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====================================================================
%%% BibTeX-file{
%%% author = "Nicholas J. Higham",
%%% date = "April 22, 2021",
%%% filename = "njhigham.bib",
%%% address = "School of Mathematics
%%% University of Manchester
%%% Manchester M13 9PL
%%% UK",
%%% telephone = "+44 (0)161 275 5800",
%%% FAX = "+44 (0)161 275 5819",
%%% checksum = ""
%%% email = "nick.higham at manchester.ac.uk (Internet)",
%%% codetable = "ISO/ASCII",
%%% keywords = "bibliography, numerical analysis, N. J. Higham",
%%% supported = "yes",
%%% docstring = "BibTeX bibliography for papers, books,
%%% EPrints, articles, etc. of Nicholas J. Higham."
%%% }
%%% ====================================================================
%%% The latest version of this file is available at
%%%
%%% https://github.com/higham/njhigham-bib
%%% (or http://www.maths.manchester.ac.uk/~higham/papers).
%%%
%%% String definitions needed by this file are in strings.bib at the
%%% above URLs.
@article{aabc21,
author = "Ahmad Abdelfattah and Hartwig Anzt and Erik G. Boman and Erin
Carson and Terry Cojean and Jack Dongarra and Alyson Fox
and Mark Gates and Nicholas J. Higham and Xiaoye S. Li and
Jennifer Loe and Piotr Luszczek and Srikara Pranesh and
Siva Rajamanickam and Tobias Ribizel and Barry F. Smith
and Kasia Swirydowicz and Stephen Thomas and Stanimire
Tomov and Yaohung M. Tsai and Ulrike Meier Yang",
title = "A Survey of Numerical Linear Algebra Methods Utilizing
Mixed-Precision Arithmetic",
journal = j-IJHPCA,
pages = 109434202110033,
month = mar,
year = 2021,
doi = "10.1177/10943420211003313",
created = "2020.07.15",
updated = "2021.03.22"
}
@article{acdg20,
author = "Ahmad Abdelfattah and Timothy Costa and Jack Dongarra and
Mark Gates and Azzam Haidar and Sven Hammarling and
Nicholas J. Higham and Jakub Kurzak and Piotr Luszczek and
Stanimire Tomov and Mawussi Zounon",
title = "A Set of {Batched Basic Linear Algebra Subprograms} and {LAPACK}
Routines",
journal = j-TOMS,
year = 2020,
note = "To appear",
created = "2020.10.27",
updated = "2020.10.27"
}
@article{alhi09,
author = "Awad H. Al-Mohy and Nicholas J. Higham",
title = "Computing the {Fr\'echet} Derivative of the Matrix Exponential,
with an Application to Condition Number Estimation",
journal = j-SIMAX,
volume = 30,
number = 4,
pages = "1639-1657",
year = 2009,
doi = "10.1137/080716426",
bibdate = "Thu Jan 29 10:22:19 GMT 2009",
created = "2009.01.29",
updated = "2014.05.22"
}
@article{alhi09a,
author = "Awad H. Al-Mohy and Nicholas J. Higham",
title = "A New Scaling and Squaring Algorithm for the Matrix Exponential",
journal = j-SIMAX,
volume = 31,
number = 3,
pages = "970-989",
year = "2009",
doi = "10.1137/09074721X",
bibdate = "Thu Aug 13 12:23:42 GMT 2009",
created = "2009.08.13",
updated = "2009.08.13"
}
@article{alhi10,
author = "Awad H. Al-Mohy and Nicholas J. Higham",
title = "The Complex Step Approximation to the
{Fr\'echet} Derivative of a Matrix Function",
journal = j-NUM-ALG,
volume = 53,
number = 1,
pages = "133-148",
year = 2010,
doi = "10.1007/s11075-009-9323-y",
bibdate = "Tue Nov 17 09:10:04 GMT 2009",
created = "2009.11.17",
updated = "2014.05.22"
}
@article{alhi11,
author = "Awad H. Al-Mohy and Nicholas J. Higham",
title = "Computing the Action of the Matrix Exponential,
with an Application to Exponential Integrators",
journal = j-SISC,
volume = 33,
number = 2,
pages = "488-511",
year = 2011,
doi = "10.1137/100788860",
created = "2009.11.17",
updated = "2011.03.07"
}
@article{alhi12g,
author = "Awad H. Al-Mohy and Nicholas J. Higham",
title = "Improved Inverse Scaling and Squaring Algorithms for
the Matrix Logarithm",
journal = j-SISC,
volume = 34,
number = 4,
pages = "C153-C169",
year = 2012,
doi = "10.1137/110852553",
created = "2011.10.19",
updated = "2012.09.04"
}
@article{ahr13,
author = "Awad H. Al-Mohy and Nicholas J. Higham and Samuel D. Relton",
title = "Computing the {Fr{\'e}chet} Derivative of the Matrix Logarithm
and Estimating the Condition Number",
journal = j-SISC,
volume = 35,
number = 4,
pages = "C394-C410",
year = 2013,
doi = "10.1137/120885991",
created = "2012.07.05",
updated = "2013.08.06"
}
@article{ahr15,
author = "Awad H. Al-Mohy and Nicholas J. Higham and Samuel D. Relton",
title = "New Algorithms for Computing the Matrix Sine and Cosine
Separately or Simultaneously",
journal = j-SISC,
volume = 37,
number = 1,
pages = "A456-A487",
year = 2015,
doi = "10.1137/140973979",
created = "2014.06.20",
updated = "2015.02.13"
}
@techreport{abhl21,
author = "Patrick Amestoy and Alfredo Buttari and Nicholas J. Higham and
Jean-Yves L'Excellent and Theo Mary and Bastien Vieubl{\'e}",
title = "Five-Precision {GMRES}-based Iterative Refinement",
institution = inst-MIMS,
year = 2021,
type = t-MIMS-EPrint,
number = "2021.5",
address = inst-MIMS:adr,
month = apr,
pages = 21,
url = "http://eprints.maths.manchester.ac.uk/id/eprint/2807",
created = "2021.04.04",
updated = "2021.04.04"
}
@article{adfh19,
author = "Hartwig Anzt and Jack Dongarra and
Goran Flegar and Nicholas J. Higham and
Enrique S. Quintana-Ort{\'\i}",
title = "Adaptive Precision in Block-{Jacobi} Preconditioning for
Iterative Sparse Linear System Solvers",
journal = j-CONCCPE,
volume = 31,
number = 6,
pages = "e4460",
year = 2019,
doi = "10.1002/cpe.4460",
created = "2018.03.12",
updated = "2019.02.19"
}
@article{ahh16,
author = "Mary Aprahamian and Desmond J. Higham and Nicholas J. Higham",
title = "Matching Exponential-Based and Resolvent-Based Centrality
Measures",
journal = "Journal of Complex Networks",
volume = 4,
number = 2,
pages = "157-176",
year = 2016,
doi = "10.1093/comnet/cnv016",
created = "2015.01.07",
updated = "2016.10.07"
}
@article{aphi14,
author = "Mary Aprahamian and Nicholas J. Higham",
title = "The Matrix Unwinding Function, with an Application to Computing the
Matrix Exponential",
journal = j-SIMAX,
volume = 35,
number = 1,
pages = "88-109",
year = 2014,
doi = "10.1137/130920137",
created = "2013.05.04",
updated = "2014.01.31"
}
@article{aphi16,
author = "Mary Aprahamian and Nicholas J. Higham",
title = "Matrix Inverse Trigonometric and Inverse Hyperbolic Functions:
{Theory} and Algorithms",
journal = j-SIMAX,
volume = 37,
number = 4,
pages = "1453-1477",
year = 2016,
doi = "10.1137/16M1057577",
created = "2015.08.12",
updated = "2016.10.19"
}
@techreport{aphi15b,
author = "Mary Aprahamian and Nicholas J. Higham",
title = "Argument Reduction for Computing Periodic Functions",
institution = inst-MIMS,
address = inst-MIMS:adr,
type = t-MIMS-EPrint,
_number = "2015.xx",
year = 2015,
_url = "http://eprints.ma.man.ac.uk/xxxx",
note = "In preparation",
created = "2015.08.12",
updated = "2015.09.09"
}
@article{amrh16,
author = "Wayne Arter and J. Guy Morgan and Samuel D. Relton
and Nicholas J. Higham",
title = "Ranking the Importance of Nuclear Reactions for Activation and
Transmutation Events",
journal = "Nuclear Science and Engineering",
volume = 184,
number = 4,
pages = "561-574",
month = dec,
year = 2016,
doi = "10.13182/NSE15-23",
created = "2015.02.27",
updated = "2017.01.08"
}
@misc{nlevp,
author = "Timo Betcke and Nicholas J. Higham and Volker Mehrmann
and Christian Schr{\"o}der and Fran\c{c}oise Tisseur",
title = "{NLEVP}: {A} Collection of Nonlinear Eigenvalue Problems",
note = "\url{https://github.com/ftisseur/nlevp}",
_note = "\url{http://www.maths.manchester.ac.uk/our-research/research-groups/numerical-analysis-and-scientific-computing/numerical-analysis/software/nlevp/}",
bibdate = "Fri Mar 28 14:19:55 GMT 2008",
created = "2008.03.28",
updated = "2020.10.03"
}
@techreport{bhms11,
author = "Timo Betcke and Nicholas J. Higham and Volker Mehrmann
and Christian Schr{\"o}der and Fran\c{c}oise Tisseur",
title = "{NLEVP}: {A} Collection of Nonlinear Eigenvalue Problems",
institution = inst-MIMS,
address = inst-MIMS:adr,
type = t-MIMS-EPrint,
number = "2011.116",
pages = "27",
month = dec,
year = "2011",
created = "2011.11.22",
updated = "2011.12.22"
}
@techreport{bhms11-UG,
author = "Timo Betcke and Nicholas J. Higham and Volker Mehrmann
and Christian Schr{\"o}der and Fran\c{c}oise Tisseur",
title = "{NLEVP}: {A} Collection of Nonlinear Eigenvalue Problems.
