A,
  author =       "W. Kahan",
  title =        "Abstracts",
  howpublished = "World-Wide Web document",
  pages =        "26",
  day =          "1",
  month =        nov,
  year =         "2004",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Abstracts of some of the online documents.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/abstrcts",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2004:ASC,
  author =       "W. Kahan",
  title =        "Assignment: Solve ${A}_4z = b$ by Conjugate Gradient
                 Iteration without ever storing the matrix ${A}_4$",
  howpublished = "World-Wide Web document",
  pages =        "1",
  day =          "19",
  month =        apr,
  year =         "2004",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/a4d2.txt",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2004:ASE,
  author =       "W. Kahan",
  title =        "Angle subtended at the eye by neighboring stars",
  howpublished = "World-Wide Web document",
  pages =        "1",
  day =          "17",
  month =        sep,
  year =         "2004",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/angle.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2004:CFP,
  author =       "W. Kahan",
  title =        "On the Cost of Floating-Point Computation Without
                 Extra-Precise Arithmetic",
  howpublished = "World-Wide Web document",
  pages =        "21",
  day =          "20",
  month =        nov,
  year =         "2004",
  bibdate =      "Mon Apr 25 17:44:03 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "See \cite{Boldo:2009:KAC} for a proof of this
                 algorithm for accurate computation of the discriminant
                 needed for the solution of quadratic equations.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Qdrtcs.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2004:DCP,
  author =       "W. Kahan",
  title =        "Derivatives in the Complex $z$-plane",
  howpublished = "World-Wide Web document",
  day =          "26",
  month =        may,
  year =         "2004",
  bibdate =      "Mon Apr 25 17:45:58 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 185.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math185/Derivative.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2004:FMD,
  author =       "W. Kahan",
  title =        "Failure Mode: Do {MATLAB}'s {\tt lu(\ldots{})}, {\tt
                 inv(\ldots{})}, {\tt /} and {\tt\char92} have a Failure
                 Mode?",
  howpublished = "World-Wide Web document",
  pages =        "4",
  day =          "17",
  month =        feb,
  year =         "2004",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/FailMode.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2004:HFM,
  author =       "W. Kahan",
  title =        "How Futile are Mindless Assessments of Roundoff in
                 Floating-Point Computation?",
  howpublished = "World-Wide Web document",
  pages =        "37",
  day =          "1",
  month =        nov,
  year =         "2004",
  bibdate =      "Mon Apr 25 17:41:28 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Mind1ess.pdf;
                 http://www.cs.berkeley.edu/~wkahan/Mindless.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; rounding errors",
}

