## Higham, Nicholas J.

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 Author ID: higham.nicholas-j Published as: Higham, Nicholas J.; Higham, N. J.; Higham, Nicholas; Higham, Nick more...less Homepage: https://nhigham.com/ External Links: MGP · Wikidata · Google Scholar · dblp · GND · IdRef · theses.fr
 Documents Indexed: 173 Publications since 1986, including 10 Books 3 Contributions as Editor · 2 Further Contributions Biographic References: 1 Publication Co-Authors: 89 Co-Authors with 123 Joint Publications 2,114 Co-Co-Authors
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### Co-Authors

 53 single-authored 18 Tisseur, Françoise 10 Higham, Desmond J. 9 Al-Mohy, Awad H. 7 Mary, Theo A. 6 Mackey, D. Steven 6 Pranesh, Srikara 5 Cheng, Sheung Hun 5 Fasi, Massimiliano 5 Lin, Lijing 5 Relton, Samuel D. 4 Cox, Anthony J. 4 Davies, Philip I. 4 Guo, Chun-Hua 3 Blanchard, Pierre 3 Carson, Erin Claire 3 Demmel, James Weldon 3 Dongarra, Jack J. 3 Knight, Philip A. 3 Mackey, Niloufer 3 Strabić, Nataša 2 Aprahamian, Mary 2 Bojanczyk, Adam W. 2 Borsdorf, Rüdiger 2 Gautschi, Walter 2 Haidar, Azzam 2 Kim, Hyunmin 2 Lettington, Matthew C. 2 Nakatsukasa, Yuji 2 Papadimitriou, Pythagoras 2 Patel, Harikrishna 2 Schreiber, Robert S. 2 Stewart, Gilbert Wright 2 Tomov, Stanimire Z. 2 Zounon, Mawussi 1 Abdelfattah, Ahmad 1 Bai, Zhaojun 1 Bayraktar, Harun H. 1 Benzi, Michele 1 Betcke, Timo 1 Bini, Dario Andrea 1 Björk, Åke 1 Braconnier, Thierry 1 Brezinski, Claude 1 Chan, Raymond Hon-Fu 1 Connolly, Michael P. 1 Corless, Robert Malcolm 1 Costa, Timothy B. 1 Deadman, Edvin 1 Dennis, Mark R. 1 Ding, Hui 1 Dingle, Nicholas J. 1 Du Croz, Jeremy J. 1 Elman, Howard C. 1 Garvey, Seamus D. 1 Gates, Mark 1 Glendinning, Paul Alexander 1 Golub, Gene Howard 1 Grammont, Laurence 1 Greenbaum, Anne 1 Greif, Chen 1 Grigori, Laura 1 Hale, Nicholas 1 Hammarling, Sven J. 1 Hargreaves, Gareth I. 1 Horn, Roger Alan 1 Iannazzo, Bruno 1 Jeffrey, David J. 1 Kandolf, Peter 1 Kenney, Charles S. 1 Kilmer, Misha E. 1 Kurzak, Jakub 1 Laffey, Thomas J. 1 Laub, Alan J. 1 Li, Rencang 1 Lopez, Florent 1 Luszczek, Piotr 1 Martin, Paul Andrew 1 Mehl, Christian 1 Mehrman, Volker 1 Mehrmann, Volker 1 Meini, Beatrice 1 Mikaitis, Mantas 1 Nadukandi, Prashanth 1 Noferini, Vanni 1 O’Leary, Dianne P. 1 Pan, Jianxin 1 Pothen, Alex 1 Puerta, Ferran 1 Raydan, Marcos 1 Sameh, Ahmed H. 1 Santosa, Fadil N. 1 Schmidt, Karl Michael 1 Schröder, Christian 1 Šego, Vedran 1 Segura, Javier 1 Smith, Matthew I. 1 Spalević, Miodrag M. 1 Tanner, Jared W. 1 Trefethen, Lloyd Nicholas 1 Van Dooren, Paul M.
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### Serials

 49 SIAM Journal on Matrix Analysis and Applications 25 SIAM Journal on Scientific Computing 18 Linear Algebra and its Applications 9 IMA Journal of Numerical Analysis 9 ACM Transactions on Mathematical Software 8 BIT 8 Numerical Algorithms 4 SIAM Journal on Scientific and Statistical Computing 4 SIAM Review 2 Mathematics of Computation 2 Numerische Mathematik 2 SIAM Journal on Numerical Analysis 2 Other Titles in Applied Mathematics 1 American Mathematical Monthly 1 International Journal for Numerical Methods in Engineering 1 Parallel Computing 1 Bulletin. The Institute of Mathematics and its Applications 1 Computational Statistics and Data Analysis 1 Numerical Linear Algebra with Applications 1 Acta Numerica 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Contemporary Mathematicians 1 Cambridge Tracts in Mathematics and Mathematical Physics 1 London Mathematical Society. Newsletter
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### Fields

 164 Numerical analysis (65-XX) 73 Linear and multilinear algebra; matrix theory (15-XX) 7 Statistics (62-XX) 7 Computer science (68-XX) 6 General and overarching topics; collections (00-XX) 6 Operations research, mathematical programming (90-XX) 3 History and biography (01-XX) 2 Combinatorics (05-XX) 2 Ordinary differential equations (34-XX) 2 Approximations and expansions (41-XX) 2 Mechanics of deformable solids (74-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Systems theory; control (93-XX) 1 Number theory (11-XX) 1 Special functions (33-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX) 1 Mathematics education (97-XX)

### Citations contained in zbMATH Open

164 Publications have been cited 4,913 times in 3,204 Documents Cited by Year
Accuracy and stability of numerical algorithms. 2nd ed. Zbl 1011.65010
Higham, Nicholas J.