{Users'} Guide",
institution = inst-MIMS,
address = inst-MIMS:adr,
type = t-MIMS-EPrint,
number = "2011.117",
pages = "8",
month = dec,
year = "2011",
created = "2011.11.22",
updated = "2011.12.22"
}
@article{bhms13,
author = "Timo Betcke and Nicholas J. Higham and Volker Mehrmann
and Christian Schr{\"o}der and Fran\c{c}oise Tisseur",
title = "{NLEVP}: {A} Collection of Nonlinear Eigenvalue Problems",
journal = j-TOMS,
volume = 39,
number = 2,
pages = "7:1-7:28",
month = feb,
year = "2013",
doi = "10.1145/2427023.2427024",
created = "2013.02.21",
updated = "2013.02.21"
}
@techreport{bbdh11,
author = "Iain Bethune and J. Mark Bull and Nicholas J. Dingle and
Nicholas J. Higham",
title = "Investigating the Performance of Asynchronous
{Jacobi}'s Method for Solving Systems of Linear Equations",
institution = inst-MIMS,
address = inst-MIMS:adr,
type = t-MIMS-EPrint,
number = "2011.82",
pages = "8",
month = oct,
year = "2011",
url = "http://eprints.ma.man.ac.uk/1988/",
created = "2011.10.19",
updated = "2015.11.14"
}
@article{bbdh14,
author = "Iain Bethune and J. Mark Bull and Nicholas J. Dingle and
Nicholas J. Higham",
title = "Performance Analysis of Asynchronous {Jacobi's} Method Implemented
in {MPI}, {SHMEM} and {OpenMP}",
journal = j-IJHPCA,
volume = 28,
number = 1,
pages = "97-111",
year = 2014,
doi = "10.1177/1094342013493123",
created = "2013.07.15",
updated = "2014.01.27"
}
@article{bhm05,
author = "Dario A. Bini and Nicholas J. Higham and Beatrice Meini",
title = "Algorithms for the Matrix {$p$}th Root",
journal = j-NUM-ALG,
volume = 39,
number = 4,
pages = "349-378",
year = 2005,
doi = "10.1007/s11075-004-6709-8",
bibdate = "Tue Apr 19 16:16:51 GMT 2005",
created = "2005.04.19",
updated = "2014.05.22"
}
@article{bhh20,
author = "Pierre Blanchard and Desmond J. Higham and Nicholas J. Higham",
title = "Accurately Computing the Log-Sum-Exp and Softmax Functions",
journal = j-IMAJNA,
volume = "",
number = "",
pages = "1-20",
year = 2020,
doi = "10.1093/imanum/draa038",
note = "Advance access",
created = "2019.09.06",
updated = "2020.05.26"
}
@article{bhm20,
author = "Pierre Blanchard and Nicholas J. Higham and Theo Mary",
title = "A Class of Fast and Accurate Summation Algorithms",
journal = j-SISC,
volume = 42,
number = 3,
pages = "A1541-A1557",
month = jan,
year = 2020,
doi = "10.1137/19M1257780",
created = "2019.04.23",
updated = "2020.03.01"
}
@article{bhlm20,
author = "Pierre Blanchard and Nicholas J. Higham and Florent Lopez
and Theo Mary and Srikara Pranesh",
title = "Mixed Precision Block Fused Multiply-Add: {Error} Analysis and
Application to {GPU} Tensor Cores",
journal = j-SISC,
volume = 42,
number = 3,
pages = "C124-C141",
year = 2020,
doi = "10.1137/19M1289546",
created = "2019.09.24",
updated = "2020.05.27"
}
@article{bhp03,
author = "Adam Bojanczyk and Nicholas J. Higham and Harikrishna Patel",
title = "Solving the Indefinite Least Squares Problem by Hyperbolic {QR}
Factorization",
journal = j-SIMAX,
volume = 24,
number = 4,
pages = "914-931",
year = 2003,
doi = "10.1137/S0895479802401497",
bibdate = "Tue Feb 25 11:33:29 GMT 2003",
created = "2003.02.25",
updated = "2014.05.22"
}
@article{bhp03a,
author = "Adam Bojanczyk and Nicholas J. Higham and Harikrishna Patel",
title = "The Equality Constrained Indefinite Least Squares Problem:
{Theory} and Algorithms",
journal = j-BIT,
volume = 43,
number = 3,
pages = "505-517",
year = 2003,
doi = "10.1023/B:BITN.0000007020.58972.07",
bibdate = "Mon Dec 15 11:37:51 GMT 2003",
created = "2003.12.15",
updated = "2010.09.16"
}
@article{bohi10,
author = "R{\"u}diger Borsdorf and Nicholas J. Higham",
title = "A Preconditioned {Newton} Algorithm for the Nearest Correlation
Matrix",
journal = j-IMAJNA,
volume = 30,
number = 1,
pages = "94-107",
year = 2010,
doi = "10.1093/imanum/drn085",
bibdate = "Thu Jan 28 09:28:15 GMT 2010",
created = "2010.01.28",
updated = "2010.01.28"
}
@article{bhr10,
author = "R{\"u}diger Borsdorf and Nicholas J. Higham and Marcos Raydan",
title = "Computing a Nearest Correlation Matrix with Factor Structure",
journal = j-SIMAX,
volume = 31,
number = 5,
pages = "2603-2622",
year = 2010,
doi = "10.1137/090776718",
bibdate = "Thu Sep 16 09:35:37 GMT 2010",
created = "2010.09.16",
updated = "2014.05.22"
}
@article{brhi96,
author = "Thierry Braconnier and Nicholas J. Higham",
title = "Computing the Field of Values and Pseudospectra
Using the {Lanczos} Method with Continuation",
journal = j-BIT,
volume = 36,
number = 3,
pages = "422-440",
year = 1996,
doi = "10.1007/BF01731925",
bibdate = "Thu Sep 19 12:16:51 GMT 1996",
created = "1996.09.19",
updated = "2014.05.22"
}
@article{cahi17,
author = "Erin Carson and Nicholas J. Higham",
title = "A New Analysis of Iterative Refinement and its Application to
Accurate Solution of Ill-Conditioned Sparse Linear Systems",
journal = j-SISC,
volume = 39,
number = 6,
pages = "A2834-A2856",
year = 2017,
doi = "10.1137/17M1122918",
created = "2017.03.28",
updated = "2017.12.11"
}
@article{cahi18,
author = "Erin Carson and Nicholas J. Higham",
title = "Accelerating the Solution of Linear Systems by Iterative
Refinement in Three Precisions",
journal = j-SISC,
volume = 40,
number = 2,
pages = "A817-A847",
year = 2018,
doi = "10.1137/17M1140819",
created = "2017.07.22",
updated = "2018.03.16"
}
@article{chp20,
author = "Erin Carson and Nicholas J. Higham and Srikara Pranesh",
title = "Three-Precision {GMRES}-Based Iterative Refinement for Least
Squares Problems",
journal = j-SISC,
volume = 42,
number = 6,
pages = "A4063-A4083",
year = 2020,
doi = "10.1137/20m1316822",
created = "2020.12.17",
updated = "2020.12.17"
}
@article{chhi98,
author = "Sheung Hun Cheng and Nicholas J. Higham",
title = "A Modified {Cholesky} Algorithm Based on a Symmetric Indefinite
Factorization",
journal = j-SIMAX,
volume = 19,
number = 4,
pages = "1097-1110",
month = oct,
year = 1998,
doi = "10.1137/S0895479896302898",
bibdate = "Tue Oct 6 10:33:08 GMT 1998",
created = "1998.10.06",
updated = "1998.10.06"
}
@article{chhi99,
author = "Sheung Hun Cheng and Nicholas J. Higham",
title = "The Nearest Definite Pair for the
{Hermitian} Generalized Eigenvalue Problem",
journal = j-LAA,
volume = "302-303",
pages = "63-76",
year = 1999,
doi = "10.1016/S0024-3795(99)00026-9",
bibdate = "Wed Jan 12 21:29:23 GMT 2000",
created = "2000.01.12",
updated = "2014.05.22"
}
@inproceedings{chkl00,
author = "Sheung Hun Cheng and Nicholas J. Higham and Charles S. Kenney
and Alan J. Laub",
title = "Return to the Middle Ages: {A} Half-Angle Iteration for the
Logarithm of a Unitary Matrix",
booktitle = "Proceedings of the Fourteenth International Symposium of
Mathematical Theory of Networks and Systems,
Perpignan, France",
year = 2000,
note = "CD ROM",
bibdate = "Wed Jun 28 08:44:15 GMT 2000",
created = "2000.06.28",
updated = "2000.06.28"
}
@article{chkl01,
author = "Sheung Hun Cheng and Nicholas J. Higham and Charles S. Kenney
and Alan J. Laub",
title = "Approximating the Logarithm of a Matrix to Specified Accuracy",
journal = j-SIMAX,
volume = 22,
number = 4,
pages = "1112-1125",
year = 2001,
doi = "10.1137/S0895479899364015",
bibdate = "Thu May 17 12:06:55 GMT 2001",
created = "2001.05.17",
updated = "2014.05.22"
}
@inproceedings{chhi01,
author = "Sheung Hun Cheng and Nicholas J. Higham",
title = "Parallel Implementation of a Block Algorithm for Matrix 1-Norm
Estimation",
booktitle = "Euro-Par \textup{2001}, Parallel Processing",
editor = "Rizos Sakellariou and John Keane and John Gurd and Len Freeman",
series = "Lecture Notes in Computer Science",
volume = 2150,
pages = "568-577",
publisher = pub-Springer # ", " # pub-Springer:adr-B,
year = "2001",
bibdate = "Wed Aug 29 11:08:31 GMT 2001",
created = "2001.08.29",
updated = "2001.08.29"
}
@techreport{chhi01a,
author = "Sheung Hun Cheng and Nicholas J. Higham",
title = "Implementation for {LAPACK} of a Block Algorithm for Matrix 1-Norm
Estimation",
institution = inst-MCCM,
address = inst-MCCM:adr,
type = t-NAREP,
number = "No. 393",
pages = "19",
month = aug,
year = "2001",
note = "LAPACK Working Note 152",
bibdate = "Tue Aug 21 07:48:56 GMT 2001",
created = "2001.08.21",
updated = "2001.08.21"
}
@article{chm21,
author = "Michael P. Connolly and Nicholas J. Higham and Theo Mary",
title = "Stochastic Rounding and Its Probabilistic Backward Error Analysis",
journal = j-SISC,
volume = 43,
number = 1,
pages = "A566-A585",
month = jan,
year = 2021,
doi = "10.1137/20m1334796",
created = "2020.03.19",
updated = "2020.11.16"
}
@inproceedings{cohi98,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Stability of {Householder QR} Factorization
for Weighted Least Squares Problems",
booktitle = "Numerical Analysis \textup{1997}, Proceedings of the
\textup{17}th Dundee Biennial Conference",
series = "Pitman Research Notes in Mathematics",
volume = 380,
editor = "D. F. Griffiths and D. J. Higham and G. A. Watson",
pages = "57-73",
publisher = pub-AWLongman # ", " # pub-AWLongman:adr,
year = 1998,
bibdate = "Mon Feb 2 07:55:26 GMT 1998",
created = "1998.02.02",
updated = "1998.02.02"
}
@inproceedings{cdhj07,
author = "Robert M. Corless and Hui Ding and Nicholas J. Higham and
David J. Jeffrey",
title = "The Solution of {$S \exp(S) = A$} is Not Always
the {Lambert} {$W$} Function of {$A$}",
booktitle = "{ISSAC} '\textup{07}: Proceedings of the \textup{2007}
International Symposium on Symbolic and Algebraic Computation",
pages = "116-121",
location = "Waterloo, Ontario, Canada",
publisher = pub-ACM,
address = pub-ACM:adr,
year = "2007",
isbn = "978-1-59593-743-8",
doi = "10.1145/1277548.1277565",
bibdate = "Fri Aug 17 22:03:56 GMT 2007",
created = "2007.08.17",
updated = "2007.08.17"
}
@article{cht20,
author = "Robert M. Corless and Nicholas J. Higham and Steven E. Thornton",
title = "Cover Image: {Bohemian} Matrices",
journal = "LMS Newsletter",
volume = 491,
pages = 16,
month = nov,
year = 2020,
url = "https://www.lms.ac.uk/publications/lms-newsletter-back-issues",
created = "2020.11.11",
updated = "2020.11.11"
}
@article{cohi99r,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Row-Wise Backward Stable Elimination Methods
for the Equality Constrained Least Squares Problem",
journal = j-SIMAX,
volume = 21,
number = 1,
pages = "313-326",
year = 1999,
doi = "10.1137/S0895479898335957",
bibdate = "Wed Feb 23 14:21:17 GMT 2000",
created = "2000.02.23",
updated = "2014.05.25"
}
@article{cohi99,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Accuracy and Stability of the Null Space Method for Solving the
Equality Constrained Least Squares Problem",
journal = j-BIT,
volume = 39,
number = 1,
pages = "34-50",
year = 1999,
doi = "10.1023/A:1022365107361",
bibdate = "Wed Mar 17 08:32:57 GMT 1999",
created = "1999.03.17",
updated = "2014.05.25"
