%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.80", %%% date = "29 August 2024", %%% time = "10:01:59 MDT", %%% filename = "kahan-william-m.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "https://www.math.utah.edu/~beebe", %%% checksum = "15488 7383 29859 314148", %%% 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 %%% was made an ACM Fellow in 1995 and a member %%% of the National Academy of Engineering in %%% 2005. 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 His personal Web site at %%% %%% http://www.cs.berkeley.edu/~wkahan/ %%% %%% contains many published and unpublished %%% documents and software.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 1.80, the year coverage looked %%% like this: %%% %%% 1955 ( 1) 1979 ( 5) 2003 ( 2) %%% 1956 ( 0) 1980 ( 6) 2004 ( 16) %%% 1957 ( 0) 1981 ( 3) 2005 ( 6) %%% 1958 ( 1) 1982 ( 6) 2006 ( 3) %%% 1959 ( 0) 1983 ( 7) 2007 ( 5) %%% 1960 ( 0) 1984 ( 1) 2008 ( 1) %%% 1961 ( 0) 1985 ( 4) 2009 ( 1) %%% 1962 ( 0) 1986 ( 5) 2010 ( 2) %%% 1963 ( 4) 1987 ( 8) 2011 ( 0) %%% 1964 ( 1) 1988 ( 6) 2012 ( 3) %%% 1965 ( 6) 1989 ( 4) 2013 ( 2) %%% 1966 ( 6) 1990 ( 8) 2014 ( 0) %%% 1967 ( 4) 1991 ( 8) 2015 ( 2) %%% 1968 ( 3) 1992 ( 7) 2016 ( 5) %%% 1969 ( 5) 1993 ( 3) 2017 ( 0) %%% 1970 ( 3) 1994 ( 6) 2018 ( 1) %%% 1971 ( 3) 1995 ( 4) 2019 ( 2) %%% 1972 ( 4) 1996 ( 10) 2020 ( 2) %%% 1973 ( 4) 1997 ( 9) 2021 ( 1) %%% 1974 ( 1) 1998 ( 25) 2022 ( 0) %%% 1975 ( 4) 1999 ( 35) 2023 ( 1) %%% 1976 ( 3) 2000 ( 23) 2024 ( 1) %%% 1977 ( 3) 2001 ( 8) %%% 1978 ( 2) 2002 ( 22) %%% %%% Article: 72 %%% Book: 3 %%% InCollection: 2 %%% InProceedings: 23 %%% Manual: 1 %%% MastersThesis: 1 %%% Misc: 131 %%% PhdThesis: 1 %%% Proceedings: 18 %%% TechReport: 51 %%% Unpublished: 35 %%% %%% Total entries: 338 %%% %%% 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}" # "\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi" }

%%% ==================================================================== %%% 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-BIT-NUM-MATH= "BIT Numerical Mathematics"} @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-COMPUT-MATH-APPL= "Computers and Mathematics with Applications"} @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 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-LIN-ALG-APPL= "Numerical Linear Algebra with Applications"} @String{j-NUM-MATH= "Numerische Mathematik"} @String{j-NUMER-ALGORITHMS= "Numerical Algorithms"} @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-COMP= "SIAM Journal on Scientific Computing"} @String{j-SIAM-J-SCI-STAT-COMP= "SIAM Journal on Scientific and Statistical Computing"} @String{j-SIAM-REVIEW= "SIAM Review"} @String{j-SIGNUM= "ACM SIGNUM Newsletter"} @String{j-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-ACADEMIC= "Academic Press"} @String{pub-ACADEMIC:adr= "New York, NY, USA"} @String{pub-ACM= "ACM Press"} @String{pub-ACM:adr= "New York, NY 10036, 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-PRINCETON= "Princeton University Press"} @String{pub-PRINCETON:adr= "Princeton, NJ, USA"} @String{pub-SV= "Spring{\-}er-Ver{\-}lag"} @String{pub-SV:adr= "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."}

%%% ==================================================================== %%% Series abbreviations:

@String{ser-LNCS= "Lecture Notes in Computer Science"}

%%% ==================================================================== %%% Part 1 (of 2): publications of William Kahan %%% %%% 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 = "https://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 = "https://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 (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "47.48", MRnumber = "MR0149309 (26 \#6799)", MRreviewer = "J. Rovnyak", bibdate = "Mon Apr 25 05:36:25 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", note = "See \cite{Davis:1965:REP,Davis:1970:REP}.", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", } @Article{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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", } @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 (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "47.48", MRnumber = "MR0180852 (31 \#5082)", MRreviewer = "J. Rovnyak", bibdate = "Mon Apr 25 05:36:25 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", note = "See \cite{Davis:1963:REP,Davis:1970:REP}.", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", } @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)", ISSN-L = "0887-459X", MRclass = "65.35", MRnumber = "MR0183105 (32 \#587)", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis", journal-URL = "http://epubs.siam.org/loi/sjnaam.1", 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 = "https://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", DOI = "https://doi.org/10.1145/363707.363723", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 00:18:17 1994", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nj # " and " # ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "See \cite{Moller:1965:QDP}.", acknowledgement = ack-nj # " and " # ack-nhfb, journal-URL = "http://link.springer.com/journal/10543", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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:PFR}. Extends Gill's earlier fixed-point result \cite{Gill:1951:PSS}.", journal-URL = "http://link.springer.com/journal/10543", remark = "Gives summation error estimate formula `s = fl(a + b); error = (a - s) + b', also discovered independently by \cite{Kahan:1965:PFR}. 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", acknowledgement = ack-jr, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @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 = "https://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 = "https://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://cms.math.ca/cmb/v9/; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, fjournal = "Canadian mathematical bulletin = Bulletin canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-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:EEB, author = "W. M. Kahan", title = "An ellipsoidal error bound for linear systems of ordinary differential equations", type = "Report", institution = "Computer Science, University of Toronto", address = "Toronto, Canada", pages = "????", year = "1967", bibdate = "Fri Jun 02 14:05:30 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", acknowledgement = ack-nhfb, } @InProceedings{Kahan:1967:ISS, author = "W. M. Kahan", booktitle = "{Proceedings of the 1967 Army Numerical Analysis Conference (Wisconsin, May 1967)}", title = "{7094-II} System Support for Numerical Analysis", publisher = "U.S. Army Research Office", address = "Research Triangle Park, NC", pages = "175--208 + errata", year = "1967", LCCN = "????", bibdate = "Fri Jun 02 14:07:53 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", note = "ARO-D Report 67-3. Reprint of \cite{Kahan:1966:ISS}", acknowledgement = ack-nhfb, } @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, ON, Canada", year = "1967", bibdate = "Mon Apr 25 18:24:02 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, } @Article{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", DOI = "https://doi.org/10.1137/0704042", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", } @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 = "https://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://cms.math.ca/cmb/v11/; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", acknowledgement = ack-jr # "\slash " # ack-nhfb, fjournal = "Canadian mathematical bulletin = Bulletin canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", 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/; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM SIGNUM Newsletter", journal-URL = "https://dl.acm.org/loi/signum", } @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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", URL = "http://projecteuclid.org/euclid.bams/1183530664", ZMnumber = "0175.43204", acknowledgement = ack-nhfb, fjournal = "Bulletin of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", } @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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", note = "Published in \cite{Nickel:1970:KBS}.", acknowledgement = ack-jr, language = "German", } @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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", note = "See \cite{Davis:1963:REP,Davis:1965:REP}.", ZMnumber = "0198.47201", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik}", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001", language = "German", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", note = "See response \cite{Dorr:1973:REC}.", acknowledgement = ack-nhfb, fjournal = "ACM SIGNUM Newsletter", journal-URL = "https://dl.acm.org/loi/signum", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", series = "Information Processing 71", URL = "http://dblp.uni-trier.de/db/conf/ifip/ifip71-2.html#Kahan71", acknowledgement = ack-jr # " and " # ack-nhfb, keywords = "accurate floating-point summation", 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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-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://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/signum.bib", acknowledgement = ack-nhfb, fjournal = "ACM SIGNUM Newsletter", journal-URL = "https://dl.acm.org/loi/signum", } @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/; https://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", fjournal = "ACM SIGNUM Newsletter", journal-URL = "https://dl.acm.org/loi/signum", 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_2 n + 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", } @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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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", type = "Memo", number = "ERL-M467", institution = "University of California, Berkeley", address = "Berkeley, CA, USA", year = "1974", bibdate = "Mon Apr 25 18:24:02 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", acknowledgement = ack-nhfb, fjournal = "SIGSAM Bulletin", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", } @InProceedings{Laveuve:1975:DKA, author = "S. E. Laveuve", title = "{Definition Einer Kahan-Arithmetik Und Ihre Implementierung}. ({German}) [{Definition} of a {Kahan} Arithmetic and its Implementation]", crossref = "Nickel:1975:IMP", pages = "236--245", year = "1975", bibdate = "Fri Jan 12 11:37:56 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", acknowledgement = ack-jr, language = "German", } @InProceedings{Kahan:1976:HFS, author = "W. Kahan and B. N. Parlett", title = "How far should you go with the {Lanczos} process?", crossref = "Bunch:1976:SMC", pages = "131--144", year = "1976", MRclass = "65F15", MRnumber = "MR0458836 (56 \#17036)", MRreviewer = "Michael S. Martin", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", ZMnumber = "0345.65017", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 15A18 Eigenvalues of matrices, etc", } @Article{Kahan:1976:PIP, author = "W. M. Kahan", title = "Pitfalls in Ill-Posed Problems", journal = j-SIAM-REVIEW, volume = "18", number = "4", pages = "810--811", month = "????", year = "1976", CODEN = "SIREAD", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Fri Jun 21 11:25:02 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", note = "German Transl. Published In: Jahrbuch {\"U}berblicke Mathematik 1978, Ed. by B. Fuchssteiner and others, Bibliographisches Institut, Mannheim-Wien-Z{\"u}rich, 199--216, 1978", URL = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-jr, } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/sigsam.bib", acknowledgement = ack-nhfb, fjournal = "SIGSAM Bulletin", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", } @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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "0397.65081", acknowledgement = ack-nhfb, classmath = "*65Y99 Computer aspects of numerical algorithms 65D20 Computation of special functions 00A99 Miscellaneous topics in general mathematics", keywords = "Automated Algorithms; Error of Computation; Pocket Calculator", language = "German", } @Article{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 = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/signum.bib", acknowledgement = ack-nhfb # " and " # ack-nj, classcodes = "C5230 (Digital arithmetic methods)", fjournal = "ACM SIGNUM Newsletter", journal-URL = "https://dl.acm.org/loi/signum", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/hpj.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 = "https://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 = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/signum.bib", 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", fjournal = "ACM SIGNUM Newsletter", journal-URL = "https://dl.acm.org/loi/signum", 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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/hpj.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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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-ACADEMIC, address = pub-ACADEMIC:adr, pages = "355--366", year = "1980", bibdate = "Fri Jan 12 11:37:56 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", acknowledgement = ack-jr, language = "German", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", acknowledgement = ack-nhfb, fjournal = "ACM SIGNUM Newsletter", journal-URL = "https://dl.acm.org/loi/signum", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", note = "See \cite{Meinguet:1986:DKW}.", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", } @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; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.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); https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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", bookpages = "vi + 344", pages = "12--26", year = "1983", bibdate = "Fri May 03 12:02:15 2002", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://www.cs.berkeley.edu/~wkahan/MathSand.pdf", acknowledgement = ack-nhfb, 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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 = jul # "\slash " # aug, year = "1984", CODEN = "IEMIDZ", DOI = "https://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; https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/bibnet/authors/g/gay-david-m.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/standard.bib; Science Citation Index database (1980--2000)", acknowledgement = ack-nj # " and " # ack-nhfb, classcodes = "C5230 (Digital arithmetic methods)", classification = "723; 902; 921", corpsource = "Argonne Nat. Lab., IL, USA", fjournal = "IEEE Micro", journal-URL = "http://www.computer.org/csdl/mags/mi/index.html", 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 = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/signum.bib", acknowledgement = ack-nj, fjournal = "ACM SIGNUM Newsletter", journal-URL = "https://dl.acm.org/loi/signum", } @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 = "https://doi.org/10.1109/ARITH.1985.6158956", bibdate = "Fri Jan 12 11:37:56 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", URL = "http://www.eecs.berkeley.edu/~wkahan/Math128/Cubic.pdf", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/nummath.