@Misc{Kahan:2004:ICG,
  author =       "W. Kahan",
  title =        "Iterate: Conjugate Gradients and Overrelaxation",
  howpublished = "World-Wide Web document",
  pages =        "1",
  day =          "7",
  month =        apr,
  year =         "2004",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/Iterate.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2004:LNR,
  author =       "W. Kahan",
  title =        "Lecture Notes on Real Root-Finding",
  howpublished = "World-Wide Web document",
  pages =        "63",
  day =          "23",
  month =        jun,
  year =         "2004",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128. Work in progress: not for
                 redistribution.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/RealRoots.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2004:LTC,
  author =       "W. Kahan",
  title =        "A Logarithm Too Clever by Half",
  howpublished = "World-Wide Web document",
  pages =        "9",
  day =          "9",
  month =        aug,
  year =         "2004",
  bibdate =      "Mon Apr 25 17:39:08 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/LOG10HAF.TXT",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2004:PMG,
  author =       "W. Kahan",
  title =        "{Prof. Ming Gu}'s Transparencies",
  howpublished = "World-Wide Web document",
  pages =        "4 + 6 + 1 + 1",
  day =          "5",
  month =        may,
  year =         "2004",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/MGu;
                 http://www.cs.berkeley.edu/~wkahan/Math128/MGu/kahanbvp.pdf;
                 http://www.cs.berkeley.edu/~wkahan/Math128/MGu/kahanss.pdf;
                 http://www.cs.berkeley.edu/~wkahan/Math128/MGu/pendi.pdf;
                 http://www.cs.berkeley.edu/~wkahan/Math128/MGu/tridi.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2004:SSR,
  author =       "W. Kahan",
  title =        "$128$ Squares of $128$ Square Roots",
  howpublished = "World-Wide Web document",
  pages =        "3",
  day =          "29",
  month =        jan,
  year =         "2004",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/SqSqrts.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2004:THT,
  author =       "W. Kahan",
  title =        "Take-Home Test for Math. 128{B}",
  howpublished = "World-Wide Web document",
  pages =        "1",
  day =          "8",
  month =        mar,
  year =         "2004",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/M128Bprob5Mar04.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2004:TPM,
  author =       "W. Kahan",
  title =        "Three Problems for Math. 128{B}",
  howpublished = "World-Wide Web document",
  pages =        "15",
  day =          "10",
  month =        feb,
  year =         "2004",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/M128Bsoln09Feb04.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2004:TSC,
  author =       "W. Kahan",
  title =        "Is there a Skew {Cayley} Transform with Zero
                 Diagonal?",
  howpublished = "World-Wide Web document",
  pages =        "4",
  day =          "6",
  month =        aug,
  year =         "2004",
  bibdate =      "Mon Apr 25 17:32:17 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/skcayley.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2004:TSD,
  author =       "W. Kahan",
  title =        "{Taylor} Series for Differential Equation Solvers'
                 Local Error",
  howpublished = "World-Wide Web document",
  pages =        "2",
  day =          "25",
  month =        aug,
  year =         "2004",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/Truncate.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Anonymous:2005:MGP,
  author =       "Anonymous",
  title =        "The {Mathematics Genealogy Project}: {William Morton
                 Kahan}",
  howpublished = "World-Wide Web document",
  year =         "2005",
  bibdate =      "Mon Apr 25 08:09:46 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=16049",
  acknowledgement = ack-nhfb,
  remark =       "Lists doctoral thesis, and doctoral students of W. M.
                 Kahan: Deb Chowdhury (1964), James Demmel (1983),
                 Jerome Coonen (1984), Pingtak Peter Tang (1987),
                 Ren-Cang Li (1995).",
}

@TechReport{Demmel:2005:EBE,
  author =       "James Demmel and Yozo Hida and W. Kahan and Xiaoye S.
                 Li and Soni Mukherjee and E. Jason Riedy",
  title =        "Error Bounds from Extra Precise Iterative Refinement",
  type =         "LAPACK Working Note",
  number =       "165",
  institution =  inst-UTK-CS,
  address =      inst-UTK-CS:adr,
  month =        feb,
  year =         "2005",
  bibdate =      "Fri Apr 22 17:06:37 2005",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/lawn.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "UT-CS-05-547, February 2005.",
  URL =          "http://www.netlib.org/lapack/lawns/lawn165.ps;
                 http://www.netlib.org/lapack/lawnspdf/lawn165.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2005:BTG,
  author =       "William Kahan",
  title =        "A Brief Tutorial on Gradual Underflow",
  howpublished = "World-Wide Web lecture notes.",
  pages =        "15",
  day =          "8",
  month =        jul,
  year =         "2005",
  bibdate =      "Fri Jul 15 11:38:13 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Prepared for ARITH 17, Tues. 28 June 2005, and
                 subsequently augmented.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ARITH_17U.pdf",
  acknowledgement = ack-nhfb,
}