}
@article{cohi99c,
author = "Anthony J. Cox and Nicholas J. Higham",
title = "Backward Error Bounds for Constrained Least Squares Problems",
journal = j-BIT,
volume = 39,
number = 2,
pages = "210-227",
year = "1999",
doi = "10.1023/A:1022385611904",
bibdate = "Mon Aug 2 12:06:15 GMT 1999",
created = "1999.08.02",
updated = "2014.05.25"
}
@techreport{dahi99j,
author = "Philip I. Davies and Nicholas J. Higham",
title = "Generating Test Matrices for the One- and Two-Sided {Jacobi} Methods",
institution = inst-MCCM,
address = inst-MCCM:adr,
type = t-NAREP,
number = "No. 338",
month = jan,
pages = "13",
year = 1999,
bibdate = "Tue Jan 19 08:51:31 GMT 1999",
created = "1999.01.19",
updated = "1999.01.19"
}
@article{dahi00,
author = "Philip I. Davies and Nicholas J. Higham",
title = "Numerically Stable Generation of
Correlation Matrices and their Factors",
journal = j-BIT,
volume = 40,
number = 4,
pages = "640-651",
year = 2000,
doi = "10.1023/A:1022384216930",
bibdate = "Wed Sep 6 15:31:15 GMT 2000",
created = "2000.09.06",
updated = "2014.05.25"
}
@article{dahi03,
author = "Philip I. Davies and Nicholas J. Higham",
title = "A {Schur--Parlett} Algorithm for Computing Matrix Functions",
journal = j-SIMAX,
volume = 25,
number = 2,
pages = "464-485",
year = 2003,
doi = "10.1137/S0895479802410815",
bibdate = "Thu Sep 18 09:13:12 GMT 2003",
created = "2003.09.18",
updated = "2014.05.25"
}
@inproceedings{dahi05,
author = "Philip I. Davies and Nicholas J. Higham",
title = "Computing {$f(A)b$} for Matrix Functions {$f$}",
booktitle = "{QCD} and Numerical Analysis {III}",
editor = "Artan Bori{\c{c}}i and Andreas Frommer and B{\'a}alint Jo{\'o}
and Anthony Kennedy and Brian Pendleton",
series = "Lecture Notes in Computational Science and Engineering",
volume = 47,
publisher = pub-Springer # ", " # pub-Springer:adr-B,
pages = "15-24",
year = 2005,
_isbn = "3-540-21257-4",
bibdate = "Sun Aug 28 09:45:49 GMT 2005",
created = "2005.08.28",
updated = "2005.08.28"
}
@article{dht01,
author = "Philip I. Davies and Nicholas J. Higham and Fran\c{c}oise Tisseur",
title = "Analysis of the {Cholesky} Method with Iterative Refinement for
Solving the Symmetric Definite Generalized Eigenproblem",
journal = j-SIMAX,
volume = 23,
number = 2,
pages = "472-493",
year = 2001,
doi = "10.1137/S0895479800373498",
bibdate = "Fri Sep 7 11:24:47 GMT 2001",
created = "2001.09.07",
updated = "2014.05.25"
}
@inproceedings{dhr13,
author = "Edvin Deadman and Nicholas J. Higham and Rui Ralha",
title = "Blocked {Schur} Algorithms for Computing the Matrix Square Root",
booktitle = "Applied Parallel and Scientific Computing:
11th International Conference, {PARA 2012, Helsinki, Finland}",
editor = "P. Manninen and P. {\"O}ster",
series = "Lecture Notes in Computer Science",
volume = 7782,
pages = "171-182",
year = 2013,
publisher = pub-Springer # ", " # pub-Springer:adr-B,
doi = "10.1007/978-3-642-36803-5_12",
created = "2012.01.31",
updated = "2013.03.08"
}
@misc{dehi14a,
author = "Edvin Deadman and Nicholas J. Higham",
title = "Testing Matrix Function Algorithms Using Identities",
year = 2014,
howpublished = "\url{http://blog.nag.com/2014/04/testing-matrix-function-algorithms.html}",
howpublished2= "\url{http://www.nag.co.uk/content/testing-matrix-function-algorithms-using-identities}",
created = "2014.10.20",
updated = "2016.07.28"
}
@article{dehi16,
author = "Edvin Deadman and Nicholas J. Higham",
title = "Testing Matrix Function Algorithms Using Identities",
journal = j-TOMS,
volume = 42,
number = 1,
pages = "4:1--4:15",
month = jan,
year = 2016,
doi = "10.1145/2723157",
created = "2016.02.29",
updated = "2016.02.29"
}
@article{dehi92,
author = "James W. Demmel and Nicholas J. Higham",
title = "Stability of Block Algorithms with Fast Level-3 {BLAS}",
journal = j-TOMS,
volume = 18,
number = 3,
pages = "274-291",
month = sep,
year = 1992,
doi = "10.1145/131766.131769",
mynote = "Also LAPACK Working Note 22.",
created = "1994.01.01",
updated = "2014.05.25"
}
@article{dehi93,
author = "James W. Demmel and Nicholas J. Higham",
title = "Improved Error Bounds for Underdetermined System Solvers",
journal = j-SIMAX,
volume = 14,
number = 1,
pages = "1-14",
month = jan,
year = 1993,
doi = "10.1137/0614001",
mynote = "Also LAPACK Working Note 23.",
created = "1994.01.01",
updated = "2014.05.25"
}
@article{dhs95,
author = "James W. Demmel and Nicholas J. Higham and Robert S. Schreiber",
title = "Stability of Block {$LU$} Factorization",
journal = j-NLAA,
volume = 2,
number = 2,
pages = "173-190",
year = 1995,
doi = "10.1002/nla.1680020208",
bibdate = "Wed Apr 5 12:48:23 GMT 1995",
created = "1995.04.05",
updated = "2014.05.25"
}
@article{dihi13,
author = "Nicholas J. Dingle and Nicholas J. Higham",
title = "Reducing the Influence of Tiny Normwise Relative Errors on
Performance Profiles",
journal = j-TOMS,
volume = 39,
number = 4,
pages = "24:1-24:11",
year = 2013,
doi = "10.1145/2491491.2491494",
created = "2011.09.15",
updated = "2013.08.23"
}
@techreport{ddgh16,
author = "Jack Dongarra and Iain Duff and Mark Gates and Azzam Haidar and
Sven Hammarling and Nicholas J. Higham and Jonathon Hogg
and Pedro Valero-Lara and Samuel D. Relton and Stanimire
Tomov and Mawussi Zounon",
title = "A Proposed {API} for {Batched Basic Linear Algebra Subprograms}",
institution = inst-MIMS,
address = inst-MIMS:adr,
type = t-MIMS-EPrint,
number = "2016.25",
year = 2016,
month = apr,
pages = 20,
url = "http://eprints.ma.man.ac.uk/2464/",
created = "2016.04.23",
updated = "2016.04.23"
}
@article{dgh20,
author = "Jack Dongarra and Laura Grigori and Nicholas J. Higham",
title = "Numerical Algorithms for High-Performance Computational Science",
journal = j-PHIL-RSA,
volume = 378,
number = 2166,
pages = "1-18",
year = 2020,
doi = "10.1098/rsta.2019.0066",
created = "2020.01.20",
updated = "2020.01.20"
}
@inproceedings{dhhr16,
author = "Jack Dongarra and Sven Hammarling and Nicholas J. Higham and
Samuel D. Relton and Pedro Valero-Lara and Mawussi Zounon",
title = "Creating a Standardised Set of Batched {BLAS} Routines",
booktitle = "Proceedings of the Fourth Workshop on Sustainable Software
for Science: Practice and Experiences (WSSSPE4)",
year = 2016,
editor = "Gabrielle Allen and Jeffrey Carver and Sou-Cheng T. Choi and others",
_editor = "Gabrielle Allen and Jeffrey Carver and Sou-Cheng T. Choi and
Tom Crick and Michael R. Crusoe and Sandra Gesing and
Robert Haines and Michael Heroux and Lorraine J. Hwang
and Daniel S. Katz and Kyle E. Niemeyer and Manish
Pararshar and Colin C. Venters",
volume = 1686,
publisher = "CEUR Workshop Proceedings",
url = "http://ceur-ws.org/Vol-1686/WSSSPE4_paper_3.pdf",
created = "2016.09.16",
updated = "2016.09.16"
}
@article{dhhr17,
author = "Jack Dongarra and Sven Hammarling and Nicholas J. Higham and
Samuel D. Relton and Pedro Valero-Lara and Mawussi Zounon",
title = "The Design and Performance of Batched {BLAS} on Modern
High-Performance Computing Systems",
journal = "Procedia Computer Science",
volume = 108,
pages = "495-504",
year = 2017,
mynote = "International Conference on Computational Science, ICCS 2017,
12-14 June 2017, Zurich, Switzerland",
doi = "10.1016/j.procs.2017.05.138",
created = "2017.06.27",
updated = "2017.06.27"
}
@inproceedings{dhhr17a,
author = "Jack Dongarra and Sven Hammarling and Nicholas J. Higham and
Samuel D. Relton and Mawussi Zounon",
title = "Optimized Batched Linear Algebra for Modern Architectures",
booktitle = "Euro-Par 2017: Parallel Processing",
series = "Lecture Notes in Computer Science",
volume = 10417,
year = 2017,
editor = "Rivera, Francisco F. and Pena, Tom{\'a}s F.
and Cabaleiro, Jos{\'e} C.",
pages = "511-522",
publisher = pub-Springer # ", " # pub-Springer:adr-C,
isbn = "978-3-319-64203-1",
doi = "10.1007/978-3-319-64203-1_37",
created = "2017.09.01",
updated = "2017.09.01"
}
@article{duhi92,
author = "Du Croz, Jeremy J. and Nicholas J. Higham",
title = "Stability of Methods for Matrix Inversion",
journal = j-IMAJNA,
volume = 12,
pages = "1-19",
year = 1992,
doi = "10.1093/imanum/12.1.1",
created = "1994.01.01",
updated = "2014.05.25"
}
@article{fahi18,
author = "Massimiliano Fasi and Nicholas J. Higham",
title = "Multiprecision Algorithms for Computing the Matrix Logarithm",
journal = j-SIMAX,
volume = 39,
number = 1,
pages = "472-491",
year = 2018,
doi = "10.1137/17M1129866",
created = "2017.04.12",
updated = "2018.03.16"
}
@article{fahi19,
author = "Massimiliano Fasi and Nicholas J. Higham",
title = "An Arbitrary Precision Scaling and Squaring Algorithm for the Matrix
Exponential",
journal = j-SIMAX,
volume = 40,
number = 4,
pages = "1233-1256",
year = 2019,
doi = "10.1137/18M1228876",
created = "2018.11.26",
updated = "2019.10.02"
}
@article{fahi21a,
author = "Massimiliano Fasi and Nicholas J. Higham",
title = "Generating Extreme-Scale Matrices with Specified Singular Values
or Condition Numbers",
journal = j-SISC,
volume = 43,
number = 1,
pages = "A663-A684",
year = 2021,
doi = "10.1137/20M1327938",
created = "2020.03.27",
updated = "2021.02.23"
}
@article{fahi21b,
author = "Massimiliano Fasi and Nicholas J. Higham",
title = "Matrices with Tunable Infinity-Norm Condition Number and No Need
for Pivoting in {LU} Factorization",
journal = j-SIMAX,
volume = 42,
number = 1,
pages = "417-435",
month = jan,
year = 2021,
doi = "10.1137/20m1357238",
created = "2020.08.01",
updated = "2020.12.29"
}
@article{fhi15,
author = "Massimiliano Fasi and Nicholas J. Higham and Bruno Iannazzo",
title = "An Algorithm for the Matrix {Lambert $W$} Function",
journal = j-SIMAX,
volume = 36,
number = 2,
pages = "669-685",
year = 2015,
doi = "10.1137/140997610",
created = "2014.11.26",
updated = "2015.07.12"
}
@article{fhmp21,
author = "Massimiliano Fasi and Nicholas J. Higham and Mantas Mikaitis
and Srikara Pranesh",
title = "Numerical Behavior of {NVIDIA} Tensor Cores",
journal = j-PEERJ-CS,
volume = 7,
pages = "e330(1--19)",
month = feb,
year = 2021,
doi = "10.7717/peerj-cs.330",
created = "2020.04.27",
updated = "2021.02.10"
}
@article{geor20,
author = "Dan I. Georgescu",
title = "Professor {Nick Higham: Northern} Light",
journal = "The Actuary",
volume = "",
pages = "12-14",
month = jun,
year = 2020,
url = "https://www.theactuary.com/features/2020/06/04/professor-nick-higham-northern-light",
note = "Also at \url{https://www.theactuary.com/archive/2020/2020/06/03/june-2020-digital-issue}",
created = "2020.11.05",
updated = "2020.11.05"
}
@misc{gehi18,
author = "Dan I. Georgescu and Nicholas J. Higham",
title = "Completing Correlation Matrices",
year = 2018,
month = feb,
howpublished = "\url{https://bankunderground.co.uk/2018/02/01/completing-correlation-matrices/}",
created = "2018.09.04",
updated = "2018.09.04"
}
@article{gehi20,