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", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", 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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", series = "Inst. Math. Appl. Conf. Ser. New Ser.", URL = "http://people.freebsd.org/~das/kahan86branch.pdf; 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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Manuscript", acknowledgement = ack-nhfb, remark = "Cited in \cite{Higham:1993:AFP}.", } @TechReport{Kahan:1987:HAE, author = "W. Kahan", title = "Handling Arithmetic Exceptions", type = "Report", institution = inst-BERKELEY-MATH-EECS, address = inst-BERKELEY-MATH-EECS:adr, day = "14", month = may, year = "1987", bibdate = "Mon Aug 26 10:42:10 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://www.arithmazium.org/classroom/lib//Kahan_Handling_Arithmetic_Exceptions.pdf", abstract = "An {\em Exception\/} arises when an operation performed by a computer has to produce a result to which some people might reasonably take exception. Examples are {\em Division by Zero}, {\em Overflow\/ } and Floating-Point {\em Underflow}. Though most (but not all) exceptions must be rare, too rare to be topics cf everyday conversation, they are not so rare that computer programmers and users can ignore them altogether. This paper presents proposals, many of them now implemented on a few computers, to handle arithmetic exceptions in a generally satisfactory way at a tolerable cost. The proposals are designed to be fully compatible with concurrent, overlapped, parallel, pipelined and vectorized computing on new hardware that will be designed to support them without {\em precise interrupts}. {\em Flags\/} and {\em Modes\/} are proposed to help programmers cope with exceptions; {\em Retrospective Diagnostics\/} are proposed to help most of the rest of us, who aspire to use computers without having to program them. The features of IEEE Standards 754 and 854 are supported by but not obligatory for the proposals.", acknowledgement = ack-nhfb, } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", note = "Manuscript, revised 24 April 1987 (shortened to 7 pages).", URL = "http://www.arithmazium.org/classroom/lib/Kahan_Presubstitution_and_Continued_Fractions.pdf", abstract = "This is a case study of attempts to program the computation of a continued fraction and its first derivative in a way that avoids spurious behavior caused by roundoff, over\slash underflow and, most important, division by zero. The program is easier to find for a machine that does not merely abort computation but continues in a reasonable way after division by zero, as do machines that meet IEEE standards 754 and 854 for floating-point arithmetic. And machines that offered a feature that I call ``Presubstitution'' would be particularly easy to program. But programming on other machines is a challenge that I prefer to leave to someone else.", acknowledgement = ack-nhfb, } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/lawn.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, } @Misc{Kahan:1988:AFP, author = "William Kahan", title = "Arithmazium: The Floating Point Expos{\'e}", howpublished = "Web site", month = may # "\slash " # jul, year = "1988", bibdate = "Wed Jun 05 09:50:01 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "This site includes 27 lectures with notes and videos for CS 279 (Computer System Support for Scientific and Engineering Computation). The class handouts amount to more than 2000 pages.", URL = "https://www.arithmazium.org/classroom/wk88_toc.html", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", note = "Manuscript", acknowledgement = ack-nhfb, } @TechReport{Kahan:1988:CSS, author = "W. Kahan and David Goldberg", title = "Computer System Support for Scientific and Engineering Computation", type = "Report", institution = inst-BERKELEY-CS, address = inst-BERKELEY-CS:adr, day = "26", month = jul, year = "1988", bibdate = "Mon Aug 26 10:39:23 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Revised 14 June 1990.", URL = "http://www.arithmazium.org/classroom/lib//Lecture_25_notes_slides.pdf", acknowledgement = ack-nhfb, } @Unpublished{Kahan:1988:TWB, author = "W. Kahan", title = "To Test Whether Binary Floating-Point Multiplication is Correctly Rounded", institution = inst-BERKELEY-CS, address = inst-BERKELEY-CS:adr, month = jul, year = "1988", bibdate = "Thu Dec 15 14:07:12 GMT 1994", bibsource = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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; https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/lawn.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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://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", journal-URL = "http://epubs.siam.org/loi/sijcd4", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/lawn.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; https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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 = "Fri Jan 5 07:58:42 MST 1996", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/signum.bib", acknowledgement = ack-nhfb, fjournal = "ACM SIGNUM Newsletter", journal-URL = "https://dl.acm.org/loi/signum", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.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 = "https://doi.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://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/sigplan1990.bib", 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, fjournal = "ACM SIGPLAN Notices", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706", 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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "See \cite{Kahan:1965:PFR}.", 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)", fjournal = "Systems and computers in Japan", 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", 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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1994&volume=16&issue=1-2; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/applnummath.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, fjournal = "Applied Numerical Mathematics: Transactions of IMACS", journal-URL = "http://www.sciencedirect.com/science/journal/01689274", } @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.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/dr-dobbs-1990.bib; UnCover database", 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, fjournal = "Dr. Dobb's Journal of Software Tools", }

%%% 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 (March/April) and 3 (May/June), %%% 1995, edited by James R. Bunch and dedicated to Beresford Parlett %%% and William Kahan on the occasion of their 60th birthdays. See %%% %%% http://onlinelibrary.wiley.com/doi/10.1002/nla.v2:2/issuetoc %%% http://onlinelibrary.wiley.com/doi/10.1002/nla.v2:3/issuetoc %%% %%% There is a link to a PDF of the editorial in v2n2 at the first %%% of those, but the link is broken.

@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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", 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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/linala1990.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, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/jcryptology.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, fjournal = "Journal of Cryptology", journal-URL = "http://link.springer.com/journal/145", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", URL = "http://www.cs.berkeley.edu/~wkahan/tests/; http://www.cs.berkeley.edu/~wkahan/tests/numbeast.ps", 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, } @TechReport{Kahan:1996:CAN, author = "W. Kahan", title = "A Computation with Almost No Significance", type = "Report", institution = inst-BERKELEY-MATH-EECS, address = inst-BERKELEY-MATH-EECS:adr, pages = "8", day = "6", month = may, year = "1996", bibdate = "Fri Nov 04 08:39:51 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", URL = "http://www.eecs.berkeley.edu/~wkahan/CS279/Div754.pdf", abstract = "An amusing little program computes $ Z = 2.0 $ correctly, despite roundoff, only on computers that round products and quotients in the way specified by IEEE Standard 754 for Binary Floating-Point Arithmetic. On every other commercially significant computer the program computes the same wrong result $ Z = 1.0 $. What makes the program act this way are properties of rounded multiplication and division unobvious enough to justify writing this note to explain them. No other reason for the program's existence is known.", 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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", note = "See note \cite{Zheng:1998:NFS}.", acknowledgement = ack-nhfb, ajournal = "SIAM J. Matrix Anal. Appl.", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @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.ams.org/mcom/1997-66-219; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.