@Manual{Kahan:2005:DP,
  author =       "William Kahan",
  title =        "A Demonstration of Presubstitution for
                 $\infty/\infty$",
  pages =        "10",
  day =          "5",
  month =        jul,
  year =         "2005",
  bibdate =      "Fri Jul 15 11:47:46 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Grail.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2005:FPA,
  author =       "William Kahan",
  title =        "Floating-Point Arithmetic Besieged by ``Business
                 Decisions''",
  howpublished = "World-Wide Web lecture notes.",
  pages =        "28",
  day =          "5",
  month =        jul,
  year =         "2005",
  bibdate =      "Fri Jul 15 12:07:31 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "A Keynote Address, prepared for the IEEE-Sponsored
                 ARITH 17 Symposium on Computer Arithmetic, delivered on
                 Mon. 27 June 2005 in Hyannis, Massachusetts.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ARITH_17.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:2005:OQD,
  author =       "William Kahan and Dan Zuras",
  title =        "An Open Question to Developers of Numerical Software",
  journal =      j-COMPUTER,
  volume =       "38",
  number =       "5",
  pages =        "91--94",
  month =        may,
  year =         "2005",
  CODEN =        "CPTRB4",
  DOI =          "http://dx.doi.org/10.1109/MC.2005.148",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Wed May 04 15:33:06 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://csdl.computer.org/comp/mags/co/2005/05/r5091abs.htm;
                 http://csdl.computer.org/comp/mags/co/2005/05/r5toc.htm;
                 http://csdl.computer.org/dl/mags/co/2005/05/r5091.pdf",
  abstract =     "IEEE 754 a standard for binary floating-point
                 arithmetic has revolutionized the portability and
                 reliability of programs that use binary floating-point
                 arithmetic. Floating point is almost universally
                 implemented with special-purpose hardware that tucks
                 into a small corner of the CPU chip and runs in the
                 hundreds of Mflops to Gflops range. Single-stepping
                 through today's floating-point software to debug it
                 often turns out to be futile. The concept of a NaN,
                 standing for ``not a number'', evolved from an
                 ``indefinite'' in Seymour Cray's CDC 6600. IEEE 754, by
                 default, requires an untrapped ``invalid operation'',
                 to signal itself by raising a flag and to deliver a NaN
                 just when any other result, be it finite or infinite,
                 would cause worse confusion. The NaN lets a program
                 retain control unless the program or programmer directs
                 its cancellation upon an invalid operation. Thus, a
                 program conducting a search can return to the realm
                 being searched after an accidental foray beyond a
                 boundary whose existence and location were previously
                 unknown. A sNaN differs from the other quiet NaNs by
                 trapping any attempt to perform arithmetic upon it;
                 then a trap-handler must interpret this sNaN.",
  acknowledgement = ack-nhfb,
}