author = "Dan I. Georgescu and Nicholas J. Higham",
title = "Completing the Matrix",
journal = "The Actuary",
volume = "",
pages = "24-27",
month = nov,
year = 2020,
url = "https://www.theactuary.com/features/2020/11/04/completing-matrix",
note = "Also at \url{https://www.theactuary.com/issues/2020/11/november-2020}",
created = "2020.11.05",
updated = "2020.11.05"
}
@article{ghp18,
author = "Dan I. Georgescu and Nicholas J. Higham and Gareth W. Peters",
title = "Explicit Solutions to Correlation Matrix Completion Problems, with
an Application to Risk Management and Insurance",
journal = j-RSOS,
volume = 5,
number = 3,
pages = "1-11",
year = 2018,
doi = "10.1098/rsos.172348",
created = "2017.10.13",
updated = "2018.03.16"
}
@article{ght11,
author = "Laurence Grammont and Nicholas J. Higham and Fran\c{c}oise Tisseur",
title = "A Framework for Analyzing Nonlinear Eigenproblems
and Parametrized Linear Systems",
journal = j-LAA,
volume = "435",
number = "3",
pages = "623-640",
year = "2011",
doi = "10.1016/j.laa.2009.12.038",
created = "2010.02.15",
updated = "2011.05.06"
}
@article{guhi06p,
author = "Chun-Hua Guo and Nicholas J. Higham",
title = "A {Schur--Newton} Method for the Matrix {$p$th} Root and its
Inverse",
journal = j-SIMAX,
volume = 28,
number = 3,
pages = "788-804",
year = 2006,
doi = "10.1137/050643374",
bibdate = "Mon Oct 9 12:06:38 GMT 2006",
created = "2006.10.09",
updated = "2006.10.09"
}
@article{guhi07,
author = "Chun-Hua Guo and Nicholas J. Higham",
title = "Iterative Solution of a Nonsymmetric Algebraic {Riccati} Equation",
journal = j-SIMAX,
volume = 29,
number = 2,
pages = "396-412",
year = 2007,
doi = "10.1137/050647669",
bibdate = "Thu Mar 29 19:24:05 GMT 2007",
created = "2007.03.29",
updated = "2014.05.25"
}
@article{ght09,
author = "Chun-Hua Guo and Nicholas J. Higham and Fran\c{c}oise Tisseur",
title = "Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems",
journal = j-SIMAX,
volume = 30,
number = 4,
pages = "1593-1613",
year = 2009,
doi = "10.1137/070704058",
bibdate = "Sat Jan 17 17:35:31 GMT 2009",
created = "2009.01.17",
updated = "2014.05.25"
}
@article{ght09a,
author = "Chun-Hua Guo and Nicholas J. Higham and Fran\c{c}oise Tisseur",
title = "An Improved Arc Algorithm for Detecting Definite
{Hermitian} Pairs",
journal = j-SIMAX,
volume = 31,
number = 3,
pages = "1131-1151",
year = 2009,
doi = "10.1137/08074218X",
bibdate = "Fri Sep 18 17:34:11 GMT 2009",
created = "2009.09.18",
updated = "2014.05.25"
}
@article{hbtd20,
author = "Azzam Haidar and Harun Bayraktar and Stanimire Tomov and
Jack Dongarra and Nicholas J. Higham",
title = "Mixed-Precision Iterative Refinement Using Tensor Cores on {GPUs}
to Accelerate Solution of Linear Systems",
journal = j-PROC-RSA,
volume = 476,
number = 2243,
pages = 20200110,
year = 2020,
doi = "10.1098/rspa.2020.0110",
created = "2020.01.24",
updated = "2020.11.25"
}
@inproceedings{htdh18,
author = "Azzam Haidar and Stanimire Tomov and Jack Dongarra and
Nicholas J. Higham",
title = "Harnessing {GPU} Tensor Cores for Fast {FP16} Arithmetic to Speed up
Mixed-Precision Iterative Refinement Solvers",
booktitle = "Proceedings of the International Conference for High
Performance Computing, Networking, Storage, and Analysis",
year = 2018,
series = "SC18 (Dallas, TX)",
pages = "47:1--47:11",
address = "Piscataway, NJ, USA",
publisher = pub-IEEE,
doi = "10.1109/SC.2018.00050",
created = "2018.08.18",
updated = "2020.10.09"
}
@article{hht08,
author = "Nicholas Hale and Nicholas J. Higham and Lloyd N. Trefethen",
title = "Computing {$A^\alpha$}, {$\log(A)$}, and Related Matrix Functions by
Contour Integrals",
journal = j-SINUM,
volume = 46,
number = 5,
pages = "2505-2523",
year = 2008,
doi = "10.1137/070700607",
bibdate = "Mon Aug 18 08:51:21 GMT 2008",
created = "2008.08.18",
updated = "2014.05.31"
}
@article{hahi19a,
author = "Sven J. Hammarling and Nicholas J. Higham",
title = "Celebrating {James Hardy Wilkinson}",
journal = j-MATH-TODAY,
volume = 55,
number = 4,
pages = "131",
month = sep,
year = 2019,
created = "2019.09.13",
updated = "2019.09.13"
}
@inproceedings{hhl07,
author = "Sven Hammarling and Nicholas J. Higham and Craig Lucas",
title = "{LAPACK}-Style Codes for Pivoted {Cholesky} and {QR} Updating",
booktitle = "Applied Parallel Computing. State of the Art in Scientific
Computing. 8th International Workshop, PARA 2006",
series = "Lecture Notes in Computer Science",
number = 4699,
editor = "Bo K{\aa}gstr{\"o}m and Erik Elmroth and Jack Dongarra and
Jerzy Wa{\'s}niewski",
pages = "137-146",
publisher = pub-Springer # ", " # pub-Springer:adr-B,
year = "2007",
doi = "10.1007/978-3-540-75755-9_17",
bibdate = "Fri Sep 28 19:05:19 GMT 2007",
created = "2007.09.28",
updated = "2014.05.31"
}
@article{hahi05c,
author = "Gareth I. Hargreaves and Nicholas J. Higham",
title = "Efficient Algorithms for the Matrix Cosine and Sine",
journal = j-NUM-ALG,
volume = 40,
number = 4,
pages = "383-400",
year = 2005,
doi = "10.1007/s11075-005-8141-0",
bibdate = "Mon Nov 14 08:52:54 GMT 2005",
created = "2005.11.14",
updated = "2014.04.20"
}
@article{hihi92,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "Backward Error and Condition of Structured Linear Systems",
journal = j-SIMAX,
volume = 13,
number = 1,
month = jan,
pages = "162-175",
year = 1992,
doi = "10.1137/0613014",
created = "1994.01.01",
updated = "1994.01.01"
}
@article{hihi92a,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "Componentwise Perturbation Theory for Linear Systems
with Multiple Right-Hand Sides",
journal = j-LAA,
volume = "174",
pages = "111-129",
year = 1992,
doi = "10.1016/0024-3795(92)90046-D",
created = "1994.01.01",
updated = "2014.05.31"
}
@article{hihi98,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "Structured Backward Error and Condition of
Generalized Eigenvalue Problems",
journal = j-SIMAX,
volume = 20,
number = 2,
pages = "493-512",
year = 1998,
doi = "10.1137/S0895479896313188",
bibdate = "Thu Jan 28 15:29:35 GMT 1999",
created = "1999.01.28",
updated = "2014.05.31"
}
@book{hihi:MG,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "{MATLAB} Guide",
publisher = pub-SIAM,
address = pub-SIAM:adr,
year = 2000,
pages = "xxii+283",
_isbn = "0-89871-469-9",
isbn = "0-89871-516-4",
_bibdate = "Tue Aug 29 15:40:50 GMT 2000",
bibdate = "Thu Jan 24 08:21:41 GMT 2002",
created = "2002.01.24",
updated = "2002.01.24"
}
@book{hihi:MG2,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "{MATLAB} Guide",
edition = "Second",
publisher = pub-SIAM,
address = pub-SIAM:adr,
year = 2005,
pages = "xxiii+382",
doi = "10.1137/1.9780898717891",
isbn = "0-89871-578-4",
bibdate = "Thu Jan 27 12:10:11 GMT 2005",
created = "2005.01.27",
updated = "2014.05.30"
}
@book{hihi:MG3,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "{MATLAB} Guide",
edition = "Third",
publisher = pub-SIAM,
address = pub-SIAM:adr,
year = 2017,
pages = "xxvi+476",
doi = "10.1137/1.9781611974669",
isbn = "978-1-61197-465-2",
created = "2016.11.18",
updated = "2019.01.29"
}
@book{hihi:MG2-K,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "{MATLAB} Guide",
edition = "Second",
publisher = "A-Jin Publishing Company",
address = "Koea",
year = 2006,
pages = "450",
isbn = "89-5761-168-1",
note = "Korean edition of \cite{hihi:MG2}",
bibdate = "Mon Nov 12 11:26:07 GMT 2007",
created = "2007.11.12",
updated = "2007.11.12"
}
@article{hhp21,
author = "Desmond J. Higham and Nicholas J. Higham and Srikara Pranesh",
title = "Random Matrices Generating Large Growth in {LU} Factorization
with Pivoting",
journal = j-SIMAX,
volume = 42,
number = 1,
pages = "185–201",
year = "2021",
doi = "10.1137/20M1338149",
created = "2020.03.19",
updated = "2021.02.02"
}
@mastersthesis{high83m,
author = "N. J. Higham",
title = "Matrix Condition Numbers",
school = inst-U-Manchester,
address = inst-U-Manchester:adr,
type = "{M.Sc.} {Thesis}",
month = oct,
pages = "iv+86",
year = 1983,
url = "http://eprints.ma.man.ac.uk/2499/",
bibdate = "Tue Mar 21 16:29:28 GMT 1995",
created = "1995.03.21",
updated = "2016.09.06"
}
@phdthesis{high85p,
author = "Nicholas J. Higham",
title = "Nearness Problems in Numerical Linear Algebra",
school = inst-U-Manchester,
address = inst-U-Manchester:adr,
month = jul,
pages = 173,
year = 1985,
url = "http://eprints.ma.man.ac.uk/2555/",
bibdate = "Tue Mar 21 16:29:32 GMT 1995",
created = "1995.03.21",
updated = "2017.06.09"
}
@techreport{high85b,
author = "Nicholas J. Higham",
title = "Matrix Computations in {Basic} on a Microcomputer",
institution = "Department of Mathematics, University of Manchester",
address = "Manchester, M13 9PL, UK",
type = t-NAREP,
number = "No. 101",
pages = "62",
month = jun,
year = "1985",
note = "Reissued as MIMS EPrint 2013.51, Manchester Institute for
Mathematical Sciences, The University of Manchester, UK, October 2013",
url = "http://eprints.ma.man.ac.uk/2029/",
created = "2013.10.02",
updated = "2016.11.20"
}
@article{high86b,
author = "Nicholas J. Higham",
title = "Matrix Computations in {Basic} on a Microcomputer",
journal = j-IMA-BULL,
volume = 22,
number = "1/2",
pages = "13-20",
year = 1986,
mynote = "Jan/Feb",
created = "1994.01.01",
updated = "2013.06.04"
}
@article{high86n,
author = "Nicholas J. Higham",
title = "{Newton's} Method for the Matrix Square Root",
journal = j-MATH-COMP,
volume = 46,
number = 174,
month = apr,
pages = "537-549",
year = 1986,
doi = "10.1090/S0025-5718-1986-0829624-5",
created = "1994.01.01",
updated = "2014.05.31"
}
@article{high86p,
author = "Nicholas J. Higham",
title = "Computing the Polar Decomposition---with Applications",
journal = j-SISSC,
volume = 7,
number = 4,
month = oct,
pages = "1160-1174",
year = 1986,
doi = "10.1137/0907079",
mynote = "N.A. Report 94, November 1984. (Proof in Appendix is not in paper).",
created = "1994.01.01",
updated = "2014.05.31"
}
@article{high86t,
author = "Nicholas J. Higham",
title = "Efficient Algorithms for Computing the Condition Number
of a Tridiagonal Matrix",
journal = j-SISSC,
volume = 7,
number = 1,
pages = "150-165",
year = 1986,
doi = "10.1137/0907011",
created = "1994.01.01",
updated = "2014.05.31"
}
@article{high87s,
author = "Nicholas J. Higham",
title = "Computing Real Square Roots of a Real Matrix",
journal = j-LAA,
volume = "88/89",
pages = "405-430",
year = 1987,
doi = "10.1016/0024-3795(87)90118-2",
created = "1994.01.01",
updated = "2014.05.31"
}
@article{high87t,
author = "Nicholas J. Higham",
title = "A Survey of Condition Number Estimation for Triangular Matrices",
journal = j-SIREV,
volume = 29,
number = 4,
month = dec,
pages = "575-596",
year = 1987,
doi = "10.1137/1029112",
created = "1994.01.01",
updated = "2014.05.31"
}
@article{high87v,
author = "Nicholas J. Higham",
title = "Error Analysis of the {Bj\"orck}-{Pereyra} Algorithms for