2002
Functions of matrices. Theory and computation. Zbl 1167.15001
Higham, Nicholas J.
2008
Accuracy and stability of numerical algorithms. Zbl 0847.65010
Higham, Nicholas J.
1996
Computing the nearest correlation matrix – a problem from finance. Zbl 1006.65036
Higham, Nicholas J.
2002
Computing a nearest symmetric positive semidefinite matrix. Zbl 0649.65026
Higham, Nicholas J.
1988
Computing the action of the matrix exponential, with an application to exponential integrators. Zbl 1234.65028
Al-Mohy, Awad H.; Higham, Nicholas J.
2011
The scaling and squaring method for the matrix exponential revisited. Zbl 1081.65037
Higham, Nicholas J.
2005
NLEVP, a collection of nonlinear eigenvalue problems. Zbl 1295.65140
Betcke, Timo; Higham, Nicholas J.; Mehrmann, Volker; Schröder, Christian; Tisseur, Françoise
2013
The numerical stability of barycentric Lagrange interpolation. Zbl 1067.65016
Higham, Nicholas J.
2004
Computing the polar decomposition - with applications. Zbl 0607.65014
Higham, Nicholas J.
1986
A new scaling and squaring algorithm for the matrix exponential. Zbl 1194.15021
Al-Mohy, Awad H.; Higham, Nicholas J.
2010
Computing $$A^\alpha, \log(A)$$, and related matrix functions by contour integrals. Zbl 1176.65053
Hale, Nicholas; Higham, Nicholas J.; Trefethen, Lloyd N.
2008
Matrix nearness problems and applications. Zbl 0681.65029
Higham, N. J.
1989
Computing real square roots of a real matrix. Zbl 0625.65032
Higham, Nicholas J.
1987
Symmetric linearizations for matrix polynomials. Zbl 1137.15006
Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise
2006
The scaling and squaring method for the matrix exponential revisited. Zbl 1178.65040
Higham, Nicholas J.
2009
Structured pseudospectra for polynomial eigenvalue problems, with applications. Zbl 0996.65042
Tisseur, Françoise; Higham, Nicholas J.
2001
Structured backward error and condition of generalized eigenvalue problems. Zbl 0935.65032
Higham, Desmond J.; Higham, Nicholas J.
1998
A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra. Zbl 0959.65061
Higham, Nicholas J.; Tisseur, Françoise
2000
Bounds for eigenvalues of matrix polynomials. Zbl 1055.15030
Higham, Nicholas J.; Tisseur, Françoise
2003
A Schur-Parlett algorithm for computing matrix functions. Zbl 1052.65031
Davies, Philip I.; Higham, Nicholas J.
2003
Newton’s method for the matrix square root. Zbl 0614.65045
Higham, Nicholas J.
1986
Backward error and condition of structured linear systems. Zbl 0747.65028
Higham, Desmond J.; Higham, Nicholas J.
1992
The conditioning of linearizations of matrix polynomials. Zbl 1131.65034
Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise
2006
Numerical analysis of a quadratic matrix equation. Zbl 0966.65040
Higham, Nicholas J.; Kim, Hyun-Min
2000
Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042
Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise
2008
Iterative solution of a nonsymmetric algebraic Riccati equation. Zbl 1146.65035
Guo, Chun-Hua; Higham, Nicholas J.
2008
$$J$$-orthogonal matrices: Properties and generation. Zbl 1034.65026
Higham, Nicholas J.
2003
A survey of condition number estimation for triangular matrices. Zbl 0635.65049
Higham, Nicholas J.
1987
Computing matrix functions. Zbl 1242.65090
Higham, Nicholas J.; Al-Mohy, Awad H.
2010
A survey of componentwise perturbation theory in numerical linear algebra. Zbl 0815.65062
Higham, Nicholas J.
1994
Error analysis of the Björck-Pereyra algorithms for solving Vandermonde systems. Zbl 0595.65029
Higham, Nicholas J.
1987
FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimations. Zbl 0665.65043
Higham, Nicholas J.
1988
Stable iterations for the matrix square root. Zbl 0884.65035
Higham, Nicholas J.
1997
Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems. Zbl 1004.65045
Higham, Nicholas J.; Tisseur, Françoise; Van Dooren, Paul M.
2002
The accuracy of floating point summation. Zbl 0788.65053
Higham, Nicholas J.
1993
A Schur-Newton method for the matrix $$p$$th root and its inverse. Zbl 1128.65030
Guo, Chun-Hua; Higham, Nicholas J.
2006
Solving a quadratic matrix equation by newton’s method with exact line searches. Zbl 1017.65038
Higham, Nicholas J.; Kim, Hyun-Min
2001
The symmetric Procrustes problem. Zbl 0641.65034
Higham, Nicholas J.
1988
More on pseudospectra for polynomial eigenvalue problems and applications in control theory. Zbl 1004.65046
Higham, Nicholas J.; Tisseur, Françoise
2002
The matrix sign decomposition and its relation to the polar decomposition. Zbl 0816.15012
Higham, Nicholas J.