@Article{Demmel:2006:EBE,
  author =       "James Demmel and Yozo Hida and William Kahan and
                 Xiaoye S. Li and Sonil Mukherjee and E. Jason Riedy",
  title =        "Error bounds from extra-precise iterative refinement",
  journal =      j-TOMS,
  volume =       "32",
  number =       "2",
  pages =        "325--351",
  month =        jun,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/1141885.1141894",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Aug 23 10:29:48 MDT 2006",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  abstract =     "We present the design and testing of an algorithm for
                 iterative refinement of the solution of linear
                 equations where the residual is computed with extra
                 precision. This algorithm was originally proposed in
                 1948 and analyzed in the 1960s as a means to compute
                 very accurate solutions to all but the most
                 ill-conditioned linear systems. However, two obstacles
                 have until now prevented its adoption in standard
                 subroutine libraries like LAPACK: (1) There was no
                 standard way to access the higher precision arithmetic
                 needed to compute residuals, and (2) it was unclear how
                 to compute a reliable error bound for the computed
                 solution. The completion of the new BLAS Technical
                 Forum Standard has essentially removed the first
                 obstacle. To overcome the second obstacle, we show how
                 the application of iterative refinement can be used to
                 compute an error bound in any norm at small cost and
                 use this to compute both an error bound in the usual
                 infinity norm, and a componentwise relative error
                 bound. We report extensive test results on over $6.2$
                 million matrices of dimensions $5$, $10$, $100$, and
                 $1000$. As long as a normwise (componentwise) condition
                 number computed by the algorithm is less than
                 $1/max\{10,\sqrt{n}\}\varepsilon_w$, the computed
                 normwise (componentwise) error bound is at most $2
                 max\{10, \sqrt{n}\} \cdot \varepsilon_w$, and indeed
                 bounds the true error. Here, $n$ is the matrix
                 dimension and $\varepsilon_w = 2^{-24}$ is the working
                 precision. Residuals were computed in double precision
                 (53 bits of precision). In other words, the algorithm
                 always computed a tiny error at negligible extra cost
                 for most linear systems. For worse conditioned problems
                 (which we can detect using condition estimation), we
                 obtained small correct error bounds in over 90\% of
                 cases.",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2006:AIR,
  author =       "William Kahan",
  title =        "Applications of {IEEE 754r}'s Rounding Modes",
  howpublished = "World-Wide Web document.",
  day =          "16",
  month =        feb,
  year =         "2006",
  bibdate =      "Fri Feb 17 17:54:50 2006",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://nonabelian.com/754/RNDGMODE.TXT",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:2006:TSS,
  author =       "W. Kahan",
  title =        "Is there a small skew {Cayley} transform with zero
                 diagonal?",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "417",
  number =       "2--3",
  pages =        "335--341",
  year =         "2006",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/j.laa.2005.08.027",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A57 (15A18)",
  MRnumber =     "2250315 (2007e:15019)",
  bibdate =      "Mon Sep 26 09:57:45 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  fjournal =     "Linear Algebra and its Applications",
}

@InProceedings{Boldo:2007:PCA,
  author =       "Sylvie Boldo and Marc Daumas and William Kahan and
                 Guillaume Melquiond",
  title =        "Proof and certification of an accurate discriminant",
  crossref =     "Luther:2007:GII",
  pages =        "??--??",
  year =         "2007",
  bibdate =      "Wed Jun 24 22:27:02 2009",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  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 =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.netlib.org/lapack/lawnspdf/lawn181.pdf",
  acknowledgement = ack-nhfb,
  utknumber =    "UT-CS-07-592",
}

@InProceedings{Kahan:2007:WCD,
  author =       "William Kahan",
  title =        "Why {I} can debug some programs and you can't",
  crossref =     "Du:2007:SSA",
  pages =        "??--??",
  year =         "2007",
  bibdate =      "Sat Apr 07 09:00:14 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.stanford.edu/group/compmath50/docs/CompMath50Pgm21.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2008:BFU,
  author =       "William Kahan",
  title =        "Back to the Future of Undebuggable Floating-Point
                 Computation in Science and Engineering",
  howpublished = "Web document",
  day =          "30",
  month =        mar,
  year =         "2008",
  bibdate =      "Mon Mar 31 16:50:19 2008",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "The Bay Area Scientific Computing Day, BASCD08,
                 honoring Profs. Kahan and Parlett, 29--30 March,
                 2008.",
  URL =          "http://www.eecs.berkeley.edu/~wkahan/BASCD08K.pdf;
                 http://math.berkeley.edu/bascd08",
  abstract =     "When I began to program an electronic computer in
                 1953, von Neumann was still disparaging floating-point
                 computation, which was generally deemed impervious to
                 error-analysis. Occasional anomalous results were
                 expected. Often they were attributed wrongly to
                 ``Ill-Condition''. Putting one's data through several
                 numerical methods some of whose results might agree was
                 a prudent policy. Those days are back. Their challenges
                 will be illustrated by a program like some used by
                 structural engineers for forty years. To cope, we need
                 debugging aids like those in Section 14 of my web
                 page's {\tt Mindless.pdf}. Help can come only from the
                 designers of hardware, compilers and software
                 development systems after they are persuaded that the
                 demand for such aids is commercially significant.",
  acknowledgement = ack-nhfb,
}