Solving {Vandermonde} Systems",
journal = j-NUM-MATH,
volume = 50,
number = 5,
pages = "613-632",
year = 1987,
doi = "10.1007/BF01408579",
created = "1994.01.01",
updated = "2014.05.31"
}
@article{high88d,
author = "Nicholas J. Higham",
title = "Computing a Nearest Symmetric Positive Semidefinite Matrix",
journal = j-LAA,
volume = 103,
pages = "103-118",
year = 1988,
doi = "10.1016/0024-3795(88)90223-6",
created = "1994.01.01",
updated = "2014.05.31"
}
@article{high88f,
author = "Nicholas J. Higham",
title = "{FORTRAN} Codes for Estimating the One-norm of a Real or
Complex Matrix, with Applications to Condition Estimation
({Algorithm} 674)",
journal = j-TOMS,
volume = 14,
number = 4,
month = dec,
pages = "381-396",
year = 1988,
doi = "10.1145/63522.214391",
created = "1994.01.01",
updated = "2014.05.31"
}
@article{high88s,
author = "Nicholas J. Higham",
title = "The Symmetric {Procrustes} Problem",
journal = j-BIT,
volume = 28,
pages = "133-143",
year = 1988,
doi = "10.1007/BF01934701",
created = "1994.01.01",
updated = "2014.05.31"
}
@article{high88v,
author = "Nicholas J. Higham",
title = "Fast Solution of {Vandermonde}-like Systems Involving
Orthogonal Polynomials",
journal = j-IMAJNA,
volume = 8,
pages = "473-486",
year = 1988,
doi = "10.1093/imanum/8.4.473",
created = "1994.01.01",
updated = "2014.05.31"
}
@inproceedings{high89n,
author = "Nicholas J. Higham",
title = "Matrix Nearness Problems and Applications",
booktitle = "Applications of Matrix Theory",
editor = "M. J. C. Gover and S. Barnett",
pages = "1-27",
publisher = pub-OUP,
year = 1989,
created = "1994.01.01",
updated = "1994.01.01"
}
@article{high89t,
author = "Nicholas J. Higham",
title = "The Accuracy of Solutions to Triangular Systems",
journal = j-SINUM,
volume = 26,
number = 5,
month = oct,
pages = "1252-1265",
year = 1989,
doi = "10.1137/0726070",
created = "1994.01.01",
updated = "2014.05.31"
}
@inproceedings{high90c,
author = "Nicholas J. Higham",
title = "Analysis of the {Cholesky} Decomposition of a Semi-definite Matrix",
booktitle = "Reliable Numerical Computation",
editor = "M. G. Cox and S. J. Hammarling",
pages = "161-185",
publisher = pub-OUP,
year = 1990,
created = "1994.01.01",
updated = "1994.01.01"
}
@article{high90e,
author = "Nicholas J. Higham",
title = "Experience with a Matrix Norm Estimator",
journal = j-SISSC,
volume = 11,
number = 4,
pages = "804-809",
month = jul,
year = 1990,
doi = "10.1137/0911047",
mynote = "Timely Communication.",
created = "1994.01.01",
updated = "2014.05.31"
}
@inproceedings{high90g,
author = "Nicholas J. Higham",
title = "How Accurate is {Gaussian} Elimination?",
booktitle = "Numerical Analysis \textup{1989}, Proceedings of the
\textup{13}th Dundee Conference",
series = "Pitman Research Notes in Mathematics",
volume = 228,
editor = "D. F. Griffiths and G. A. Watson",
pages = "137-154",
publisher = pub-Longman-ST # ", " # pub-Longman-ST:adr,
year = 1990,
created = "1994.01.01",
updated = "1994.01.01"
}
@inproceedings{high90r,
author = "Nicholas J. Higham",
title = "Computing Error Bounds for Regression Problems",
booktitle = "Statistical Analysis of Measurement Error Models and
Applications, Contemporary Mathematics 112",
editor = "Philip J. Brown and Wayne A. Fuller",
pages = "195-208",
publisher = pub-AMS # ", " # pub-AMS:adr,
year = 1990,
created = "1994.01.01",
updated = "1994.01.01"
}
@article{high90s,
author = "Nicholas J. Higham",
title = "Exploiting Fast Matrix Multiplication within the Level 3 {BLAS}",
journal = j-TOMS,
volume = 16,
number = 4,
month = dec,
pages = "352-368",
year = 1990,
doi = "10.1145/98267.98290",
created = "1994.01.01",
updated = "2014.05.31"
}
@article{high90t,
author = "Nicholas J. Higham",
title = "Bounding the Error in {Gaussian} Elimination for
Tridiagonal Systems",
journal = j-SIMAX,
volume = 11,
number = 4,
month = oct,
pages = "521-530",
year = 1990,
doi = "10.1137/0611036",
created = "1994.01.01",
updated = "2014.05.31"
}
@article{high90v,
author = "Nicholas J. Higham",
title = "Stability Analysis of Algorithms for Solving Confluent
{Vandermonde}-like Systems",
journal = j-SIMAX,
volume = 11,
number = 1,
month = jan,
pages = "23-41",
year = 1990,
doi = "10.1137/0611002",
created = "1994.01.01",
updated = "2014.05.31"
}
@article{high91i,
author = "Nicholas J. Higham",
title = "Iterative Refinement Enhances the Stability of {$QR$}
Factorization Methods for Solving Linear Equations",
journal = j-BIT,
volume = 31,
pages = "447-468",
year = 1991,
doi = "10.1007/BF01933262",
bibdate = "Tue Mar 21 16:18:34 GMT 1995",
created = "1995.03.21",
updated = "2014.05.31"
}
@article{high91m,
author = "Nicholas J. Higham",
title = "Algorithm {$694$}: {A} Collection of Test Matrices in {MATLAB}",
journal = j-TOMS,
volume = 17,
number = 3,
month = sep,
pages = "289-305",
year = 1991,
doi = "10.1145/114697.116805",
created = "1994.01.01",
updated = "2020.03.23"
}
@incollection{high91l,
author = "Nicholas J. Higham",
title = "Solving Linear Equations",
editor = "Christine Bondi",
booktitle = "New Applications of Mathematics",
publisher = pub-Penguin,
address = pub-Penguin:adr-L,
pages = "33-56",
year = 1991,
mynote = "Chapter 2",
created = "1994.01.01",
updated = "1994.01.01"
}
@article{high92x,
author = "Nicholas J. Higham",
title = "Stability of a Method for Multiplying Complex Matrices
with Three Real Matrix Multiplications",
journal = j-SIMAX,
volume = 13,
number = 3,
month = jul,
pages = "681-687",
year = 1992,
doi = "10.1137/0613043",
created = "1994.01.01",
updated = "2014.05.31"
}
@article{high92e,
author = "Nicholas J. Higham",
title = "Estimating the Matrix {$p$}-Norm",
journal = j-NUM-MATH,
volume = 62,
pages = "539-555",
year = 1992,
doi = "10.1007/BF01396242",
created = "1994.01.01",
updated = "2014.06.20"
}
@article{high93d,
author = "Nicholas J. Higham",
title = "Optimization by Direct Search in Matrix Computations",
journal = j-SIMAX,
volume = 14,
number = 2,
month = apr,
pages = "317-333",
year = 1993,
doi = "10.1137/0614023",
created = "1994.01.01",
updated = "1994.01.01"
}
@article{high93s,
author = "Nicholas J. Higham",
title = "The Accuracy of Floating Point Summation",
journal = j-SISC,
volume = 14,
number = 4,
pages = "783-799",
month = jul,
year = 1993,
doi = "10.1137/0914050",
created = "1994.01.01",
updated = "2014.06.20"
}
@article{high93y,
author = "Nicholas J. Higham",
title = "Perturbation Theory and Backward Error for {$AX-XB=C$}",
journal = j-BIT,
volume = 33,
pages = "124-136",
year = 1993,
doi = "10.1007/978-94-015-8196-7_39",
created = "1994.01.01",
updated = "2014.06.20"
}
@inproceedings{high94c,
author = "Nicholas J. Higham",
title = "A Survey of Componentwise Perturbation Theory in
Numerical Linear Algebra",
booktitle = "{Mathematics of Computation} \textup{1943--1993}: {A} Half
Century of Computational Mathematics",
series = "Proceedings of Symposia in Applied Mathematics",
volume = 48,
editor = "Walter Gautschi",
pages = "49-77",
publisher = pub-AMS # ", " # pub-AMS:adr,
year = 1994,
bibdate = "Fri Mar 24 08:51:18 GMT 1995",
created = "1995.03.24",
updated = "1995.03.24"
}
@article{high94p,
author = "Nicholas J. Higham",
title = "The Matrix Sign Decomposition and Its Relation to the
Polar Decomposition",
journal = j-LAA,
volume = "212/213",
pages = "3-20",
year = 1994,
doi = "10.1016/0024-3795(94)90393-X",
bibdate = "Tue Jan 3 12:21:48 GMT 1995",
created = "1995.01.03",
updated = "2014.06.20"
}
@article{high95t,
author = "Nicholas J. Higham",
title = "Stability of Parallel Triangular System Solvers",
journal = j-SISC,
volume = 16,
number = 2,
pages = "400-413",
month = mar,
year = 1995,
doi = "10.1137/0916025",
bibdate = "Wed Jul 5 10:32:41 GMT 1995",
created = "1995.07.05",
updated = "1995.07.05"
}
@book{high:ASNA,
author = "Nicholas J. Higham",
title = "Accuracy and Stability of Numerical Algorithms",
publisher = pub-SIAM,
address = pub-SIAM:adr,
year = 1996,
pages = "xxviii+688",
isbn = "0-89871-355-2",
mynote = "This version of bib entry here for compatibility with
older cites to it.",
bibdate = "Mon Jan 8 12:38:23 GMT 1996",
created = "1996.01.08",
updated = "1996.01.08"
}
@book{high:ASNA1,
author = "Nicholas J. Higham",
title = "Accuracy and Stability of Numerical Algorithms",
publisher = pub-SIAM,
address = pub-SIAM:adr,
year = 1996,
pages = "xxviii+688",
isbn = "0-89871-355-2",
bibdate = "Mon Jan 8 12:38:23 GMT 1996",
created = "1996.01.08",
updated = "1996.01.08"
}
@book{high:ASNA2,
author = "Nicholas J. Higham",
title = "Accuracy and Stability of Numerical Algorithms",
publisher = pub-SIAM,
address = pub-SIAM:adr,
edition = "Second",
year = 2002,
pages = "xxx+680",
doi = "10.1137/1.9780898718027",
isbn = "0-89871-521-0",
bibdate = "Mon Aug 19 13:30:30 GMT 2002",
created = "2002.08.19",
updated = "2014.05.30"
}
@article{high97i,
author = "Nicholas J. Higham",
title = "Iterative Refinement for Linear Systems and {LAPACK}",
journal = j-IMAJNA,
volume = 17,
number = 4,
pages = "495-509",
year = 1997,
doi = "10.1093/imanum/17.4.495",
bibdate = "Mon Nov 10 11:33:49 GMT 1997",
created = "1997.11.10",
updated = "1997.11.10"
}
@incollection{high98l,
author = "Nicholas J. Higham",
title = "{Commentary on Lanczos's
`{``Introduction'' to the ``Tables of Chebyshev Polynomials
$S_n(x)$ and $C_n(x)$''}'}",
editor = "Davis, William R. and others",
booktitle = "Cornelius Lanczos Collected Published Papers with Commentaries",
publisher = "North Carolina State University, Raleigh, NC 27695-8202, USA",
volume = "VI",
pages = "3:557-3:559",
year = 1998,
mynote = "Volume VI, Part 3, pp. 557-559",
bibdate = "Mon Jan 4 08:38:45 GMT 1999",
created = "1999.01.04",
updated = "1999.01.04"
}
@inproceedings{high97r,
author = "Nicholas J. Higham",
title = "Recent Developments in Dense Numerical Linear Algebra",
booktitle = "The State of the Art in Numerical Analysis",
editor = "I. S. Duff and G. A. Watson",
pages = "1-26",
publisher = pub-OUP,
year = "1997",
bibdate = "Fri Jul 11 16:11:28 GMT 1997",
created = "1997.07.11",
updated = "1997.07.11"
}
@inproceedings{high97t,
author = "Nicholas J. Higham",
title = "Testing Linear Algebra Software",
booktitle = "Quality of Numerical Software: {Assessment} and Enhancement",
editor = "Ronald F. Boisvert",
publisher = pub-CH # ", " # pub-CH:adr-L,
pages = "109-122",
year = 1997,
bibdate = "Mon Feb 3 09:14:23 GMT 1997",
created = "1997.02.03",
updated = "1997.02.03"
}
@article{high97d,
author = "Nicholas J. Higham",
title = "Stability of the Diagonal Pivoting Method with Partial Pivoting",
journal = j-SIMAX,
volume = 18,
number = 1,
pages = "52-65",
month = jan,
year = 1997,
doi = "10.1137/S0895479895290371",
bibdate = "Sun Mar 2 11:16:54 GMT 1997",
created = "1997.03.02",
updated = "2014.06.20"
}
@article{high97s,