1994
A Schur-Padé algorithm for fractional powers of a matrix. Zbl 1242.65091
Higham, Nicholas J.; Lin, Lijing
2011
A preconditioned Newton algorithm for the nearest correlation matrix. Zbl 1188.65055
Borsdorf, Rüdiger; Higham, Nicholas J.
2010
Algorithms for the matrix $$p$$th root. Zbl 1103.65046
Bini, Dario A.; Higham, Nicholas; Meine, Beatrice
2005
Stability analysis of algorithms for solving confluent Vandermonde-like systems. Zbl 0724.65025
Higham, Nicholas J.
1990
Perturbation theory and backward error for $$AX - XB = C$$. Zbl 0781.65034
Higham, Nicholas J.
1993
An improved Schur-Padé algorithm for fractional powers of a matrix and their Fréchet derivatives. Zbl 1279.65050
Higham, Nicholas J.; Lin, Lijing
2013
Stability of block. Zbl 0834.65010
Demmel, James W.; Higham, Nicholas J.; Schreiber, Robert S.
1995
Efficient algorithms for the matrix cosine and sine. Zbl 1084.65039
Hargreaves, Gareth I.; Higham, Nicholas J.
2005
Solving the indefinite least squares problem by hyperbolic QR factorization. Zbl 1036.65035
Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna
2003
Fast solution of Vandermonde-like systems involving orthogonal polynomials. Zbl 0666.65025
Higham, Nicholas J.
1988
Functions preserving matrix groups and iterations for the matrix square root. Zbl 1079.65053
Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise
2005
Approximating the logarithm of a matrix to specified accuracy. Zbl 0989.65057
Cheng, Sheung Hun; Higham, Nicholas J.; Kenney, Charles S.; Laub, Alan J.
2001
Computing the Fréchet derivative of the matrix exponential, with an application to condition number estimation. Zbl 1180.65049
Al-Mohy, Awad H.; Higham, Nicholas J.
2009
Computing the Fréchet derivative of the matrix logarithm and estimating the condition number. Zbl 1362.65051
Al-Mohy, Awad H.; Higham, Nicholas J.; Relton, Samuel D.
2013
Factorizing complex symmetric matrices with positive definite real and imaginary parts. Zbl 0909.65016
Higham, Nicholas J.
1998
Accelerating the solution of linear systems by iterative refinement in three precisions. Zbl 1453.65067
Carson, Erin; Higham, Nicholas J.
2018
Numerically stable generation of correlation matrices and their factors. Zbl 0969.65036
Davies, Philip I.; Higham, Nicholas J.
2000
Computing the field of values and pseudospectra using the Lanczos method with continuation. Zbl 0861.65033
Braconnier, Thierry; Higham, Nicholas J.
1996
A modified Cholesky algorithm based on a symmetric indefinite factorization. Zbl 0949.65022
Cheng, Sheung Hun; Higham, Nicholas J.
1998
New algorithms for computing the matrix sine and cosine separately or simultaneously. Zbl 1315.65045
Al-Mohy, Awad H.; Higham, Nicholas J.; Relton, Samuel D.
2015
Exploiting fast matrix multiplication within the level 3 BLAS. Zbl 0900.65118
Higham, Nicholas J.
1990
Algorithm 694: A collection of test matrices in MATLAB. Zbl 0900.65120
Higham, Nicholas J.
1991
Detecting and solving hyperbolic quadratic eigenvalue problems. Zbl 1180.65042
Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise
2009
Computing the polar decomposition and the matrix sign decomposition in matrix groups. Zbl 1066.65033
Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise
2004
Large growth factors in Gaussian elimination with pivoting. Zbl 0681.65012
Higham, Nicholas J.; Higham, Desmond J.
1989
An improved arc algorithm for detecting definite Hermitian pairs. Zbl 1202.65054
Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise
2010
A new analysis of iterative refinement and its application to accurate solution of ill-conditioned sparse linear systems. Zbl 1379.65019
Carson, Erin; Higham, Nicholas J.
2017
Estimating the matrix $$p$$-norm. Zbl 0741.65040
Higham, Nicholas J.
1992
A framework for analyzing nonlinear eigenproblems and parametrized linear systems. Zbl 1288.65049
Grammont, Laurence; Higham, Nicholas J.; Tisseur, Françoise
2011
Componentwise perturbation theory for linear systems with multiple right- hand sides. Zbl 0801.65043
Higham, Desmond J.; Higham, Nicholas J.
1992
Improved inverse scaling and squaring algorithms for the matrix logarithm. Zbl 1252.15027
Al-Mohy, Awad H.; Higham, Nicholas J.
2012
A new approach to probabilistic rounding error analysis. Zbl 07123205
Higham, Nicholas J.; Mary, Theo
2019
Anderson acceleration of the alternating projections method for computing the nearest correlation matrix. Zbl 1347.65074
Higham, Nicholas J.; Strabić, Nataša
2016
The complex step approximation to the Fréchet derivative of a matrix function. Zbl 1188.65054
Al-Mohy, Awad H.; Higham, Nicholas J.
2010
Bounding the error in Gaussian elimination for tridiagonal systems. Zbl 0716.65025
Higham, Nicholas J.
1990
Analysis of the Cholesky decomposition of a semi-definite matrix. Zbl 0721.65014
Higham, Nicholas J.
1990
Scaling, sensitivity and stability in the numerical solution of quadratic eigenvalue problems. Zbl 1166.74009
Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise; Garvey, Seamus D.