@Article{Li:2012:FAN,
  author =       "Ren-Cang Li and William Kahan",
  title =        "A family of {Anadromic} numerical methods for matrix
                 {Riccati} differential equations",
  journal =      j-MATH-COMPUT,
  volume =       "81",
  number =       "277",
  pages =        "233--265",
  month =        "????",
  year =         "2012",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  bibdate =      "Mon Oct 24 10:33:38 MDT 2011",
  bibsource =    "http://www.ams.org/mcom/2012-81-277;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://www.ams.org/journals/mcom/2012-81-277/S0025-5718-2011-02498-1;
                 http://www.ams.org/journals/mcom/2012-81-277/S0025-5718-2011-02498-1/S0025-5718-2011-02498-1.pdf",
  acknowledgement = ack-nhfb,
}

%%% ====================================================================
%%% Cross-referenced entries must come last:

@Proceedings{Freiman:1971:PIC,
  editor =       "C. V. Freiman and J. E. Griffith and J. L. Rosenfeld",
  booktitle =    "Information processing 71: proceedings of IFIP
                 Congress 71 organized by the International Federation
                 for Information Processing, Ljubljana, Yugoslavia,
                 August 23--28, 1971",
  title =        "Information processing 71: proceedings of {IFIP}
                 Congress 71 organized by the International Federation
                 for Information Processing, Ljubljana, Yugoslavia,
                 August 23--28, 1971",
  publisher =    pub-NH,
  address =      pub-NH:adr,
  pages =        "xviii + 1621 (two volumes)",
  year =         "1971",
  ISBN =         "0-7204-2063-6",
  ISBN-13 =      "978-0-7204-2063-0",
  LCCN =         "QA76 .I575 1971",
  bibdate =      "Sat Nov 29 07:10:48 2003",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Eight booklets in two volumes.",
  acknowledgement = ack-nhfb,
}

@Proceedings{ACM:1972:PAA,
  key =          "ACM '72",
  title =        "Proceedings of the {ACM} Annual Conference, August
                 1972, Boston",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xiii + 1156",
  year =         "1972",
  LCCN =         "TK 7885 A84p 1972",
  bibdate =      "Wed Sep 07 10:13:52 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Two volumes.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Gentleman:1979:PCS,
  editor =       "Jane F. Gentleman",
  booktitle =    "Proceedings of the Computer science and statistics:
                 12th annual symposium on the interface, {May 10--11,
                 1979, University of Waterloo, Waterloo, Ontario,
                 Canada}",
  title =        "Proceedings of the Computer science and statistics:
                 12th annual symposium on the interface, {May 10--11,
                 1979, University of Waterloo, Waterloo, Ontario,
                 Canada}",
  publisher =    "University of Waterloo,",
  address =      "Waterloo, ON, Canada",
  pages =        "xiii + 500",
  year =         "1979",
  LCCN =         "QA276.4",
  bibdate =      "Tue Apr 26 07:11:54 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  xxISBN =       "none",
}

@Proceedings{Nickel:1980:IMP,
  editor =       "Karl L. E. Nickel",
  booktitle =    "Interval mathematics 1980: proceedings of an
                 International Symposium on Interval Mathematics, held
                 at the Institut f{\"u}r Angewandte Mathematik,
                 Universit{\"a}t Freiburg i. Br., Germany, May 27--31,
                 1980",
  title =        "Interval mathematics 1980: proceedings of an
                 International Symposium on Interval Mathematics, held
                 at the Institut f{\"u}r Angewandte Mathematik,
                 Universit{\"a}t Freiburg i. Br., Germany, May 27--31,
                 1980",
  publisher =    pub-AP,
  address =      pub-AP:adr,
  pages =        "xv + 554",
  year =         "1980",
  ISBN =         "0-12-518850-1",
  ISBN-13 =      "978-0-12-518850-0",
  LCCN =         "QA297.75 .I57 1980",
  bibdate =      "Mon Apr 25 07:40:03 MDT 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 z3950.loc.gov:7090/Voyager;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
  subject =      "Interval analysis (Mathematics); Congresses",
}