author = "Nicholas J. Higham",
title = "Stable Iterations for the Matrix Square Root",
journal = j-NUM-ALG,
volume = 15,
number = 2,
pages = "227-242",
year = "1997",
doi = "10.1023/A:1019150005407",
bibdate = "Tue Sep 30 08:34:02 GMT 1997",
created = "1997.09.30",
updated = "2014.06.20"
}
@book{high:HWMS1,
author = "Nicholas J. Higham",
title = "Handbook of Writing for the Mathematical Sciences",
publisher = pub-SIAM,
address = pub-SIAM:adr,
year = 1993,
isbn = "0-89871-314-5",
pages = "xii+241",
created = "1994.01.01",
updated = "1994.01.01"
}
@book{high:HWMS1-J,
author = "Nicholas J. Higham",
title = "Handbook of Writing for the Mathematical Sciences",
publisher = "Nippon Hyoron Sha",
address = "Tokyo",
year = 1994,
isbn = "4-535-78211-3",
pages = "x+235",
note = "Japanese edition of \cite{high:HWMS1},
translated by Shoji Okumura and Takemitsu Hasegawa",
bibdate = "Wed Sep 28 09:02:11 GMT 1994",
created = "1994.09.28",
updated = "1994.09.28"
}
@book{high:HWMS2,
author = "Nicholas J. Higham",
title = "Handbook of Writing for the Mathematical Sciences",
publisher = pub-SIAM,
address = pub-SIAM:adr,
edition = "Second",
year = 1998,
doi = "10.1137/1.9780898719550",
isbn = "978-0-898714-20-3",
pages = "xvi+302",
bibdate = "Fri Aug 28 11:49:13 GMT 1998",
created = "1998.08.28",
updated = "2019.01.02"
}
@book{high:HWMS3,
author = "Nicholas J. Higham",
title = "Handbook of Writing for the Mathematical Sciences",
publisher = pub-SIAM,
address = pub-SIAM:adr,
edition = "Third",
year = 2020,
isbn = "978-1-611976-09-0",
pages = "xxi+353",
created = "2019.09.22",
updated = "2019.09.27"
}
@inproceedings{high99n,
author = "Nicholas J. Higham",
title = "Notes on Accuracy and Stability of Algorithms in
Numerical Linear Algebra",
booktitle = "The Graduate Student's Guide to Numerical Analysis
'\textup{98}",
editor = "Mark Ainsworth and Jeremy Levesley and Marco Marletta",
pages = "48-82",
publisher = pub-Springer # ", " # pub-Springer:adr-B,
year = "1999",
bibdate = "Mon Jul 5 10:12:14 GMT 1999",
created = "1999.07.05",
updated = "1999.07.05"
}
@article{high98c,
author = "Nicholas J. Higham",
title = "Factorizing Complex Symmetric Matrices with
Positive Definite Real and Imaginary Parts",
journal = j-MATH-COMP,
volume = 67,
number = 224,
month = oct,
pages = "1591-1599",
year = 1998,
doi = "10.1090/S0025-5718-98-00978-8",
bibdate = "Thu Nov 12 11:36:35 GMT 1998",
created = "1998.11.12",
updated = "2014.06.20"
}
@article{high99b,
author = "Nicholas J. Higham",
title = "Stability of Block $\mathrm{LDL^T}$ Factorization of a
Symmetric Tridiagonal Matrix",
journal = j-LAA,
volume = "287",
pages = "181-189",
year = 1999,
doi = "10.1016/S0024-3795(98)10074-5",
bibdate = "Wed Jan 13 11:48:13 GMT 1999",
created = "1999.01.13",
updated = "2014.06.20"
}
@techreport{high99s,
author = "Nicholas J. Higham",
title = "A New \texttt{sqrtm} for {MATLAB}",
institution = inst-MCCM,
address = inst-MCCM:adr,
type = t-NAREP,
number = "No. 336",
month = jan,
pages = 11,
year = 1999,
bibdate = "Tue Jan 5 09:43:08 GMT 1999",
created = "1999.01.05",
updated = "1999.01.05"
}
@article{high00q,
author = "Nicholas J. Higham",
title = "{QR} Factorization with Complete Pivoting
and Accurate Computation of the {SVD}",
journal = j-LAA,
volume = "309",
pages = "153-174",
year = 2000,
doi = "10.1016/S0024-3795(99)00230-X",
bibdate = "Mon Apr 17 13:40:40 GMT 2000",
created = "2000.04.17",
updated = "2014.06.20"
}
@article{high01p,
author = "Nicholas J. Higham",
title = "Evaluating {Pad\'e} Approximants of the Matrix Logarithm",
journal = j-SIMAX,
volume = 22,
number = 4,
pages = "1126-1135",
year = 2001,
doi = "10.1137/S0895479800368688",
bibdate = "Mon Mar 26 08:01:03 GMT 2001",
created = "2001.03.26",
updated = "2001.03.26"
}
@article{high02c,
author = "Nicholas J. Higham",
title = "Computing the Nearest Correlation Matrix---{A} Problem from Finance",
journal = j-IMAJNA,
volume = 22,
number = 3,
pages = "329-343",
year = 2002,
doi = "10.1093/imanum/22.3.329",
bibdate = "Thu Aug 1 17:22:35 GMT 2002",
created = "2002.08.01",
updated = "2002.08.01"
}
@article{high03j,
author = "Nicholas J. Higham",
title = "{$J$}-Orthogonal Matrices: {Properties} and Generation",
journal = j-SIREV,
volume = 45,
number = 3,
month = sep,
pages = "504-519",
year = 2003,
doi = "10.1137/S0036144502414930",
bibdate = "Tue Aug 19 11:38:01 GMT 2003",
created = "2003.08.19",
updated = "2003.08.19"
}
@article{high04b,
author = "Nicholas J. Higham",
title = "The Numerical Stability of Barycentric {Lagrange} Interpolation",
journal = j-IMAJNA,
volume = 24,
number = 4,
pages = "547-556",
year = 2004,
doi = "10.1093/imanum/24.4.547",
bibdate = "Tue Oct 26 09:17:39 GMT 2004",
created = "2004.10.26",
updated = "2004.10.26"
}
@article{high05e,
author = "Nicholas J. Higham",
title = "The Scaling and Squaring Method for the Matrix Exponential
Revisited",
journal = j-SIMAX,
volume = 26,
number = 4,
pages = "1179-1193",
year = 2005,
doi = "10.1137/04061101X",
bibdate = "Mon Jun 13 12:23:20 GMT 2005",
created = "2005.06.13",
updated = "2005.06.13"
}
@incollection{high06f,
author = "Nicholas J. Higham",
title = "Functions of Matrices",
editor = "Leslie Hogben",
booktitle = "Handbook of Linear Algebra",
publisher = pub-CHCRC,
address = pub-CRC:adr,
year = 2006,
pages = "{11.1}--{11.13}",
_isbn = "1-58488-510-6",
bibdate = "Mon Dec 18 16:00:39 GMT 2006",
created = "2006.12.18",
updated = "2006.12.18"
}
@incollection{high07g,
author = "Nicholas J. Higham",
title = "Commentary on Matrix Factorizations and Applications",
editor = "Raymond H. Chan and Chen Greif and Dianne P. O'Leary",
booktitle = "Milestones in Matrix Computation:
{The} Selected Works of {Gene H. Golub}, with Commentaries",
publisher = pub-OUP,
pages = "227-235",
year = 2007,
bibdate = "Tue Feb 27 12:01:38 GMT 2007",
created = "2007.02.27",
updated = "2007.02.27"
}
@article{high08c,
author = "Nicholas J. Higham",
title = "{Cayley}, {Sylvester}, and Early Matrix Theory",
journal = j-LAA,
volume = "428",
pages = "39-43",
year = 2008,
doi = "10.1016/j.laa.2007.10.004",
bibdate = "Thu Nov 1 16:09:52 GMT 2007",
created = "2007.11.01",
updated = "2013.08.20"
}
@book{high:FM,
author = "Nicholas J. Higham",
title = "Functions of Matrices: {Theory} and Computation",
publisher = pub-SIAM,
address = pub-SIAM:adr,
year = 2008,
pages = "xx+425",
doi = "10.1137/1.9780898717778",
isbn = "978-0-898716-46-7",
bibdate = "Thu Feb 7 21:51:54 GMT 2008",
created = "2008.02.07",
updated = "2014.05.30"
}
@article{high09c,
author = "Nicholas J. Higham",
title = "Cholesky Factorization",
journal = j-WIRES-CompStat,
volume = 1,
number = 2,
pages = "251-254",
year = "2009",
doi = "10.1002/wics.18",
bibdate = "Mon Dec 27 10:39:14 GMT 2010",
created = "2010.12.27",
updated = "2020.07.27"
}
@article{high09e,
author = "Nicholas J. Higham",
title = "The Scaling and Squaring Method for the Matrix Exponential
Revisited",
journal = j-SIREV,
volume = 51,
number = 4,
_month = dec,
pages = "747-764",
year = 2009,
doi = "10.1137/090768539",
bibdate = "Wed Nov 4 14:48:33 GMT 2009",
created = "2009.11.04",
updated = "2012.01.19"
}
@article{high11g,
author = "Nicholas J. Higham",
title = "Gaussian Elimination",
journal = j-WIRES-CompStat,
volume = "3",
number = "3",
pages = "230-238",
year = "2011",
doi = "10.1002/wics.164",
created = "2011.02.13",
updated = "2011.05.09"
}
@misc{high13b,
author = "Nicholas J. Higham",
title = "{Arthur Buchheim (1859--1888)}",
year = 2013,
month = jan,
howpublished = "\url{http://nhigham.com/2013/01/31/arthur-buchheim}",
created = "2013.11.02",
updated = "2016.05.23"
}
@misc{high13g,
author = "Nicholas J. Higham",
title = "{Gene Golub SIAM Summer School} 2013",
year = 2013,
month = aug,
howpublished = "\url{http://nhigham.com/2013/08/09/gene-golub-siam-summer-school-2013}",
created = "2013.11.16",
updated = "2016.05.23"
}
@misc{high13c,
author = "Nicholas J. Higham",
title = "The Nearest Correlation Matrix",
year = 2013,
month = feb,
howpublished = "\url{https://nhigham.com/2013/02/13/the-nearest-correlation-matrix}",
created = "2015.02.10",
updated = "2016.05.23"
}
@misc{high14c,
author = "Nicholas J. Higham",
title = "Confessions of a Vice President At Large",
year = 2014,
month = jan,
howpublished = "\url{http://blogs.siam.org/confessions-of-a-vice-president-at-large}",
created = "2014.10.20",
updated = "2016.05.23"
}
@misc{high13w,
author = "Nicholas J. Higham",
title = "Why to Nominate for Prizes",
year = 2013,
month = dec,
howpublished = "\url{http://blogs.siam.org/why-to-nominate-for-prizes}",
created = "2014.10.20",
updated = "2016.05.23"
}
@incollection{high14g,
author = "Nicholas J. Higham",
title = "Numerical Conditioning",
editor = "Claude Brezinski and Ahmed Sameh",
booktitle = "Walter {Gautschi}. {Selected} Works with Commentaries",
volume = 1,
publisher = pub-BH,
address = pub-Springer:adr-NY,
isbn = "978-1-4614-7033-5",
doi = "10.1007/978-1-4614-7034-2_5",
pages = "37-40",
year = 2014,
created = "2013.10.25",
updated = "2015.08.22"
}
@incollection{high14f,
author = "Nicholas J. Higham",
title = "Functions of Matrices",
editor = "Leslie Hogben",
edition = "Second",
booktitle = "Handbook of Linear Algebra",
publisher = pub-CHCRC,
address = pub-CRC:adr,
year = 2014,
pages = "{17.1}--{17.15}",
_isbn = "978-1-4665-0728-9",
created = "2013.05.18",
updated = "2014.01.20"
}
@article{high14s,
author = "Nicholas J. Higham",
title = "Sylvester's Influence on Applied Mathematics",
journal = j-MATH-TODAY,
volume = 50,
number = 4,
month = aug,
pages = "202-206",
year = 2014,
created = "2014.08.04",
updated = "2014.08.04"
}
@misc{high14p,
author = "Nicholas J. Higham",
title = "The Spotlight Factor",
year = 2014,
month = sep,
howpublished = "\url{https://nhigham.com/2014/09/10/the-spotlight-factor}",
created = "2019.06.23",
updated = "2019.06.23"
}
@incollection{high15a,
author = "Nicholas J. Higham",
title = "Algorithms",
editor = "Nicholas J. Higham and Mark R. Dennis and Paul Glendinning and
Paul A. Martin and Fadil Santosa and Jared Tanner",
booktitle = "The Princeton Companion to Applied Mathematics",
publisher = pub-PUP,
address = pub-PUP:adr,
pages = "40-49",
year = 2015,
created = "2015.07.26",
updated = "2015.07.26"
}
@incollection{high15c,
author = "Nicholas J. Higham",
title = "Color Spaces and Digital Imaging",
editor = "Nicholas J. Higham and Mark R. Dennis and Paul Glendinning and
Paul A. Martin and Fadil Santosa and Jared Tanner",
booktitle = "The Princeton Companion to Applied Mathematics",
publisher = pub-PUP,
address = pub-PUP:adr,
pages = "808-813",
year = 2015,
created = "2015.02.03",
updated = "2015.06.27"
}
@incollection{high15fl,
author = "Nicholas J. Higham",
title = "Floating-Point Arithmetic",
editor = "Nicholas J. Higham and Mark R. Dennis and Paul Glendinning and