2008
Accuracy and stability of the null space method for solving the equality constrained least squares problem. Zbl 0924.65033
Cox, Anthony J.; Higham, Nicholas J.
1999
Matlab guide. 2nd ed. Zbl 1067.68180
Higham, Desmond J; Higham, Nicholas J.
2005
Definite matrix polynomials and their linearization by definite pencils. Zbl 1232.65059
Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise
2009
Improved error bounds for undetermined system solvers. Zbl 0770.65025
Demmel, James W.; Higham, Nicholas J.
1993
Experience with a matrix norm estimator. Zbl 0752.65036
Higham, Nicholas J.
1990
Computing the matrix cosine. Zbl 1033.65027
Higham, Nicholas J.; Smith, Matthew I.
2003
Stable and efficient spectral divide and conquer algorithms for the symmetric eigenvalue decomposition and the SVD. Zbl 1326.65049
Nakatsukasa, Yuji; Higham, Nicholas J.
2013
Stability of methods for matrix inversion. Zbl 0748.65021
Du Croz, Jeremy J.; Higham, Nicholas J.
1992
Efficient algorithms for computing the condition number of a tridiagonal matrix. Zbl 0599.65026
Higham, Nicholas J.
1986
Stability of block algorithms with fast level-3 BLAS. Zbl 0892.65016
Demmel, James W.; Higham, Nicholas J.
1992
On $$p$$th roots of stochastic matrices. Zbl 1223.15042
Higham, Nicholas J.; Lin, Lijing
2011
Stability of the diagonal pivoting method with partial pivoting. Zbl 0884.65024
Higham, Nicholas J.
1997
Iterative refinement enhances the stability of $$QR$$ factorization methods for solving linear equations. Zbl 0736.65016
Higham, Nicholas J.
1991
Computing a nearest correlation matrix with factor structure. Zbl 1213.65022
Borsdorf, Rüdiger; Higham, Nicholas J.; Raydan, Marcos
2010
Matlab guide. Zbl 0953.68642
Higham, Desmond J.; Higham, Nicholas J.
2000
Computing $$f(A)b$$ for matrix functions $$f$$. Zbl 1117.65319
Davies, Philip I.; Higham, Nicholas J.
2005
Fast polar decomposition of an arbitrary matrix. Zbl 0711.65024
Higham, Nicholas J.; Schreiber, Robert S.
1990
The canonical generalized polar decomposition. Zbl 1222.15018
Higham, Nicholas J.; Mehl, Christian; Tisseur, Françoise
2010
Finite precision behavior of stationary iteration for solving singular systems. Zbl 0787.65021
Higham, Nicholas J.; Knight, Philip A.
1993
Iterative refinement for linear systems and LAPACK. Zbl 0887.65034
Higham, Nicholas J.
1997
Stability of Householder QR factorization for weighted least squares problems. Zbl 0903.65036
Cox, A. J.; Higham, N. J.
1998
The equality constrained indefinite least squares problem: Theory and algorithms. Zbl 1050.65035
Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna
2003
Arbitrary precision algorithms for computing the matrix cosine and its Fréchet derivative. Zbl 07487115
Al-Mohy, Awad H.; Higham, Nicholas J.; Liu, Xiaobo
2022
Optimizing and factorizing the Wilson matrix. Zbl 07525560
Higham, Nicholas J.; Lettington, Matthew C.
2022
Exploiting lower precision arithmetic in solving symmetric positive definite linear systems and least squares problems. Zbl 1467.65023
Higham, Nicholas J.; Pranesh, Srikara
2021
A multiprecision derivative-free Schur-Parlett algorithm for computing matrix functions. Zbl 1476.65067
Higham, Nicholas J.; Liu, Xiaobo
2021
Integer matrix factorisations, superalgebras and the quadratic form obstruction. Zbl 1467.15009
Higham, Nicholas J.; Lettington, Matthew C.; Schmidt, Karl Michael
2021
Random matrices generating large growth in LU factorization with pivoting. Zbl 1459.65036
Higham, Desmond J.; Higham, Nicholas J.; Pranesh, Srikara
2021
Stochastic rounding and its probabilistic backward error analysis. Zbl 1462.65050
Connolly, Michael P.; Higham, Nicholas J.; Mary, Theo
2021
Generating extreme-scale matrices with specified singular values or condition number. Zbl 1462.65041
Fasi, Massimiliano; Higham, Nicholas J.
2021
Matrices with tunable infinity-norm condition number and no need for pivoting in LU factorization. Zbl 1467.65035
Fasi, Massimiliano; Higham, Nicholas J.
2021
Accurately computing the log-sum-exp and softmax functions. Zbl 07528305
Blanchard, Pierre; Higham, Desmond J.; Higham, Nicholas J.
2021
Mixed precision block fused multiply-add: error analysis and application to GPU tensor cores. Zbl 1452.65425
Blanchard, Pierre; Higham, Nicholas J.; Lopez, Florent; Mary, Theo; Pranesh, Srikara
2020
Three-precision GMRES-based iterative refinement for least squares problems. Zbl 1461.65032
Carson, Erin; Higham, Nicholas J.; Pranesh, Srikara
2020
A class of fast and accurate summation algorithms. Zbl 1471.65035
Blanchard, Pierre; Higham, Nicholas J.; Mary, Theo
2020
Sharper probabilistic backward error analysis for basic linear algebra kernels with random data. Zbl 1452.65090
Higham, Nicholas J.; Mary, Theo
2020
Numerical algorithms for high-performance computational science. Zbl 1462.65231
Dongarra, Jack; Grigori, Laura; Higham, Nicholas J.