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", journal-URL = "http://www.ams.org/mcom/", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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", day = "1", month = jul, year = "1997", CODEN = "JCTPAH", DOI = "https://doi.org/10.1006/jcph.1997.5710", ISSN = "0021-9991 (print), 1090-2716 (electronic)", ISSN-L = "0021-9991", MRclass = "65L05 (65M99)", MRnumber = "MR1458831 (98b:65078)", bibdate = "Mon Jan 2 07:55:18 MST 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0021999197957107", acknowledgement = ack-nhfb, fjournal = "Journal of Computational Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00219991/", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/dr-dobbs-1990.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/java.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, fjournal = "Dr. Dobb's Journal of Software Tools", } @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.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/linala1990.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, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/java.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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/java.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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/matlab.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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/computer1990.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://pdf.computer.org/co/books/co1998/pdf/r3114.pdf", acknowledgement = ack-nhfb, fjournal = "Computer", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2", } @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", DOI = "https://doi.org/10.1137/S0895479896314431", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Fri Dec 4 12:14:09 MST 1998", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/19/1; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", note = "See \cite{Zheng:1996:FSG}.", URL = "http://epubs.siam.org/sam-bin/dbq/article/31443", acknowledgement = ack-nhfb, ajournal = "SIAM J. Matrix Anal. Appl.", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/sigsam.bib", acknowledgement = ack-nhfb, fjournal = "SIGSAM Bulletin", issue = "128", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", } @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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 - e x p( - p z)) / (p z) $ 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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/lawn.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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/supercomputing2000.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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/lawn.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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/fparith.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 = "https://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 = "https://doi.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.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", 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", journal-URL = "http://portal.acm.org/toc.cfm?idx=J782", } @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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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.abs; http://www.cs.berkeley.edu/~wkahan/Math128/RefinEig.pdf", 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 = "https://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/Math128/Separate.pdf; http://www.cs.berkeley.edu/~wkahan/MathH110/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 = "https://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 = "https://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", DOI = "https://doi.org/10.1145/567806.567808", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", 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, fjournal = "ACM Transactions on Mathematical Software", journal-URL = "http://portal.acm.org/toc.cfm?idx=J782", } @Misc{Parlett:2002:QA, author = "Beresford N. Parlett", title = "The {QR} Algorithm", howpublished = "World-Wide Web document", pages = "15", day = "22", month = apr, year = "2002", bibdate = "Mon Apr 25 18:25:57 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/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 = "https://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 = "https://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 = "https://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 = "https://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}_4 z = 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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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. {128B}", howpublished = "World-Wide Web document", pages = "1", day = "8", month = mar, year = "2004", bibdate = "Mon Apr 25 18:25:57 2005", bibsource = "https://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. {128B}", howpublished = "World-Wide Web document", pages = "15", day = "10", month = feb, year = "2004", bibdate = "Mon Apr 25 18:25:57 2005", bibsource = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/lawn.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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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, fjournal = "Computer", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2", } @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 = "https://doi.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/; https://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 / m a x \{ 10, \sqrt {n} \} \varepsilon_w $, the computed normwise (componentwise) error bound is at most $ 2 m a x \{ 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, fjournal = "ACM Transactions on Mathematical Software", journal-URL = "http://portal.acm.org/toc.cfm?idx=J782", } @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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @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 = "https://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 = "https://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 = "https://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 = "https://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://math.berkeley.edu/bascd08; http://www.eecs.berkeley.edu/~wkahan/BASCD08K.pdf", 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, } @Misc{Kahan:2010:PUC, author = "W. Kahan", title = "{Pete}'s unsung contribution to {IEEE Standard 754} for binary floating-point: a talk at a conference to celebrate {G. W. ``Pete'' Stewart}'s 70th Birthday", howpublished = "Lecture slides", pages = "18", day = "19", month = jul, year = "2010", bibdate = "Wed Aug 07 15:43:36 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "https://people.eecs.berkeley.edu/~wkahan/19July10.pdf", acknowledgement = ack-nhfb, } @TechReport{Kahan:2012:WMA, author = "W. Kahan", title = "What might {Alan Turing} say about the Inevitable Fallibility of Software?", type = "Report", institution = inst-BERKELEY-MATH-EECS, address = inst-BERKELEY-MATH-EECS:adr, pages = "1--12", day = "15", month = jun, year = "2012", bibdate = "Mon Aug 26 11:16:49 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib", note = "Prepared for the ACM's Celebration in San Francisco, 15--16 June 2012, of the Centennial of Alan Turing's Birth.", URL = "https://people.eecs.berkeley.edu/~wkahan/15June12.pdf", acknowledgement = ack-nhfb, keywords = "Crash of Air France's Flight \#447 (1 June 2009) over Atlantic northeast of Rio de Janeiro, Brazil.", } @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)", ISSN-L = "0025-5718", bibdate = "Mon Oct 24 10:33:38 MDT 2011", bibsource = "http://www.ams.org/mcom/2012-81-277; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://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, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @TechReport{Kahan:2012:DNR, author = "W. Kahan", title = "Desperately Needed Remedies for the Undebuggability of Large Floating-Point Computations in Science and Engineering", type = "Report", institution = inst-BERKELEY-EECS, address = inst-BERKELEY-EECS:adr, pages = "90", day = "24", month = apr, year = "2012", bibdate = "Mon Aug 26 10:36:06 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "https://people.eecs.berkeley.edu/~wkahan/Boulder.pdf", acknowledgement = ack-nhfb, } @InProceedings{Rubio-Gonzalez:2013:PTA, author = "Cindy Rubio-Gonz{\'a}lez and Cuong Nguyen and Hong Diep Nguyen and James Demmel and William Kahan and Koushik Sen and David H. Bailey and Costin Iancu and David Hough", booktitle = "Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis", title = "Precimonious: Tuning assistant for floating-point precision", publisher = pub-ACM, address = pub-ACM:adr, pages = "27", year = "2013", bibdate = "Sat Jun 4 17:18:19 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, } @TechReport{Kahan:2015:ATP, author = "W. Kahan", title = "Accuracy Tests for Polynomials' Zero-Finders", type = "Report", institution = inst-BERKELEY-MATH-EECS, address = inst-BERKELEY-MATH-EECS:adr, pages = "17", day = "13", month = sep, year = "2015", bibdate = "Fri Nov 04 08:39:51 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", URL = "http://www.eecs.berkeley.edu/~wkahan/Math128/Fibs_2_6.pdf", acknowledgement = ack-nhfb, } @TechReport{Kahan:2015:EBZ, author = "W. Kahan", title = "Error-Bounds for a Zero of a Polynomial", type = "Report", institution = inst-BERKELEY-MATH-EECS, address = inst-BERKELEY-MATH-EECS:adr, pages = "6", day = "30", month = oct, year = "2015", bibdate = "Sat Nov 05 17:17:07 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", URL = "http://www.eecs.berkeley.edu/~wkahan/Math128/PolyZbnd.pdf", acknowledgement = ack-nhfb, } @Misc{Gustafson:2016:TGD, author = "John Gustafson and William Kahan", title = "Transcription of {``The} Great Debate'': {John Gustafson} vs. {William Kahan} on Unum Arithmetic", howpublished = "Web document.", pages = "50", day = "12", month = jul, year = "2016", bibdate = "Thu Jan 18 06:36:55 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://www.johngustafson.net/pdfs/DebateTranscription.pdf", acknowledgement = ack-nhfb, } @TechReport{Kahan:2016:CEE, author = "W. Kahan", title = "Commentary on {{\booktitle{The End of Error --- Unum Computing}}, by John L. Gustafson, (2015) CRC Press}", type = "Report", institution = inst-BERKELEY-MATH-EECS, address = inst-BERKELEY-MATH-EECS:adr, pages = "39", day = "15", month = jul, year = "2016", bibdate = "Tue Nov 01 15:46:44 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", URL = "https://people.eecs.berkeley.edu/~wkahan/EndErErs.pdf", acknowledgement = ack-nhfb, } @TechReport{Kahan:2016:KO, author = "W. Kahan", title = "{Keplerian} Orbits", type = "Report", institution = inst-BERKELEY-MATH-EECS, address = inst-BERKELEY-MATH-EECS:adr, pages = "2", day = "21", month = jun, year = "2016", bibdate = "Thu Nov 03 18:57:12 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", URL = "http://www.eecs.berkeley.edu/~wkahan/Math128/KeplerOrbits.pdf", acknowledgement = ack-nhfb, } @InProceedings{Rubio-Gonzalez:2016:FPP, author = "Cindy Rubio-Gonz{\'a}lez and Cuong Nguyen and Benjamin Mehne and Koushik Sen and James Demmel and William Kahan and Costin Iancu and Wim Lavrijsen and David H. Bailey and David Hough", booktitle = "Proceedings of the 38th International Conference on Software Engineering", title = "Floating-point precision tuning using blame analysis", publisher = pub-ACM, address = pub-ACM:adr, pages = "1074--1085", year = "2016", bibdate = "Sat Jun 04 17:19:46 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, } @Misc{Kahan:2018:TD, author = "William Kahan", title = "The tanpi Dilemma", howpublished = "Web document.", day = "16", month = apr, year = "2018", bibdate = "Tue Apr 17 06:52:47 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib", URL = "http://754r.ucbtest.org/background/tanpi.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib", abstract = "The function tanpi(x) satisfies two familiar identities, tanpi(-x) = -tanpi(x), and tanpi(x + integer) = tanpi(x), that cannot both be satisfied {\em everywhere\/} by IEEE 754's arithmetic; the obvious failures occur when tanpi is infinite: does tanpi(-2.5) = -tanpi(2.5) or does tanpi(-2.5) = tanpi(-2.5 + 4) = +tanpi(2.5) ? Whoever puts a tanpi subprogram into the Math library has no choice but to disappoint somebody.", acknowledgement = ack-nhfb, }

%%% ==================================================================== %%% Part 2 (of 2): publications about William Kahan and his works

@Article{Bunch:1995:EDB, author = "James R. Bunch", title = "Editorial: Dedicated to {Beresford Parlett} and {William Kahan}", journal = j-NUM-LIN-ALG-APPL, volume = "2", number = "2", pages = "85--85", year = "1995", CODEN = "NLAAEM", DOI = "https://doi.org/10.1002/nla.1680020202", ISSN = "1070-5325 (print), 1099-1506 (electronic)", bibdate = "Sat Jan 20 06:15:41 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/numlinaa.bib", acknowledgement = ack-nhfb, fjournal = "Numerical Linear Algebra with Applications", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506", } @Article{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 = "https://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 = "https://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, fjournal = "IEEE Transactions on Computers", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12", keywords = "Coq; discriminant; floating point; formal proof; Why platform", remark = "Extended version of ARITH-18 article \cite{Boldo:2007:FVF}.", } @Book{Golub:2010:MMQ, author = "Gene H. Golub and G{\'e}rard Meurant", title = "Matrices, Moments and Quadrature with Applications", publisher = pub-PRINCETON, address = pub-PRINCETON:adr, pages = "xii + 363", year = "2010", ISBN = "0-691-14341-2", ISBN-13 = "978-0-691-14341-5", MRclass = "65-02 (65D30)", MRnumber = "MR2582949", bibdate = "Mon May 17 14:08:36 MDT 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Princeton Series in Applied Mathematics", ZMnumber = "1217.65056", ZMnumber = "pre05661633", abstract = "This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", shorttableofcontents = "Preface / xi \\ Part 1. Theory / 1 \\ 1: Introduction / 3 \\ 2: Orthogonal Polynomials / 8 \\ 3: Properties of Tridiagonal Matrices / 24 \\ 4: The Lanczos and Conjugate Gradient Algorithms / 39 \\ 5: Computation of the Jacobi Matrices / 55 \\ 6: Gauss Quadrature / 84 \\ 7: Bounds for Bilinear Forms $u^T f(A) v$ / 112 \\ 8: Extensions to Nonsymmetric Matrices / 117 \\ 9: Solving Secular Equations / 122 \\ 10: Examples of Gauss Quadrature Rules / 139 \\ 11: Bounds and Estimates for Elements of Functions of Matrices / 162 \\ 12: Estimates of Norms of Errors in the Conjugate Gradient Algorithm / 200 \\ 13: Least Squares Problems / 227 \\ 14: Total Least Squares / 256 \\ 15: Discrete Ill-Posed Problems / 280 \\ Bibliography / 335 \\ Index / 361", tableofcontents = "Preface / xi \\ Part 1. Theory / 1 \\ 1: Introduction / 3 \\ 2: Orthogonal Polynomials / 8 \\ 2.1 Definition of Orthogonal Polynomials / 8 \\ 2.2 Three-Term Recurrences / 10 \\ 2.3 Properties of Zeros / 14 \\ 2.4 Historical Remarks / 15 \\ 2.5 Examples of Orthogonal Polynomials / 15 \\ 2.6 Variable-Signed Weight Functions / 20 \\ 2.7 Matrix Orthogonal Polynomials / 21 \\ 3: Properties of Tridiagonal Matrices / 24 \\ 3.1 Similarity / 24 \\ 3.2 Cholesky Factorizations of a Tridiagonal Matrix / 25 \\ 3.3 