Paul A. Martin and Fadil Santosa and Jared Tanner",
booktitle = "The Princeton Companion to Applied Mathematics",
publisher = pub-PUP,
address = pub-PUP:adr,
pages = "96-97",
year = 2015,
created = "2015.02.03",
updated = "2015.06.27"
}
@incollection{high15fu,
author = "Nicholas J. Higham",
title = "Functions of Matrices",
editor = "Nicholas J. Higham and Mark R. Dennis and Paul Glendinning and
Paul A. Martin and Fadil Santosa and Jared Tanner",
booktitle = "The Princeton Companion to Applied Mathematics",
publisher = pub-PUP,
address = pub-PUP:adr,
pages = "97-99",
year = 2015,
created = "2015.02.03",
updated = "2015.06.27"
}
@incollection{high15g,
author = "Nicholas J. Higham",
title = "Goals of Applied Mathematical Research",
editor = "Nicholas J. Higham and Mark R. Dennis and Paul Glendinning and
Paul A. Martin and Fadil Santosa and Jared Tanner",
booktitle = "The Princeton Companion to Applied Mathematics",
publisher = pub-PUP,
address = pub-PUP:adr,
pages = "48-55",
year = 2015,
created = "2015.02.03",
updated = "2015.06.27"
}
@incollection{high15j,
author = "Nicholas J. Higham",
title = "The {Jordan} Canonical Form",
editor = "Nicholas J. Higham and Mark R. Dennis and Paul Glendinning and
Paul A. Martin and Fadil Santosa and Jared Tanner",
booktitle = "The Princeton Companion to Applied Mathematics",
publisher = pub-PUP,
address = pub-PUP:adr,
pages = "112-113",
year = 2015,
created = "2015.07.26",
updated = "2015.07.26"
}
@incollection{high15l,
author = "Nicholas J. Higham",
title = "The Language of Applied Mathematics",
editor = "Nicholas J. Higham and Mark R. Dennis and Paul Glendinning and
Paul A. Martin and Fadil Santosa and Jared Tanner",
booktitle = "The Princeton Companion to Applied Mathematics",
publisher = pub-PUP,
address = pub-PUP:adr,
pages = "8-27",
year = 2015,
created = "2015.07.26",
updated = "2015.07.26"
}
@incollection{high15m,
author = "Nicholas J. Higham",
title = "Methods of Solution",
editor = "Nicholas J. Higham and Mark R. Dennis and Paul Glendinning and
Paul A. Martin and Fadil Santosa and Jared Tanner",
booktitle = "The Princeton Companion to Applied Mathematics",
publisher = pub-PUP,
address = pub-PUP:adr,
pages = "27-40",
year = 2015,
created = "2015.07.26",
updated = "2015.07.26"
}
@incollection{high15n,
author = "Nicholas J. Higham",
title = "Numerical Linear Algebra and Matrix Analysis",
editor = "Nicholas J. Higham and Mark R. Dennis and Paul Glendinning and
Paul A. Martin and Fadil Santosa and Jared Tanner",
booktitle = "The Princeton Companion to Applied Mathematics",
publisher = pub-PUP,
address = pub-PUP:adr,
pages = "263-281",
year = 2015,
created = "2015.07.26",
updated = "2015.07.26"
}
@incollection{high15p,
author = "Nicholas J. Higham",
title = "Programming Languages: {An} Applied Mathematics View",
editor = "Nicholas J. Higham and Mark R. Dennis and Paul Glendinning and
Paul A. Martin and Fadil Santosa and Jared Tanner",
booktitle = "The Princeton Companion to Applied Mathematics",
publisher = pub-PUP,
address = pub-PUP:adr,
pages = "828-839",
year = 2015,
created = "2015.07.26",
updated = "2015.07.26"
}
@incollection{high15r,
author = "Nicholas J. Higham",
title = "How to Read and Understand a Paper",
editor = "Nicholas J. Higham and Mark R. Dennis and Paul Glendinning and
Paul A. Martin and Fadil Santosa and Jared Tanner",
booktitle = "The Princeton Companion to Applied Mathematics",
publisher = pub-PUP,
address = pub-PUP:adr,
pages = "903-906",
year = 2015,
created = "2015.07.26",
updated = "2015.07.26"
}
@incollection{high15sv,
author = "Nicholas J. Higham",
title = "The Singular Value Decomposition",
editor = "Nicholas J. Higham and Mark R. Dennis and Paul Glendinning and
Paul A. Martin and Fadil Santosa and Jared Tanner",
booktitle = "The Princeton Companion to Applied Mathematics",
publisher = pub-PUP,
address = pub-PUP:adr,
pages = "126-127",
year = 2015,
created = "2015.07.26",
updated = "2015.07.26"
}
@incollection{high15sy,
author = "Nicholas J. Higham",
title = "The {Sylvester} and {Lyapunov} Equations",
editor = "Nicholas J. Higham and Mark R. Dennis and Paul Glendinning and
Paul A. Martin and Fadil Santosa and Jared Tanner",
booktitle = "The Princeton Companion to Applied Mathematics",
publisher = pub-PUP,
address = pub-PUP:adr,
pages = "168-169",
year = 2015,
created = "2015.07.26",
updated = "2015.07.26"
}
@incollection{high15wh,
author = "Nicholas J. Higham",
title = "What Is Applied Mathematics?",
editor = "Nicholas J. Higham and Mark R. Dennis and Paul Glendinning and
Paul A. Martin and Fadil Santosa and Jared Tanner",
booktitle = "The Princeton Companion to Applied Mathematics",
publisher = pub-PUP,
address = pub-PUP:adr,
pages = "1-8",
year = 2015,
created = "2015.07.26",
updated = "2015.07.26"
}
@incollection{high15wo,
author = "Nicholas J. Higham",
title = "Workflow",
editor = "Nicholas J. Higham and Mark R. Dennis and Paul Glendinning and
Paul A. Martin and Fadil Santosa and Jared Tanner",
booktitle = "The Princeton Companion to Applied Mathematics",
publisher = pub-PUP,
address = pub-PUP:adr,
pages = "912-916",
year = 2015,
created = "2015.07.26",
updated = "2015.07.26"
}
@article{high15k,
author = "Nicholas J. Higham",
title = "Making the {Princeton Companion to Applied Mathematics}",
journal = j-MATH-TODAY,
volume = 51,
number = 5,
pages = "212-214",
month = oct,
year = 2015,
url = "http://eprints.ma.man.ac.uk/2399",
created = "2015.10.20",
updated = "2019.03.10"
}
@incollection{high15mf,
author = "Nicholas J. Higham",
title = "Matrix Functions: {Computation}",
editor = "Bj{\"o}rn Engquist",
booktitle = "Encyclopedia of Applied and Computational Mathematics",
publisher = pub-Springer,
address = pub-Springer:adr-B,
pages = "863-865",
year = 2015,
doi = "10.1007/978-3-540-70529-1",
created = "2015.12.02",
updated = "2015.12.02"
}
@misc{high16d,
author = "Nicholas J. Higham",
title = "Distraction-Free Editing with {Emacs}",
howpublished = "\url{https://nhigham.com/2016/01/14/distraction-free-editing-with-emacs}",
month = jan,
year = 2016,
created = "2019.05.11",
updated = "2019.05.11"
}
@misc{high16t,
author = "Nicholas J. Higham",
title = "The Top 10 Algorithms in Applied Mathematics",
year = 2016,
month = mar,
howpublished = "\url{https://nhigham.com/2016/03/29/the-top-10-algorithms-in-applied-mathematics}",
created = "2016.05.01",
updated = "2016.05.01"
}
@misc{high16i,
author = "Nicholas J. Higham",
title = "Iterating {MATLAB} Commands",
year = 2016,
month = may,
howpublished = "\url{https://nhigham.com/2016/05/13/iterating-matlab-commands}",
created = "2016.06.10",
updated = "2016.06.10"
}
@misc{high16z,
author = "Nicholas J. Higham",
title = "The One-Line Maze Program in {MATLAB}",
year = 2016,
month = jun,
howpublished = "\url{https://nhigham.com/2016/06/29/the-one-line-maze-program-in-matlab}",
created = "2016.10.23",
updated = "2016.10.23"
}
@incollection{high16m,
author = "Nicholas J. Higham",
title = "Mixed Precision Computations",
booktitle = "New Directions in Numerical Computation",
editor = "Tobin A. Driscoll and Endre S{\"u}li and Alex Townsend",
volume = 63,
number = 4,
publisher = j-NAMS,
address = "",
pages = "398-400",
year = 2016,
doi = "10.1090/noti1363",
created = "2016.05.25",
updated = "2017.01.08"
}
@misc{high17c,
author = "Nicholas J. Higham",
title = "Preparing {CMYK} Figures for Book Printing",
year = 2016,
month = jun,
howpublished = "\url{https://nhigham.com/2017/02/06/preparing-cmyk-figures-for-book-printing/}",
created = "2019.04.02",
updated = "2019.04.02"
}
@misc{high17q,
author = "Nicholas J. Higham",
title = "How Fast is Quadruple Precision Arithmetic?",
year = 2016,
month = jun,
howpublished = "\url{https://nhigham.com/2017/08/31/how-fast-is-quadruple-precision-arithmetic/}",
created = "2021.02.25",
updated = "2021.02.25"
}
@incollection{high02cf,
author = "Nicholas J. Higham",
title = "Cholesky Factorization",
booktitle = "Encyclopedia of Mathematics",
publisher = pub-Springer,
address = pub-Springer:adr-B,
pages = "863-865",
url = "http://www.encyclopediaofmath.org/index.php?title=Cholesky_factorization&oldid=11469",
year = 2002,
created = "2015.12.02",
updated = "2015.12.02"
}
@techreport{high19i,
author = "Nicholas J. Higham",
title = "Error Analysis For Standard and {GMRES}-Based Iterative Refinement in
Two and Three-Precisions",
institution = inst-MIMS,
address = inst-MIMS:adr,
type = t-MIMS-EPrint,
number = "2019.19",
pages = "8",
month = nov,
year = "2019",
url = "http://eprints.maths.manchester.ac.uk/2735/",
created = "2019.11.02",
updated = "2019.11.05"
}
@article{high21m,
author = "Nicholas J. Higham",
title = "The Mathematics of Floating-Point Arithmetic",
journal = "LMS Newsletter",
volume = 493,
pages = "35-41",
month = mar,
year = 2021,
url = "https://www.lms.ac.uk/publications/lms-newsletter-back-issues",
created = "2021.04.21",
updated = "2021.04.21"
}
@article{hial10,
author = "Nicholas J. Higham and Awad H. Al-Mohy",
title = "Computing Matrix Functions",
journal = j-AN,
volume = 19,
pages = "159-208",
year = 2010,
doi = "10.1017/S0962492910000036",
bibdate = "Tue May 18 11:52:40 GMT 2010",
created = "2010.05.18",
updated = "2010.05.18"
}
@article{hich98,
author = "Nicholas J. Higham and Sheung Hun Cheng",
title = "Modifying the Inertia of Matrices Arising in Optimization",
journal = j-LAA,
volume = "275--276",
pages = "261-279",
year = 1998,
doi = "10.1016/S0024-3795(97)10015-5",
bibdate = "Mon Jul 27 12:37:04 GMT 1998",
created = "1998.07.27",
updated = "2014.04.05"
}
@techreport{hide14,
author = "Nicholas J. Higham and Edvin Deadman",
title = "A Catalogue of Software for Matrix Functions. {Version} 1.0",
institution = inst-MIMS,
address = inst-MIMS:adr,
type = t-MIMS-EPrint,
number = "2014.8",
pages = "19",
month = feb,
year = "2014",
url = "http://eprints.ma.man.ac.uk/2102",
created = "2014.02.11",
updated = "2015.09.11"
}
@techreport{hide16,
author = "Nicholas J. Higham and Edvin Deadman",
title = "A Catalogue of Software for Matrix Functions. {Version} 2.0",
institution = inst-MIMS,
address = inst-MIMS:adr,
type = t-MIMS-EPrint,
number = "2016.3",
pages = "22",
month = jan,
year = "2016",
note = "Updated March 2016",
url = "http://eprints.maths.manchester.ac.uk/2452/",
created = "2016.01.19",
updated = "2019.10.30"
}
@book{hdgm15,
editor = "Nicholas J. Higham and Mark R. Dennis and Paul Glendinning and
Paul A. Martin and Fadil Santosa and Jared Tanner",
title = "The Princeton Companion to Applied Mathematics",
publisher = pub-PUP,
address = pub-PUP:adr,
pages = "xvii + 994 + 16 color plates",
year = 2015,
isbn = "978-0-691-15039-0",
url = "http://press.princeton.edu/titles/10592.html",
created = "2015.06.27",
updated = "2015.06.27"
}
@book{hdgm18,