2020
Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems. Zbl 1472.65174
Haidar, Azzam; Bayraktar, Harun; Tomov, Stanimire; Dongarra, Jack; Higham, Nicholas J.
2020
A new approach to probabilistic rounding error analysis. Zbl 07123205
Higham, Nicholas J.; Mary, Theo
2019
Squeezing a matrix into half precision, with an application to solving Linear systems. Zbl 1420.65017
Higham, Nicholas J.; Pranesh, Srikara; Zounon, Mawussi
2019
Simulating low precision floating-point arithmetic. Zbl 07124603
Higham, Nicholas J.; Pranesh, Srikara
2019
A new preconditioner that exploits low-rank approximations to factorization error. Zbl 1408.65013
Higham, Nicholas J.; Mary, Theo
2019
An arbitrary precision scaling and squaring algorithm for the matrix exponential. Zbl 1437.65033
Fasi, Massimiliano; Higham, Nicholas J.
2019
Accelerating the solution of linear systems by iterative refinement in three precisions. Zbl 1453.65067
Carson, Erin; Higham, Nicholas J.
2018
Multiprecision algorithms for computing the matrix logarithm. Zbl 1390.15073
Fasi, Massimiliano; Higham, Nicholas J.
2018
Computing the wave-kernel matrix functions. Zbl 1403.65020
2018
A new analysis of iterative refinement and its application to accurate solution of ill-conditioned sparse linear systems. Zbl 1379.65019
Carson, Erin; Higham, Nicholas J.
2017
Matlab guide. 3rd revised and updated edition. Zbl 1357.68001
Higham, Desmond J; Higham, Nicholas J.
2017
Computing the action of trigonometric and hyperbolic matrix functions. Zbl 1365.65135
Higham, Nicholas J.; Kandolf, Peter
2017
Anderson acceleration of the alternating projections method for computing the nearest correlation matrix. Zbl 1347.65074
Higham, Nicholas J.; Strabić, Nataša
2016
Matrix inverse trigonometric and inverse hyperbolic functions: theory and algorithms. Zbl 1388.15012
Aprahamian, Mary; Higham, Nicholas J.
2016
Restoring definiteness via shrinking, with an application to correlation matrices with a fixed block. Zbl 1386.15062
Higham, Nicholas J.; Strabić, Nataša; Šego, Vedran
2016
Estimating the largest elements of a matrix. Zbl 1352.65132
Higham, Nicholas J.; Relton, Samuel D.
2016
Bounds for the distance to the nearest correlation matrix. Zbl 1347.65075
Higham, Nicholas J.; Strabić, Nataša
2016
Testing matrix function algorithms using identities. Zbl 1347.65087
2016
An algorithm to compute the polar decomposition of a $$3 \times 3$$ matrix. Zbl 1353.65020
Higham, Nicholas J.; Noferini, Vanni
2016
New algorithms for computing the matrix sine and cosine separately or simultaneously. Zbl 1315.65045
Al-Mohy, Awad H.; Higham, Nicholas J.; Relton, Samuel D.
2015
An algorithm for the matrix Lambert $$W$$ function. Zbl 1317.65116
Fasi, Massimiliano; Higham, Nicholas J.; Iannazzo, Bruno
2015
The Princeton companion to applied mathematics. Zbl 1327.00002
2015
Matrix functions: a short course. Zbl 1332.15021
Higham, Nicholas J.; Lin, Lijing
2015
Higher order Fréchet derivatives of matrix functions and the level-2 condition number. Zbl 1308.65066
Higham, Nicholas J.; Relton, Samuel D.
2014
The matrix unwinding function, with an application to computing the matrix exponential. Zbl 1300.65024
Aprahamian, Mary; Higham, Nicholas J.
2014
Covariance structure regularization via entropy loss function. Zbl 06983908
Lin, Lijing; Higham, Nicholas J.; Pan, Jianxin
2014
Estimating the condition number of the Fréchet derivative of a matrix function. Zbl 1377.65054
Higham, Nicholas J.; Relton, Samuel D.
2014
NLEVP, a collection of nonlinear eigenvalue problems. Zbl 1295.65140
Betcke, Timo; Higham, Nicholas J.; Mehrmann, Volker; Schröder, Christian; Tisseur, Françoise
2013
An improved Schur-Padé algorithm for fractional powers of a matrix and their Fréchet derivatives. Zbl 1279.65050
Higham, Nicholas J.; Lin, Lijing
2013
Computing the Fréchet derivative of the matrix logarithm and estimating the condition number. Zbl 1362.65051
Al-Mohy, Awad H.; Higham, Nicholas J.; Relton, Samuel D.
2013
Stable and efficient spectral divide and conquer algorithms for the symmetric eigenvalue decomposition and the SVD. Zbl 1326.65049
Nakatsukasa, Yuji; Higham, Nicholas J.
2013
Reducing the influence of tiny normwise relative errors on performance profiles. Zbl 1298.65086
Dingle, Nicholas J.; Higham, Nicholas J.
2013
Improved inverse scaling and squaring algorithms for the matrix logarithm. Zbl 1252.15027
Al-Mohy, Awad H.; Higham, Nicholas J.
2012
Backward stability of iterations for computing the polar decomposition. Zbl 1252.65083
Nakatsukasa, Yuji; Higham, Nicholas J.