@Proceedings{Reid:1982:RBN,
  editor =       "John K. Reid",
  title =        "The Relationship Between Numerical Computation and
                 Programming Languages: Proceedings of the {IFIP} {TC2}
                 Working Conference on the Relationship between
                 Numerical Computation and Programming Languages,
                 Boulder, Colorado, {USA}, 3--7 August, 1981",
  publisher =    pub-ENH,
  address =      pub-ENH:adr,
  pages =        "x + 377",
  year =         "1982",
  ISBN =         "0-444-86377-X",
  ISBN-13 =      "978-0-444-86377-5",
  LCCN =         "QA297 .I34 1981",
  bibdate =      "Tue Sep 06 22:34:51 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Anonymous:1983:PSC,
  editor =       "Anonymous",
  booktitle =    "1983 proceedings of the statistical computing section:
                 papers presented at the annual meeting of the American
                 Statistical Association, Toronto, Canada, August
                 15--18, 1983",
  title =        "1983 proceedings of the statistical computing section:
                 papers presented at the annual meeting of the American
                 Statistical Association, Toronto, Canada, August
                 15--18, 1983",
  publisher =    "American Statistical Association",
  address =      "Washington, DC, USA",
  year =         "1983",
  ISBN =         "????",
  ISBN-13 =      "????",
  ISSN =         "0149-9963",
  LCCN =         "QA276.4 .A43a",
  bibdate =      "Sat Nov 29 11:12:49 2003",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1983:MMW,
  editor =       "{IEEE}",
  booktitle =    "{Mini\slash Micro West '83: conference record:
                 sessions presented at Mini\slash Micro West-83, San
                 Francisco, California, November 8, 9, 10, 11, 1983}",
  title =        "{Mini\slash Micro West '83: conference record:
                 sessions presented at Mini\slash Micro West-83, San
                 Francisco, California, November 8, 9, 10, 11, 1983}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "420 (est.)",
  year =         "1983",
  ISBN =         "",
  ISBN-13 =      "",
  LCCN =         "",
  bibdate =      "Tue Apr 26 07:21:43 2005",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Hwang:1985:PSC,
  editor =       "Kai Hwang",
  booktitle =    "Proceedings: 7th Symposium on Computer Arithmetic,
                 June 4--6, 1985, University of Illinois, Urbana,
                 Illinois",
  title =        "Proceedings: 7th Symposium on Computer Arithmetic,
                 June 4--6, 1985, University of Illinois, Urbana,
                 Illinois",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 343",
  year =         "1985",
  ISBN =         "0-8186-0632-0 (paperback), 0-8186-8632-4 (hard),
                 0-8186-4632-2 (microfiche)",
  ISBN-13 =      "978-0-8186-0632-8 (paperback), 978-0-8186-8632-0
                 (hard), 978-0-8186-4632-4 (microfiche)",
  LCCN =         "QA76.9.C62 S95 1985",
  bibdate =      "Thu Sep 08 00:11:41 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nj,
  keywords =     "ARITH-7",
}

@Proceedings{Iserles:1987:SAN,
  editor =       "A. Iserles and M. J. D. Powell",
  booktitle =    "The State of the Art in Numerical Analysis:
                 Proceedings of the Joint {IMA}\slash {SIAM} Conference
                 on the State of the Art in Numerical Analysis held at
                 the University of Birmingham, 14--18 April 1986",
  title =        "The State of the Art in Numerical Analysis:
                 Proceedings of the Joint {IMA}\slash {SIAM} Conference
                 on the State of the Art in Numerical Analysis held at
                 the University of Birmingham, 14--18 April 1986",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xiv + 719",
  year =         "1987",
  ISBN =         "0-19-853614-3",
  ISBN-13 =      "978-0-19-853614-7",
  LCCN =         "QA297 .S781 1987",
  bibdate =      "Thu Sep 08 00:41:24 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  price =        "UK\pounds55.00, US\$77.50",
  acknowledgement = ack-nj,
}