editor = "Nicholas J. Higham and Mark R. Dennis and Paul Glendinning and
Paul A. Martin and Fadil Santosa and Jared Tanner",
title = "The Princeton Companion to Applied Mathematics",
publisher = "Seung San Publishers",
address = "South Korea",
pages = "936 + 16 color plates + 639",
year = 2018,
isbn = "978-89-6139-069-9 and 978-89-6139-070-5",
url = "http://seoji.nl.go.kr/landingPage?isbn=9788961390699",
url2 = "http://seoji.nl.go.kr/landingPage?isbn=9788961390705",
note = "Korean translation of \cite{hdgm15}, in two volumes",
created = "2020.08.15",
updated = "2020.08.15"
}
@article{hihi89,
author = "Nicholas J. Higham and Desmond J. Higham",
title = "Large Growth Factors in {Gaussian} Elimination with Pivoting",
journal = j-SIMAX,
volume = 10,
number = 2,
month = apr,
pages = "155-164",
year = 1989,
doi = "10.1137/0610012",
created = "1994.01.01",
updated = "2014.07.26"
}
@techreport{hiho20,
author = "Nicholas J. Higham and Edvin Hopkins",
title = "A Catalogue of Software for Matrix Functions. {Version} 3.0",
institution = inst-MIMS,
address = inst-MIMS:adr,
type = t-MIMS-EPrint,
number = "2020.7",
pages = "24",
month = mar,
year = "2020",
url = "http://eprints.maths.manchester.ac.uk/2754/",
created = "2020.03.27",
updated = "2020.03.27"
}
@article{hika17,
author = "Nicholas J. Higham and Peter Kandolf",
title = "Computing the Action of Trigonometric and Hyperbolic Matrix
Functions",
journal = j-SISC,
volume = 39,
number = 2,
pages = "A613-A627",
year = 2017,
doi = "10.1137/16M1084225",
created = "2016.07.26",
updated = "2017.04.28"
}
@article{hiki00q,
author = "Nicholas J. Higham and Hyun-Min Kim",
title = "Numerical Analysis of a Quadratic Matrix Equation",
journal = j-IMAJNA,
volume = 20,
number = 4,
pages = "499-519",
year = 2000,
doi = "10.1093/imanum/20.4.499",
bibdate = "Fri Oct 27 15:54:22 GMT 2000",
created = "2000.10.27",
updated = "2014.04.05"
}
@article{hiki01n,
author = "Nicholas J. Higham and Hyun-Min Kim",
title = "Solving a Quadratic Matrix Equation by
{Newton's} Method with Exact Line Searches",
journal = j-SIMAX,
volume = 23,
number = 2,
pages = "303-316",
year = 2001,
doi = "10.1137/S0895479899350976",
bibdate = "Mon Aug 13 09:25:59 GMT 2001",
created = "2001.08.13",
updated = "2014.04.05"
}
@inproceedings{hikn93,
author = "Nicholas J. Higham and Philip A. Knight",
title = "Componentwise Error Analysis for Stationary Iterative Methods",
booktitle = "Linear Algebra, Markov Chains, and Queueing Models",
editor = "Meyer, Carl D. and Robert J. Plemmons",
series = "IMA Volumes in Mathematics and Its Applications",
volume = 48,
pages = "29-46",
publisher = pub-Springer # ", " # pub-Springer:adr-NY,
year = 1993,
doi = "10.1007/978-1-4613-8351-2_3",
created = "1994.01.01",
updated = "2014.07.26"
}
@article{hikn93a,
author = "Nicholas J. Higham and Philip A. Knight",
title = "Finite Precision Behavior of Stationary Iteration for
Solving Singular Systems",
journal = j-LAA,
volume = 192,
pages = "165-186",
year = 1993,
doi = "10.1016/0024-3795(93)90242-G",
mynote = "Special issue for Proceedings of Workshop on Computational Linear
Algebra in Algebraic and Related Problems",
created = "1994.01.01",
updated = "2014.07.26"
}
@article{hikn95,
author = "Nicholas J. Higham and Philip A. Knight",
title = "Matrix Powers in Finite Precision Arithmetic",
journal = j-SIMAX,
volume = 16,
number = 2,
pages = "343-358",
month = apr,
year = 1995,
doi = "10.1137/S0895479893256347",
bibdate = "Tue Aug 29 09:11:08 GMT 1995",
created = "1995.08.29",
updated = "1995.08.29"
}
@article{hkmp04,
author = "Nicholas J. Higham and Mihail Konstantinov and Volker Mehrmann
and Petko Petkov",
title = "The Sensitivity of Computational Control Problems",
journal = "IEEE Control Systems Magazine",
volume = 24,
number = 1,
pages = "28-43",
month = feb,
year = 2004,
doi = "10.1109/MCS.2004.1272744",
bibdate = "Thu Mar 25 11:50:08 GMT 2004",
created = "2004.03.25",
updated = "2014.07.26"
}
@techreport{hile21,
author = "Nicholas J. Higham and Matthew C. Lettington",
title = "Optimizing and Factorizing the {Wilson} Matrix",
institution = inst-MIMS,
address = inst-MIMS:adr,
type = t-MIMS-EPrint,
number = "2021.3",
pages = "12",
month = feb,
year = "2021",
note = "To appear in " # j-AMM,
url = "http://eprints.maths.manchester.ac.uk/2803/",
created = "2021.02.18",
updated = "2021.02.22"
}
@article{hls21,
author = "Nicholas J. Higham and Matthew C. Lettington and
Karl Michael Schmidt",
title = "Integer Matrix Factorisations, Superalgebras and the Quadratic Form
Obstruction",
journal = j-LAA,
volume = 622,
pages = "250-267",
year = 2021,
doi = "10.1016/j.laa.2021.03.028",
created = "2021.03.20",
updated = "2021.04.06"
}
@article{hlt07,
author = "Nicholas J. Higham and Ren-Cang Li and Fran\c{c}oise Tisseur",
title = "Backward Error of Polynomial Eigenproblems Solved by Linearization",
journal = j-SIMAX,
volume = 29,
number = 4,
pages = "1218-1241",
year = 2007,
doi = "10.1137/060663738",
bibdate = "Thu Dec 13 20:36:37 GMT 2007",
created = "2007.12.13",
updated = "2014.07.26"
}
@article{hili11,
author = "Nicholas J. Higham and Lijing Lin",
title = "On {$p$th} Roots of Stochastic Matrices",
journal = j-LAA,
volume = "435",
number = "3",
pages = "448-463",
year = "2011",
doi = "10.1016/j.laa.2010.04.007",
created = "2010.05.13",
updated = "2011.05.06"
}
@article{hili11a,
author = "Nicholas J. Higham and Lijing Lin",
title = "A {Schur--Pad{\'e}} Algorithm for Fractional Powers of a Matrix",
journal = j-SIMAX,
volume = 32,
number = 3,
pages = "1056-1078",
year = 2011,
doi = "10.1137/10081232X",
created = "2010.10.19",
updated = "2011.10.05"
}
@article{hili13,
author = "Nicholas J. Higham and Lijing Lin",
title = "An Improved {Schur--Pad\'{e}} Algorithm for Fractional Powers
of a Matrix and their {Fr\'echet} Derivatives",
journal = j-SIMAX,
volume = 34,
number = 3,
pages = "1341-1360",
year = 2013,
doi = "10.1137/130906118",
created = "2010.10.19",
updated = "2013.09.19"
}
@incollection{hili15,
author = "Nicholas J. Higham and Lijing Lin",
title = "Matrix Functions: {A} Short Course",
booktitle = "Matrix Functions and Matrix Equations",
editor = "Zhaojun Bai and Weiguo Gao and Yangfeng Su",
series = "Series in Contemporary Applied Mathematics",
number = "19",
publisher = pub-WS,
address = pub-WS:adr,
pages = "1-27",
year = 2015,
doi = "10.1142/9789814675772_0001",
isbn = "978-9814675765",
created = "2013.11.16",
updated = "2015.12.06"
}
@techreport{hilu20,
author = "Nicholas J. Higham and Xiaobo Liu",
title = "A Multiprecision Derivative-Free {Schur--Parlett} Algorithm for
Computing Matrix Functions",
institution = inst-MIMS,
address = inst-MIMS:adr,
type = t-MIMS-EPrint,
number = "2020.19",
pages = "22",
month = sep,
year = "2020",
url = "http://eprints.maths.manchester.ac.uk/2806/",
note = "Revised March 2021",
created = "2020.09.07",
updated = "2021.03.23"
}
@article{hmmt04c,
author = "Nicholas J. Higham and D. Steven Mackey and Niloufer Mackey and
Fran\c{c}oise Tisseur",
title = "Computing the Polar Decomposition and the Matrix Sign Decomposition
in Matrix Groups",
journal = j-SIMAX,
volume = 25,
number = 4,
pages = "1178-1192",
year = 2004,
doi = "10.1137/S0895479803426644",
bibdate = "Tue Aug 10 08:32:21 GMT 2004",
created = "2004.08.10",
updated = "2004.08.10"
}
@article{hmmt05f,
author = "Nicholas J. Higham and D. Steven Mackey and Niloufer Mackey and
Fran\c{c}oise Tisseur",
title = "Functions Preserving Matrix Groups and Iterations for the
Matrix Square Root",
journal = j-SIMAX,
volume = 26,
number = 3,
pages = "849-877",
year = 2005,
doi = "10.1137/S0895479804442218",
bibdate = "Thu Apr 14 11:29:59 GMT 2005",
created = "2005.04.14",
updated = "2005.04.14"
}
@article{hmmt06s,
author = "Nicholas J. Higham and D. Steven Mackey and Niloufer Mackey and
Fran\c{c}oise Tisseur",
title = "Symmetric Linearizations for Matrix Polynomials",
journal = j-SIMAX,
volume = 29,
number = 1,
pages = "143-159",
year = 2006,
doi = "10.1137/050646202",
bibdate = "Wed Jan 10 14:45:42 GMT 2007",
created = "2007.01.10",
updated = "2014.07.26"
}
@article{hmt06c,
author = "Nicholas J. Higham and D. Steven Mackey and Fran\c{c}oise Tisseur",
title = "The Conditioning of Linearizations of Matrix Polynomials",
journal = j-SIMAX,
volume = 28,
number = 4,
pages = "1005-1028",
year = 2006,
doi = "10.1137/050628283",
bibdate = "Tue Dec 19 09:08:23 GMT 2006",
created = "2006.12.19",
updated = "2014.07.26"
}
@article{hmt09,
author = "Nicholas J. Higham and D. Steven Mackey and Fran\c{c}oise Tisseur",
title = "Definite Matrix Polynomials and their Linearization by Definite
Pencils",
journal = j-SIMAX,
volume = 31,
number = 2,
pages = "478-502",
year = 2009,
doi = "10.1137/080721406",
bibdate = "Mon May 11 13:05:28 GMT 2009",
created = "2009.05.11",
updated = "2014.07.26"
}
@article{hmtg08,
author = "Nicholas J. Higham and D. Steven Mackey and Fran\c{c}oise Tisseur
and Seamus D. Garvey",
title = "Scaling, Sensitivity and Stability in the Numerical Solution of
Quadratic Eigenvalue Problems",
journal = j-IJNME,
volume = 73,
number = 3,
pages = "344-360",
year = 2008,
doi = "10.1002/nme.2076",
bibdate = "Fri Dec 14 12:35:02 GMT 2007",
created = "2007.12.14",
updated = "2014.07.26"
}
@article{hima19,
author = "Nicholas J. Higham and Theo Mary",
title = "A New Preconditioner that Exploits Low-Rank Approximations to
Factorization Error",
journal = j-SISC,
volume = 41,
number = 1,
pages = "A59-A82",
year = 2019,
doi = "10.1137/18M1182802",
created = "2018.04.23",
updated = "2019.01.04"
}
@article{hima19a,
author = "Nicholas J. Higham and Theo Mary",
title = "A New Approach to Probabilistic Rounding Error Analysis",
journal = j-SISC,
volume = 41,
number = 5,
pages = "A2815-A2835",
year = 2019,
doi = "10.1137/18M1226312",
created = "2018.11.12",
updated = "2019.09.13"
}
@article{hima20,
author = "Nicholas J. Higham and Theo Mary",
title = "Sharper Probabilistic Backward Error Analysis
for Basic Linear Algebra Kernels with Random Data",
journal = j-SISC,
volume = 42,
number = 5,
pages = "A3427-A3446",
year = "2020",
doi = "10.1137/20M1314355",
created = "2020.01.13",
updated = "2020.10.23"
}
@article{hima21,
author = "Nicholas J. Higham and Theo Mary",
title = "Solving Block Low-Rank Linear Systems by
{LU} Factorization is Numerically Stable",
journal = j-IMAJNA,
volume = "",
number = "",
pages = "1-30",
year = 2020,
doi = "10.1093/imanum/drab020",
created = "2019.09.04",
updated = "2021.04.22"
}
@article{hmt10,
author = "Nicholas J. Higham and Christian Mehl and Fran\c{c}oise Tisseur",
title = "The Canonical Generalized Polar Decomposition",
journal = j-SIMAX,
volume = 31,
number = 4,
pages = "2163-2180",
year = 2010,
doi = "10.1137/090765018",
bibdate = "Mon Jul 5 10:33:53 GMT 2010",
created = "2010.07.05",
updated = "2010.07.05"
}