2012
Computing the action of the matrix exponential, with an application to exponential integrators. Zbl 1234.65028
Al-Mohy, Awad H.; Higham, Nicholas J.
2011
A Schur-Padé algorithm for fractional powers of a matrix. Zbl 1242.65091
Higham, Nicholas J.; Lin, Lijing
2011
A framework for analyzing nonlinear eigenproblems and parametrized linear systems. Zbl 1288.65049
Grammont, Laurence; Higham, Nicholas J.; Tisseur, Françoise
2011
On $$p$$th roots of stochastic matrices. Zbl 1223.15042
Higham, Nicholas J.; Lin, Lijing
2011
A new scaling and squaring algorithm for the matrix exponential. Zbl 1194.15021
Al-Mohy, Awad H.; Higham, Nicholas J.
2010
Computing matrix functions. Zbl 1242.65090
Higham, Nicholas J.; Al-Mohy, Awad H.
2010
A preconditioned Newton algorithm for the nearest correlation matrix. Zbl 1188.65055
Borsdorf, Rüdiger; Higham, Nicholas J.
2010
An improved arc algorithm for detecting definite Hermitian pairs. Zbl 1202.65054
Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise
2010
The complex step approximation to the Fréchet derivative of a matrix function. Zbl 1188.65054
Al-Mohy, Awad H.; Higham, Nicholas J.
2010
Computing a nearest correlation matrix with factor structure. Zbl 1213.65022
Borsdorf, Rüdiger; Higham, Nicholas J.; Raydan, Marcos
2010
The canonical generalized polar decomposition. Zbl 1222.15018
Higham, Nicholas J.; Mehl, Christian; Tisseur, Françoise
2010
The scaling and squaring method for the matrix exponential revisited. Zbl 1178.65040
Higham, Nicholas J.
2009
Computing the Fréchet derivative of the matrix exponential, with an application to condition number estimation. Zbl 1180.65049
Al-Mohy, Awad H.; Higham, Nicholas J.
2009
Detecting and solving hyperbolic quadratic eigenvalue problems. Zbl 1180.65042
Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise
2009
Definite matrix polynomials and their linearization by definite pencils. Zbl 1232.65059
Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise
2009
Functions of matrices. Theory and computation. Zbl 1167.15001
Higham, Nicholas J.
2008
Computing $$A^\alpha, \log(A)$$, and related matrix functions by contour integrals. Zbl 1176.65053
Hale, Nicholas; Higham, Nicholas J.; Trefethen, Lloyd N.
2008
Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042
Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise
2008
Iterative solution of a nonsymmetric algebraic Riccati equation. Zbl 1146.65035
Guo, Chun-Hua; Higham, Nicholas J.
2008
Scaling, sensitivity and stability in the numerical solution of quadratic eigenvalue problems. Zbl 1166.74009
Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise; Garvey, Seamus D.
2008
The solution of $$s\exp(s)=a$$ is not always the Lambert $$w$$ function of $$a$$. Zbl 1190.34072
Corless, Robert M.; Ding, Hui; Higham, Nicholas J.; Jeffrey, David J.
2007
Milestones in matrix computation. The selected works of Gene H. Golub. With commentaries by Anne Greenbaum, Åke Björk, Nicholas Higham, Walter Gautschi and G. W. Stewart. Edited by Raymond H. Chan, Chen Greif, and Dianne P. O’Leary. Zbl 1121.65031
Golub, Gene H.
2007
Symmetric linearizations for matrix polynomials. Zbl 1137.15006
Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise
2006
The conditioning of linearizations of matrix polynomials. Zbl 1131.65034
Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise
2006
A Schur-Newton method for the matrix $$p$$th root and its inverse. Zbl 1128.65030
Guo, Chun-Hua; Higham, Nicholas J.
2006
The scaling and squaring method for the matrix exponential revisited. Zbl 1081.65037
Higham, Nicholas J.
2005
Algorithms for the matrix $$p$$th root. Zbl 1103.65046
Bini, Dario A.; Higham, Nicholas; Meine, Beatrice
2005
Efficient algorithms for the matrix cosine and sine. Zbl 1084.65039
Hargreaves, Gareth I.; Higham, Nicholas J.
2005
Functions preserving matrix groups and iterations for the matrix square root. Zbl 1079.65053
Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise
2005
Matlab guide. 2nd ed. Zbl 1067.68180
Higham, Desmond J; Higham, Nicholas J.
2005
Computing $$f(A)b$$ for matrix functions $$f$$. Zbl 1117.65319
Davies, Philip I.; Higham, Nicholas J.
2005
The numerical stability of barycentric Lagrange interpolation. Zbl 1067.65016
Higham, Nicholas J.
2004
Computing the polar decomposition and the matrix sign decomposition in matrix groups. Zbl 1066.65033
Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise
2004
Bounds for eigenvalues of matrix polynomials. Zbl 1055.15030
Higham, Nicholas J.; Tisseur, Françoise
2003
A Schur-Parlett algorithm for computing matrix functions. Zbl 1052.65031
Davies, Philip I.; Higham, Nicholas J.
2003
$$J$$-orthogonal matrices: Properties and generation. Zbl 1034.65026
Higham, Nicholas J.
2003
Solving the indefinite least squares problem by hyperbolic QR factorization. Zbl 1036.65035
Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna
2003
Computing the matrix cosine. Zbl 1033.65027
Higham, Nicholas J.; Smith, Matthew I.