Eigenvalues and Eigenvectors / 27 \\ 3.4 Elements of the Inverse / 29 \\ 3.5 The $Q D$ Algorithm / 32 \\ 4: The Lanczos and Conjugate Gradient Algorithms / 39 \\ 4.1 The Lanczos Algorithm / 39 \\ 4.2 The Nonsymmetric Lanczos Algorithm / 43 \\ 4.3 The Golub--Kahan Bidiagonalization Algorithms / 45 \\ 4.4 The Block Lanczos Algorithm / 47 \\ 4.5 The Conjugate Gradient Algorithm / 49 \\ 5: Computation of the Jacobi Matrices / 55 \\ 5.1 The Stieltjes Procedure / 55 \\ 5.2 Computing the Coefficients from the Moments / 56 \\ 5.3 The Modified Chebyshev Algorithm / 58 \\ 5.4 The Modified Chebyshev Algorithm for Indefinite Weight Functions / 61 \\ 5.5 Relations between the Lanczos and Chebyshev Semi-Iterative Algorithms / 62 \\ 5.6 Inverse Eigenvalue Problems / 66 \\ 5.7 Modifications of Weight Functions / 72 \\ 6: Gauss Quadrature / 84 \\ 6.1 Quadrature Rules / 84 \\ 6.2 The Gauss Quadrature Rules / 86 \\ 6.3 The Anti-Gauss Quadrature Rule / 92 \\ 6.4 The Gauss-Kronrod Quadrature Rule / 95 \\ 6.5 The Nonsymmetric Gauss Quadrature Rules / 99 \\ 6.6 The Block Gauss Quadrature Rules / 102 \\ 7: Bounds for Bilinear Forms $u^T f(A) v$ / 112 \\ 7.1 Introduction / 112 \\ 7.2 The Case $u = v$ / 113 \\ 7.3 The Case $u \neq v$ / 114 \\ 7.4 The Block Case / 115 \\ 7.5 Other Algorithms for $u \neq v$ / 115 \\ 8: Extensions to Nonsymmetric Matrices / 117 \\ 8.1 Rules Based on the Nonsymmetric Lanczos Algorithm / 118 \\ 8.2 Rules Based on the Arnoldi Algorithm / 119 \\ 9: Solving Secular Equations / 122 \\ 9.1 Examples of Secular Equations / 122 \\ 9.2 Secular Equation Solvers / 129 \\ 9.3 Numerical Experiments / 134 \\ Part 2. Applications / 137 \\ 10: Examples of Gauss Quadrature Rules / 139 \\ 10.1 The Golub and Welsch Approach / 139 \\ 10.2 Comparisons with Tables / 140 \\ 10.3 Using the Full $Q R$ Algorithm / 141 \\ 10.4 Another Implementation of $Q R$ / 143 \\ 10.5 Using the $Q L$ Algorithm / 144 \\ 10.6 Gauss--Radau Quadrature Rules / 144 \\ 10.7 Gauss--Lobatto Quadrature Rules / 146 \\ 10.8 Anti-Gauss Quadrature Rule / 148 \\ 10.9 Gauss--Kronrod Quadrature Rule / 148 \\ 10.10 Computation of Integrals / 149 \\ 10.11 Modification Algorithms / 155 \\ 10.12 Inverse Eigenvalue Problems / 156 \\ 11: Bounds and Estimates for Elements of Functions of Matrices / 162 \\ 11.1 Introduction / 162 \\ 11.2 Analytic Bounds for the Elements of the Inverse / 163 \\ 11.3 Analytic Bounds for Elements of Other Functions / 166 \\ 11.4 Computing Bounds for Elements of $f(A)$ / 167 \\ 11.5 Solving $A x = c$ and Looking at $d^T x$ / 167 \\ 11.6 Estimates of $\tr(A^{-1})$ and $\det(A)$ / 168 \\ 11.7 Krylov Subspace Spectral Methods / 172 \\ 11.8 Numerical Experiments / 173 \\ 12: Estimates of Norms of Errors in the Conjugate Gradient Algorithm / 200 \\ 12.1 Estimates of Norms of Errors in Solving Linear Systems / 200 \\ 12.2 Formulas for the $A$-Norm of the Error / 202 \\ 12.3 Estimates of the $A$-Norm of the Error / 203 \\ 12.4 Other Approaches / 209 \\ 12.5 Formulas for the $\ell_2$ Norm of the Error / 210 \\ 12.6 Estimates of the $\ell_2$ Norm of the Error / 211 \\ 12.7 Relation to Finite Element Problems / 212 \\ 12.8 Numerical Experiments / 214 \\ 13: Least Squares Problems / 227 \\ 13.1 Introduction to Least Squares / 227 \\ 13.2 Least Squares Data Fitting / 230 \\ 13.3 Numerical Experiments / 237 \\ 13.4 Numerical Experiments for the Backward Error / 253 \\ 14: Total Least Squares / 256 \\ 14.1 Introduction to Total Least Squares / 256 \\ 14.2 Scaled Total Least Squares / 259 \\ 14.3 Total Least Squares Secular Equation Solvers / 261 \\ 15: Discrete Ill-Posed Problems / 280 \\ 15.1 Introduction to Ill-Posed Problems / 280 \\ 15.2 Iterative Methods for Ill-Posed Problems / 295 \\ 15.3 Test Problems / 298 \\ 15.4 Study of the GCV Function / 300 \\ 15.5 Optimization of Finding the GCV Minimum / 305 \\ 15.6 Study of the $L$-Curve / 313 \\ 15.7 Comparison of Methods for Computing the Regularization Parameter / 325 \\ Bibliography / 335 \\ Index / 361", } @Article{Jeannerod:2013:FAK, author = "Claude-Pierre Jeannerod and Nicolas Louvet and Jean-Michel Muller", title = "Further analysis of {Kahan}'s algorithm for the accurate computation of $ 2 \times 2 $ determinants", journal = j-MATH-COMPUT, volume = "82", number = "284", pages = "2245--2264", month = "", year = "2013", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Mon Jul 15 12:07:58 MDT 2013", bibsource = "http://www.ams.org/mcom/2013-82-284; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib", URL = "http://www.ams.org/journals/mcom/2013-82-284/S0025-5718-2013-02679-8; http://www.ams.org/journals/mcom/2013-82-284/S0025-5718-2013-02679-8/S0025-5718-2013-02679-8.pdf", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Article{Gazzola:2016:LGK, author = "Silvia Gazzola and Enyinda Onunwor and Lothar Reichel and Giuseppe Rodriguez", title = "On the {Lanczos} and {Golub--Kahan} reduction methods applied to discrete ill-posed problems", journal = j-NUM-LIN-ALG-APPL, volume = "23", number = "1", pages = "187--204", month = jan, year = "2016", CODEN = "NLAAEM", DOI = "https://doi.org/10.1002/nla.2020", ISSN = "1070-5325 (print), 1099-1506 (electronic)", ISSN-L = "1070-5325", bibdate = "Tue Feb 9 06:31:34 MST 2016", bibsource = "http://www.interscience.wiley.com/jpages/1070-5325; http://www3.interscience.wiley.com/journalfinder.html; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/tex/bib/numlinaa.bib", acknowledgement = ack-nhfb, fjournal = "Numerical Linear Algebra with Applications", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506", onlinedate = "12 Oct 2015", } @Article{Goldenberg:2019:GKD, author = "Steven Goldenberg and Andreas Stathopoulos and Eloy Romero", title = "A {Golub--Kahan Davidson} Method for Accurately Computing a Few Singular Triplets of Large Sparse Matrices", journal = j-SIAM-J-SCI-COMP, volume = "41", number = "4", pages = "A2172--A2192", month = "????", year = "2019", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/18M1222004", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", bibdate = "Thu Oct 10 06:58:08 MDT 2019", bibsource = "http://epubs.siam.org/toc/sjoce3/41/4; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", onlinedate = "January 2019", } @Misc{Moler:2019:CCF, author = "Cleve Moler", title = "{Cleve}'s Corner: Floating Point Arithmetic Before {IEEE 754}", howpublished = "MathWorks Web site.", day = "18", month = jan, year = "2019", bibdate = "Sat Jan 19 15:18:17 2019", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "https://blogs.mathworks.com/cleve/2019/01/18/floating-point-arithmetic-before-ieee-754/", abstract = "In a comment following my post about half-precision arithmetic, ``Raj C'' asked how the parameters for IEEE Standard 754 floating point arithmetic were chosen. I replied that I didn't know but would try to find out. I called emeritus U. C. Berkeley Professor W. (Velvel) Kahan, who was the principle architect of 754. Here is what I learned.", acknowledgement = ack-nhfb, } @Article{Asgari:2020:EBG, author = "Z. Asgari and F. Toutounian and E. Babolian and E. Tohidi", title = "An extended block {Golub--Kahan} algorithm for large algebraic and differential matrix {Riccati} equations", journal = j-COMPUT-MATH-APPL, volume = "79", number = "8", pages = "2447--2457", day = "15", month = apr, year = "2020", CODEN = "CMAPDK", DOI = "https://doi.org/10.1016/j.camwa.2019.11.010", ISSN = "0898-1221 (print), 1873-7668 (electronic)", ISSN-L = "0898-1221", bibdate = "Wed Jul 8 08:11:13 MDT 2020", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/computmathappl2020.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0898122119305437", acknowledgement = ack-nhfb, fjournal = "Computers and Mathematics with Applications", journal-URL = "http://www.sciencedirect.com/science/journal/08981221", } @Article{Wang:2020:KPJ, author = "Yunjie Wang and Gang Wu", title = "On the {Kahan--Parlett--Jiang} theorem --- a globally optimal backward perturbation error for two-sided invariant subspaces", journal = j-LINEAR-ALGEBRA-APPL, volume = "602", number = "??", pages = "73--92", day = "1", month = oct, year = "2020", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2020.05.003", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Fri Mar 12 08:38:22 MST 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/linala2020.