@Proceedings{CUG:1990:PSC,
  editor =       "{CUG}",
  key =          "Cray UG '90",
  booktitle =    "Proceedings, 25th Semiannual Cray User Group Meeting,
                 Toronto, Ontario, June 1990",
  title =        "Proceedings, 25th Semiannual Cray User Group Meeting,
                 Toronto, Ontario, June 1990",
  publisher =    "Cray User Group",
  address =      "186 Mandela Road, Shepherdstown, WV 25443, USA",
  pages =        "????",
  year =         "1990",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Thu Sep 08 08:56:01 1994",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nj,
  xxnote =       "Check: is this June or April 10 meeting??",
}

@Proceedings{Griffiths:1991:NAP,
  editor =       "D. F. Griffiths and G. A. Watson",
  booktitle =    "Numerical analysis, 1991: proceedings of the 14th
                 Dundee Conference, June 1991",
  title =        "Numerical analysis, 1991: proceedings of the 14th
                 Dundee Conference, June 1991",
  publisher =    pub-LONGMAN-ST,
  address =      pub-LONGMAN-ST:adr,
  pages =        "292",
  year =         "1991",
  ISBN =         "0-582-08908-5",
  ISBN-13 =      "978-0-582-08908-2",
  LCCN =         "QA297 .D85 1991",
  bibdate =      "Mon Jan 15 11:05:56 1996",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{ACM:1997:SHP,
  editor =       "{ACM}",
  booktitle =    "{SC'97: High Performance Networking and Computing:
                 Proceedings of the 1997 ACM\slash IEEE SC97 Conference:
                 November 15--21, 1997, San Jose, California, USA}",
  title =        "{SC'97: High Performance Networking and Computing:
                 Proceedings of the 1997 ACM\slash IEEE SC97 Conference:
                 November 15--21, 1997, San Jose, California, USA}",
  publisher =    pub-ACM # " and " # pub-IEEE,
  address =      pub-ACM:adr # " and " # pub-IEEE:adr,
  pages =        "vii + 159",
  year =         "1997",
  ISBN =         "0-89791-985-8",
  ISBN-13 =      "978-0-89791-985-2",
  LCCN =         "QA76.88 1997",
  bibdate =      "Sat Mar 21 09:10:00 1998",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "ACM SIGARCH order number 415972. IEEE Computer Society
                 Press order number RS00160.",
  URL =          "http://www.supercomp.org/sc97/proceedings/",
  acknowledgement = ack-nhfb,
}

@Proceedings{ACM:1998:AWJ,
  editor =       "{ACM}",
  booktitle =    "ACM 1998 Workshop on Java for High-Performance Network
                 Computing",
  title =        "{ACM} 1998 Workshop on Java for High-Performance
                 Network Computing",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "287",
  year =         "1998",
  CODEN =        "CPEXEI",
  ISSN =         "1040-3108",
  LCCN =         "????",
  bibdate =      "Thu Apr 27 10:40:59 2000",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "Also published as {\em Concurrency: Practice and
                 Experience}, {\bf 10}(11--13), September 1998, CODEN
                 CPEXEI, ISSN 1040-3108.",
  series =       j-CPE,
  URL =          "http://www.cs.ucsb.edu/conferences/java98/program.html",
  acknowledgement = ack-nhfb,
  xxISBN =       "none",
  xxnote =       "Appears to be the same as \cite{Fox:1998:JHP}.",
}