2003
The equality constrained indefinite least squares problem: Theory and algorithms. Zbl 1050.65035
Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna
2003
Accuracy and stability of numerical algorithms. 2nd ed. Zbl 1011.65010
Higham, Nicholas J.
2002
Computing the nearest correlation matrix – a problem from finance. Zbl 1006.65036
Higham, Nicholas J.
2002
Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems. Zbl 1004.65045
Higham, Nicholas J.; Tisseur, Françoise; Van Dooren, Paul M.
2002
More on pseudospectra for polynomial eigenvalue problems and applications in control theory. Zbl 1004.65046
Higham, Nicholas J.; Tisseur, Françoise
2002
Structured pseudospectra for polynomial eigenvalue problems, with applications. Zbl 0996.65042
Tisseur, Françoise; Higham, Nicholas J.
2001
Solving a quadratic matrix equation by newton’s method with exact line searches. Zbl 1017.65038
Higham, Nicholas J.; Kim, Hyun-Min
2001
Approximating the logarithm of a matrix to specified accuracy. Zbl 0989.65057
Cheng, Sheung Hun; Higham, Nicholas J.; Kenney, Charles S.; Laub, Alan J.
2001
Evaluating Padé approximants of the matrix logarithm. Zbl 0989.65054
Higham, Nicholas J.
2001
Analysis of the Cholesky method with iterative refinement for solving the symmetric definite generalized eigenproblem. Zbl 1002.65044
Davies, Philip I.; Higham, Nicholas J.; Tisseur, Françoise
2001
A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra. Zbl 0959.65061
Higham, Nicholas J.; Tisseur, Françoise
2000
Numerical analysis of a quadratic matrix equation. Zbl 0966.65040
Higham, Nicholas J.; Kim, Hyun-Min
2000
Numerically stable generation of correlation matrices and their factors. Zbl 0969.65036
Davies, Philip I.; Higham, Nicholas J.
2000
...and 64 more Documents
all top 5

### Cited by 4,040 Authors

 57 Higham, Nicholas J. 57 Wei, Yimin 35 Peña, Juan Manuel 33 Dopico, Froilán M. 28 Kressner, Daniel 28 Rump, Siegfried Michael 26 Reichel, Lothar 24 Li, Rencang 24 Miyajima, Shinya 24 Tisseur, Françoise 23 Diao, Huaian 23 Nakatsukasa, Yuji 21 Bini, Dario Andrea 21 Li, Hanyu 21 Mehrmann, Volker 20 Ogita, Takeshi 19 Ibáñez González, Jacinto Javier 19 Noferini, Vanni 18 Van Dooren, Paul M. 17 Benner, Peter 17 Defez, Emilio 17 Sastre, Jorge 17 Soleymani, Fazlollah 16 Benzi, Michele 16 Rozlozník, Miroslav 15 Melman, Aaron 15 Simoncini, Valeria 14 Alonso, Pedro 14 Iannazzo, Bruno 14 Meini, Beatrice 14 Poloni, Federico G. 13 Graillat, Stef 13 Huang, Rong 13 Mackey, D. Steven 13 Oishi, Shin’ichi 13 Robol, Leonardo 13 Wu, Xinyuan 12 Cardoso, João R. 12 Corless, Robert Malcolm 12 Delgado, Jorge F. M. 12 Faßbender, Heike 12 Guo, Chun-Hua 12 Hu, Xiyan 12 Vabishchevich, Pëtr Nikolaevich 11 Jarlebring, Elias 11 Kim, Hyunmin 11 Marco García, Ana 11 Noschese, Silvia 11 Pérez, Javier J. 11 Smoktunowicz, Alicja 10 Cucker, Felipe 10 de Terán, Fernando 10 Gemignani, Luca 10 Gratton, Serge 10 Li, Wen 10 Lin, Wen-Wei 10 Liu, Qiaohua 10 Liu, Xinguo 10 Martínez, José-Javier 10 Mitrouli, Marilena 10 Ostermann, Alexander 10 Ozaki, Katsuhisa 10 Psarrakos, Panayiotis J. 10 Raydan, Marcos 10 Szyld, Daniel B. 10 Wang, Shaoxin 10 Wei, Musheng 10 Yang, Hu 10 Ziętak, Krystyna 9 Alam, Rafikul 9 Dongarra, Jack J. 9 Estrada, Ernesto 9 Fasi, Massimiliano 9 Frommer, Andreas 9 Liao, Anping 9 Massei, Stefano 9 Olshevsky, Vadim 9 Stanimirović, Predrag S. 9 Vandebril, Raf 9 Wang, Weiguo 9 Zhang, Lei 8 Bueno, María Isabel 8 Caliari, Marco 8 Dehghan Takht Fooladi, Mehdi 8 Duan, Xuefeng 8 Güttel, Stefan 8 Higham, Desmond J. 8 Huang, Ting-Zhu 8 Jeannerod, Claude-Pierre 8 Lin, Yiqin 8 Lu, Linzhang 8 Mehl, Christian 8 Neff, Patrizio 8 Novati, Paolo 8 Pan, Victor Yakovlevich 8 Peinado, Jesús 8 Ruiz, Pedro A. 8 Sadkane, Miloud 8 Sun, Defeng 8 Sun, Jiguang ...and 3,940 more Authors
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### Cited in 431 Serials

 408 Linear Algebra and its Applications 243 Journal of Computational and Applied Mathematics 128 Applied Mathematics and Computation 127 SIAM Journal on Matrix Analysis and Applications 121 Numerical Algorithms 111 BIT 97 SIAM Journal on Scientific Computing 76 Numerical Linear Algebra with Applications 72 Journal of Computational Physics 70 Computers & Mathematics with Applications 68 Applied Numerical Mathematics 64 Mathematics of Computation 63 Numerische Mathematik 36 Linear and Multilinear Algebra 32 Journal of Scientific Computing 31 Calcolo 31 International Journal of Computer Mathematics 28 Applied Mathematics Letters 26 Computer Methods in Applied Mechanics and Engineering 26 ELA. The Electronic Journal of Linear Algebra 23 Japan Journal of Industrial and Applied