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0024379520302342", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Bai:2021:GKV, author = "Xianglan Bai and Alessandro Buccini and Lothar Reichel", title = "{Golub--Kahan} vs. {Monte Carlo}: a comparison of bidiagonalization and a randomized {SVD} method for the solution of linear discrete ill-posed problems", journal = j-BIT-NUM-MATH, volume = "61", number = "4", pages = "1093--1114", month = dec, year = "2021", CODEN = "BITTEL, NBITAB", DOI = "https://doi.org/10.1007/s10543-021-00857-0", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", bibdate = "Thu Feb 24 10:35:56 MST 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/bit.bib", URL = "https://link.springer.com/article/10.1007/s10543-021-00857-0", acknowledgement = ack-nhfb, fjournal = "BIT Numerical Mathematics", journal-URL = "http://link.springer.com/journal/10543", } @Article{Bentbib:2023:GGK, author = "A. H. Bentbib and M. {El Ghomari} and K. Jbilou and L. Reichel", title = "The global {Golub--Kahan} method and {Gauss} quadrature for tensor function approximation", journal = j-NUMER-ALGORITHMS, volume = "92", number = "1", pages = "5--34", month = jan, year = "2023", CODEN = "NUALEG", DOI = "https://doi.org/10.1007/s11075-022-01392-x", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", bibdate = "Mon Jan 30 12:22:09 MST 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib", URL = "https://link.springer.com/article/10.1007/s11075-022-01392-x", acknowledgement = ack-nhfb, ajournal = "Numer. Algorithms", fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", } @Article{Bogfjellmo:2024:UAS, author = "Geir Bogfjellmo and Elena Celledoni and Robert I. McLachlan and Brynjulf Owren and G. R. W. Quispel", title = "Using aromas to search for preserved measures and integrals in {Kahan}'s method", journal = j-MATH-COMPUT, volume = "93", number = "348", pages = "1633--1653", month = oct, year = "2024", CODEN = "MCMPAF", DOI = "https://doi.org/10.1090/mcom/3921", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Mon May 27 15:56:46 MDT 2024", bibsource = "https://www.ams.org/mcom/2024-93-348; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp2020.bib", URL = "https://www.ams.org/journals/mcom/2024-93-348/S0025-5718-2023-03921-7", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "https://www.ams.org/mcom/", pubdate = "8 November 2023", }

%%% ==================================================================== %%% 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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", note = "Two volumes.", acknowledgement = ack-nhfb, } @Proceedings{Nickel:1975:IMP, editor = "Karl Nickel", booktitle = "{Interval mathematics: proceedings of the international symposium, Karlsruhe, West Germany, May 20--24, 1975}", title = "{Interval mathematics: proceedings of the international symposium, Karlsruhe, West Germany, May 20--24, 1975}", volume = "29", publisher = pub-SV, address = pub-SV:adr, pages = "vi + 331", year = "1975", CODEN = "LNCSD9", DOI = "????", ISBN = "0-387-07170-9", ISBN-13 = "978-0-387-07170-1", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", LCCN = "QA297 .I541", bibdate = "Fri Apr 12 07:12:39 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/m/moore-ramon-e.bib; https://www.math.utah.edu/pub/tex/bib/lncs.bib", note = "German or English.", price = "DM30.00", series = ser-LNCS, URL = "http://link.springer-ny.com/link/service/series/0558/tocs/t0029.htm; http://www.springerlink.com/content/978-0-387-07170-1; http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=29; https://link.springer.com/book/10.1007/3-540-07170-9", acknowledgement = ack-nhfb, keywords = "interval analysis (mathematics) --- congresses", tableofcontents = "Front Matter \\ Intervall-Mathematik Zum Karlsruher Symposium 1975 / Karl Nickel / 1--6 \\ A generalized interval arithmetic / E. R. Hansen / 7--18 \\ Einige Anwendungen der Kreisscheibenarithmetik in der Kettenbruchtheorie / Peter Henrici / 19--30 \\ Two--sided approximation to solutions of nonlinear operator equations--a comparison of methods from classical analysis, functional analysis, and interval analysis / R. E. Moore / 31--47 \\ Nichtnumerische Aspekte der Intervallmathematik / H. Ratschek / 48--74 \\ Tools for the analysis of interval arithmetic / Frederic N. Ris / 75--98 \\ A posteriori component--wise error estimation of approximate solutions to nonlinear equations / Minoru Urabe / 99--117 \\ Konvergente numerische Schrankenkonstruktion mit Spline--Funktionen f{\"u}r nichtlineare gew{\"o}hnliche bzw. lineare parabolische Randwertaufgaben / E. Adams, H. Spreuer / 118--126 \\ A distribution--free interval mathematical analysis of probability density functions / Rashid Ahmad / 127--134 \\ Monotonically convergent numerical two-sided bounds for a differential birth and death process / W. F. Ames, E. Adams / 135--140 \\ Verwendung von Tschebyschew-Approximation und {\"O}konomisierungsverfahren bei der Vergr{\"o}berung von Intervallpolynomen / Wolfgang Appelt / 141--149 \\ Zur Problematik der H{\"u}llenbestimmung von Intervallgleichungssystemen / H. Beeck / 150--159 \\ Einsatz der Intervallarithmetik bei der Numerischen Konvergenz von ALGOL--60 Programmen / F. Bierbaum / 160--168 \\ Einschliessung des Minimalpunktes einer streng konvexen Funktion auf einem n--dimensionalen Quader / Rainer Dussel / 169--177 \\ Beliebig genaue numerische Schranken f{\"u}r die L{\"o}sung parabolischer Randwertaufgaben / E. Faa{\ss} / 178--183 \\ Ein Versuch zur Verallgemeinerung der Intervallrechnung / Herbert Fischer / 184--190 \\ The condition problem in solution of linear multistage systems / E. A. Galperin / 191--195 \\ Parallel square root iterations / Irene Gargantini / 196--204 \\ Newton--Algorithmen zur Bestimmung von Polynomwurzeln unter Verwendung komplexer Kreisarithmetik / G. Glatz / 205--214 \\ Fehlerabsch{\"a}tzung bei linearer Optimierung / Rudolf Krawczyk / 215--222 / Einschliessungsmengen von Polynom--Nullstellen / Norbert Krier, Peter Spellucci / 223--228 \\ On approximate iterations and solutions for equations considered in function spaces / M. Kwapisz / 229--235 / Definition einer Kahan--Arithmetik und ihre Implementierung / S. E. Laveuve / 236--245 \\ The error in interval arithmetic / Webb Miller / 246--250 \\ Verbandstheoretische Grundlagen der Intervall--Mathematik / Karl Nickel / 251--262 \\ Intervallrechnung und Wirklichkeit / E. Nuding / 263--269 \\ Interval--extension of quasilinearization method / F. Aleixo Oliveira / 270--278 \\ Zur numerischen Konstruktion konvergenter Schrankenfolgen f{\"u}r Systeme nichtlinearer, gew{\"o}hnlicher Anfangswertaufgaben / G. Scheu, E. Adams / 279--287 \\ Fehlerabsch{\"a}tzung bei linearer Optimierung / Rudolf Krawczyk / 215--222 \\ Einschliessungsmengen von Polynom-Nullstellen / Norbert Krier, Peter Spellucci / 223--228 \\ On approximate iterations and solutions for equations considered in function spaces / M. Kwapisz / 229--235 \\ Definition einer Kahan-Arithmetik und ihre Implementierung / S. E. Laveuve / 236--245 \\ The error in interval arithmetic / Webb Miller / 246--250 \\ Verbandstheoretische Grundlagen der Intervall-Mathematik / Karl Nickel / 251--262 \\ Intervallrechnung und Wirklichkeit / E. Nuding / 263--269 \\ Interval--extension of quasilinearization method / F. Aleixo Oliveira / 270--278 \\ Zur numerischen Konstruktion konvergenter Schrankenfolgen f{\"u}r Systeme nichtlinearer, gew{\"o}hnlicher Anfangswertaufgaben / G. Scheu, E. Adams / 279--287 \\ Untersuchungen der Grenzgenauigkeit von Algorithmen zur Aufl{\"o}sung linearer Gleichungssysteme mit Fehlererfassung / Peter Spellucci, Norbert Krier / 288--297 \\ Konvergente numerische Schranken f{\"u}r partielle Randwertaufgaben von monotoner Art / H. Spreuer / 298--305 \\ Verbesserung von Fehlerschranken bei iterativer Matrizeninversion / Peter Thieler / 306--310 \\ Iterationsverfahren bei inklusionsmonotonen Intervallfunktionen / Peter Wisskirchen / 311--315 \\ Experimentelle Untersuchungen zur numerischen Aufl{\"o}sung von linearen Gleichungssystemen mit Fehlererfassung / Prungchan Wongwises / 316--325 \\ Back Matter", } @Proceedings{Bunch:1976:SMC, editor = "James R. Bunch and Donald J. Rose", booktitle = "{Sparse Matrix Computations: Proceedings of the Symposium on Sparse Matrix Computations at Argonne National Laboratory on September 9--11, 1975}", title = "{Sparse Matrix Computations: Proceedings of the Symposium on Sparse Matrix Computations at Argonne National Laboratory on September 9--11, 1975}", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "xi + 453", year = "1976", ISBN = "0-12-141050-1", ISBN-13 = "978-0-12-141050-6", LCCN = "QA188 .S989 1975", bibdate = "Sat Oct 22 18:13:05 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, tableofcontents = "Contributors / / ix \\ Preface / / xi \\ I. Design and Analysis of Elimination Algorithms / / 1 \\ 1. Graph Theory and Gaussian Elimination / Robert Endre Tarjan / 3 \\ 2. Partitioning Using PAQ / Thomas D. Howell / 23 \\ 3. Block Methods for Solving Sparse Linear Systems / James R. Bunch / 39 \\ 4. A Recursive Analysis of Dissection Strategies / Donald J. Rose and Gregory F. Whitten / 59 \\ 5. Applications of an Element Model for Gaussian Elimination / S. C. Eisenstat, M. H. Schultz, and 4. H. Sherman / 85 \\ 6. An Optimization Problem Arising from Tearing Methods / Alberto Sangiovanni-Vincentelli / 97 \\ II. Eigenvalue Problems / / 111 \\ 1. A Bibliographical Tour of the Large, Sparse Generalized Eigenvalue Problem / G. W. Stewart / 113 \\ 2. How Far Should You Go With the Lanczos Process? / W. Kahan and B. N. Parlett / 131 \\ III. Optimization, Least Squares and Linear Programming / / 145 \\ 1. Optimization for Sparse Systems / T. L. Magnanti / 147 \\ 2. Methods for Sparse Linear Least Squares Problems / {AA}ke Bj{\"o}rck / 177 \\ 3. The Orthogonal Factorization of a Large Sparse Matrix / Philip E. Gill and Walter Murray / 201 \\ 4. A Fast, Stable Implementation of the Simplex Method Using Bartels-Golub Updating / Michael A. Saunders / 213 \\ 5. Using the Steepest-edge Simplex Algorithm to Solve Sparse Linear Programs / D. Goldfarb / 227 \\ IV. Mathematical Software / / 241 \\ 1. Sparse Matrix Software / W. Morven Gentleman and Alan George / 243 \\ 2. Considerations in the Design of Software for Sparse Gaussian Elimination / S. C. Eisenstat, M. H. Schultz, and A. H. Sherman / 263 \\ 3. Finding the Block Lower Triangular Form of a Sparse Matrix / Fred Gustavson / 275 \\ V. Matrix Methods for Partial Difference Equations / / 291 \\ 1. Marching Algorithms and Block Gaussian Elimination / Randolph E. Bank / 293 \\ 2. A Generalized Conjugate Gradient Method for the Numerical Solution of Elliptic Partial Differential Equations / Paul Concus, Gene H. Golub, and Dianne P. O'Leary / 309 \\ 3. Preconditioned Conjugate Gradient Iteration Applied to Galerkin Methods for a Mildly-Nonlinear Dirichlet Problem / Jim Douglas, Jr. and Todd Dupont / 333 \\ 4. The Sparse Tableau Approach to Finite Element Assembly / Gary Hachtel / 349 \\ 5. A Capacitance Matrix Technique / B. L. Buzbee / 365 \\ 6. M-Matrix Theory and Recent Results in Numerical Linear Algebra / Richard S. Varga / 375 \\ VI. Applications / / 389 \\ 1. Sparse Matrix Problems in a Finite Element Open Ocean Model / Joel E. Hirsh and William L. Briggs / 391 \\ 2. Calculation of Normal Modes of Oceans Using a Lanczos Method / Alan K. Cline, Gene H. Golub, and George W. Platzman / 409 \\ 3. Application of Sparse Matrix Techniques to Reservoir Simulation / P. T. Woo, S. C. Eisenstat, M. H. Schultz, and A. H. Sherman / 427 \\ 4. On the Origins and Numerical Solution of Some Sparse Nonlinear Systems / T. A. Porsching / 439", } @Proceedings{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 = "https://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-ACADEMIC, address = pub-ACADEMIC: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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; z3950.loc.gov:7090/Voyager", 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 = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://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 = "https://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 = "https://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 = "https://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 = "{State of the Art in Numerical Analysis. Proceedings of the Joint IMA\slash SIAM Conference held at the University of Birmingham, 14--18 April 1986}", title = "{State of the Art in Numerical Analysis. Proceedings of the Joint IMA\slash SIAM Conference held at the University of Birmingham, 14--18 April 1986}", volume = "9", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "x + 719", year = "1987", ISBN = "0-19-853614-3", ISBN-13 = "978-0-19-853614-7", LCCN = "QA297.J65 1986", bibdate = "Mon Sep 9 14:56:14 MDT 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib", series = "The Institute of Mathematics and Its Applications conference series; new series", URL = "http://www.gbv.de/dms/hbz/toc/ht002967923.pdf; http://zbmath.org/?q=an:0611.00024", ZMnumber = "0611.00024", acknowledgement = ack-nhfb, confdate = "14--18 April 1986", conflocation = "Birmingham, UK", confsponsor = "Inst. Math. Appl.; SIAM", pubcountry = "UK", tableofcontents = "Contributors / / xiii \\ 1. Eigenvalue problems / J. H. Wilkinson / 1 \\ 2. Numerical linear algebra in statistical computing / N. J. Higham and G. W. Stewart / 41 \\ 3. Sparse matrices / J. K. Reid / 59 \\ 4. Multivariate approximation / Carl de Boor / 87 \\ 5. Data approximation by splines in one and two independent variables / M. G. Cox / 111 \\ 6. Methods for best approximation and regression problems / G. A. Watson / 139 \\ 7. Branch cuts for complex elementary functions / W. Kahan / 165 \\ 8. Recent developments in linear and quadratic programming / R. Fletcher / 213 \\ 9. Solving systems of nonlinear equations by tensor methods / R. B. Schnabel and P. D. Frank / 245 \\ 10. Numerical methods for bifurcation problems / A. D. Jepson and A. Spence / 273 \\ 11. On the iterative solution of differential and integral equations using secant updating techniques / A. Griewank / 299 \\ 12. Methods for nonlinear constraints in optimization calculations / M. J. D. Powell / 325 \\ 13. The influence of vector and parallel processors on numerical analysis / I. S. Duff / 359 \\ 14. Developments in stability theory for ordinary differential equations / J. D. Lambert / 409 \\ 15. Stiff ODE initial value problems and their solution / A. R. Curtis / 433 \\ 16. Order stars and stability / G. Wanner / 451 \\ 17. The state of the art in the numerical treatment of integral equations / C. T. H. Baker / 473 \\ 18. Strongly elliptic boundary integral equations / W. L. Wendland / 511 \\ 19. Collocation methods for one-dimensional Fredholm and Volterra integral equations / H. Brunner / 563 \\ 20. Numerical methods for free and moving boundary problems / C. W. Cryer / 601 \\ 21. Multigrid methods for elliptic equations / J. Walsh / 623 \\ 22. Galerkin finite element methods and their generalizations / K. W. Morton / 645 \\ 23. Recent developments in the numerical solution of nonlinear conservation laws / S. Osher and P. K. Sweby / 681 \\ Index / 701", } @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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://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 = "https://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 (print), 1096-9128 (electronic)", LCCN = "????", bibdate = "Thu Apr 27 10:40:59 2000", bibsource = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", URL = "http://csdl.computer.org/comp/proceedings/sc/2000/9802/00/9802toc.htm; http://www.sc2000.org/proceedings/info/fp.pdf", 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 = "https://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 = "https://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, }