@Proceedings{ACM:2000:SHP,
  editor =       "{ACM}",
  booktitle =    "SC2000: High Performance Networking and Computing.
                 Dallas Convention Center, Dallas, TX, USA, November
                 4--10, 2000",
  title =        "{SC2000}: High Performance Networking and Computing.
                 Dallas Convention Center, Dallas, {TX}, {USA}, November
                 4--10, 2000",
  publisher =    pub-ACM # " and " # pub-IEEE,
  address =      pub-ACM:adr # " and " # pub-IEEE:adr,
  pages =        "????",
  year =         "2000",
  ISBN =         "0-7803-9802-5",
  ISBN-13 =      "978-0-7803-9802-3",
  LCCN =         "QA76.88 2000",
  bibdate =      "Thu Feb 24 09:35:00 2000",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  URL =          "http://www.sc2000.org/proceedings/info/fp.pdf;
                 http://csdl.computer.org/comp/proceedings/sc/2000/9802/00/9802toc.htm",
  acknowledgement = ack-nhfb,
  remark =       "Proceedings published only on CD-ROM??",
}

@Proceedings{Du:2007:SSA,
  editor =       "Ding-Zhu Du and Charles Farbat and Walter Murray and
                 Michael Overton and Haesun Park and Michael Saunders
                 and James Varah",
  booktitle =    "{STANFORD 50: State of the Art \& Future Directions
                 of Computational Mathematics \& Numerical Computing: A
                 conference celebrating the 50th anniversary George
                 Forsythe's arrival at Stanford and Gene Golub's
                 75th birthday, Stanford University, March 29--31,
                 2007}",
  title =        "{STANFORD 50: State of the Art \& Future Directions
                 of Computational Mathematics \& Numerical Computing:
                 A conference celebrating the 50th anniversary George
                 Forsythe's arrival at Stanford and Gene Golub's
                 75th birthday, Stanford University, March 29--31,
                 2007}",
  publisher =    "????",
  address =      "????",
  pages =        "????",
  year =         "2007",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Apr 07 09:04:27 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Luther:2007:GII,
  editor =       "W. Luther and W. Otten",
  booktitle =    "{12th GAMM-IMACS International Symposium on Scientific
                 Computing, Computer Arithmetic and Validated Numerics:
                 SCAN 2006: conference post-proceedings: September
                 26--29, 2006, Duisburg, Germany}",
  title =        "{12th GAMM-IMACS International Symposium on Scientific
                 Computing, Computer Arithmetic and Validated Numerics:
                 SCAN 2006: conference post-proceedings: September
                 26--29, 2006, Duisburg, Germany}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2007",
  ISBN =         "0-7695-2821-X",
  ISBN-13 =      "978-0-7695-2821-2",
  LCCN =         "QA297.I5 2007",
  bibdate =      "Wed Nov 26 18:03:28 MST 2008",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "IEEE Computer Society Order Number E2821.",
  URL =          "http://ieeexplore.ieee.org/servlet/opac?punumber=4402381",
  acknowledgement = ack-nhfb,
}

@Article{Boldo:2009:KAC,
  author =       "S. Boldo",
  title =        "{Kahan}'s Algorithm for a Correct Discriminant
                 Computation at Last Formally Proven",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "2",
  pages =        "220--225",
  month =        feb,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "http://dx.doi.org/10.1109/TC.2008.200",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jun 12 08:51:00 MDT 2009",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib",
  note =         "See \cite{Kahan:2004:CFP} for the original
                 algorithm.",
  abstract =     "This article tackles Kahan's algorithm to compute
                 accurately the discriminant. This is a known difficult
                 problem, and this algorithm leads to an error bounded
                 by 2 ulps of the floating-point result. The proofs
                 involved are long and tricky and even trickier than
                 expected as the test involved may give a result
                 different from the result of the same test without
                 rounding. We give here the total demonstration of the
                 validity of this algorithm, and we provide sufficient
                 conditions to guarantee that neither overflow nor
                 underflow will jeopardize the result. The IEEE-754
                 double-precision program is annotated using the Why
                 platform and the proof obligations are done using the
                 Coq automatic proof checker.",
  acknowledgement = ack-nhfb,
  keywords =     "floating point; discriminant; formal proof; Why
                 platform; Coq",
  remark =       "Extended version of ARITH-18 article
                 \cite{Boldo:2007:FVF}.",
}