Mathematics 21 Automatica 21 Mathematical Programming. Series A. Series B 20 Advances in Computational Mathematics 19 Computational Optimization and Applications 18 Mathematics and Computers in Simulation 18 Theoretical Computer Science 18 SIAM Journal on Optimization 18 ETNA. Electronic Transactions on Numerical Analysis 17 Journal of Mathematical Analysis and Applications 17 Journal of Optimization Theory and Applications 17 SIAM Review 17 Computational and Applied Mathematics 16 SIAM Journal on Numerical Analysis 14 Computing 13 Computer Physics Communications 13 ACM Transactions on Mathematical Software 13 Journal of Complexity 12 Journal of Multivariate Analysis 12 Mathematical and Computer Modelling 12 Applied Mathematical Modelling 12 Abstract and Applied Analysis 11 Optimization Methods & Software 10 Journal of Symbolic Computation 10 Computational Statistics and Data Analysis 10 Journal of Applied Mathematics and Computing 9 International Journal of Control 9 Journal of the Franklin Institute 9 Systems & Control Letters 9 Mathematical Problems in Engineering 9 Quantitative Finance 9 Special Matrices 8 International Journal for Numerical Methods in Engineering 8 Computer Aided Geometric Design 8 European Journal of Operational Research 8 Foundations of Computational Mathematics 8 Journal of Applied Mathematics 8 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 7 Neural Computation 7 Computational Statistics 7 Engineering Analysis with Boundary Elements 7 Operators and Matrices 7 Statistics and Computing 7 JSIAM Letters 6 Journal of Mathematical Physics 6 Journal of Approximation Theory 6 Statistics & Probability Letters 6 Optimization 6 Computational Mechanics 6 Journal of Mathematical Imaging and Vision 6 Applied and Computational Harmonic Analysis 6 Nonlinear Dynamics 6 Communications in Nonlinear Science and Numerical Simulation 6 Lobachevskii Journal of Mathematics 6 Mediterranean Journal of Mathematics 6 Acta Numerica 6 Communications in Computational Physics 6 The Annals of Applied Statistics 6 Mathematical Programming Computation 5 Inverse Problems 5 Kybernetika 5 Numerical Functional Analysis and Optimization 5 Proceedings of the American Mathematical Society 5 Operations Research Letters 5 Annals of Operations Research 5 Journal of Global Optimization 5 Computational Mathematics and Mathematical Physics 5 Communications in Statistics. Simulation and Computation 5 Journal of Mathematical Sciences (New York) 5 Advances in Applied Clifford Algebras 5 Methodology and Computing in Applied Probability 5 Computational Methods in Applied Mathematics 5 Stochastic Models 5 Optimization Letters 5 S$$\vec{\text{e}}$$MA Journal 5 East Asian Journal on Applied Mathematics 5 Journal of Function Spaces 4 Journal of Fluid Mechanics 4 Scandinavian Journal of Statistics 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik ...and 331 more Serials
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### Cited in 60 Fields

 2,273 Numerical analysis (65-XX) 1,133 Linear and multilinear algebra; matrix theory (15-XX) 264 Operations research, mathematical programming (90-XX) 174 Statistics (62-XX) 172 Partial differential equations (35-XX) 155 Systems theory; control (93-XX) 148 Ordinary differential equations (34-XX) 134 Computer science (68-XX) 126 Operator theory (47-XX) 120 Approximations and expansions (41-XX) 103 Probability theory and stochastic processes (60-XX) 75 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 74 Calculus of variations and optimal control; optimization (49-XX) 69 Fluid mechanics (76-XX) 68 Combinatorics (05-XX) 61 Mechanics of deformable solids (74-XX) 53 Real functions (26-XX) 53 Biology and other natural sciences (92-XX) 50 Dynamical systems and ergodic theory (37-XX) 48 Special functions (33-XX) 46 Quantum theory (81-XX) 45 Functions of a complex variable (30-XX) 40 Information and communication theory, circuits (94-XX) 36 Mechanics of particles and systems (70-XX) 32 Number theory (11-XX) 31 Harmonic analysis on Euclidean spaces (42-XX) 29 Field theory and polynomials (12-XX) 27 Differential geometry (53-XX) 24 Statistical mechanics, structure of matter (82-XX) 22 Geophysics (86-XX) 21 Integral equations (45-XX) 21 Optics, electromagnetic theory (78-XX) 19 Functional analysis (46-XX) 18 Commutative algebra (13-XX) 17 Algebraic geometry (14-XX) 15 Difference and functional equations (39-XX) 15 Integral transforms, operational calculus (44-XX) 12 Global analysis, analysis on manifolds (58-XX) 10 Relativity and gravitational theory (83-XX) 9 Associative rings and algebras (16-XX) 8 History and biography (01-XX) 8 Convex and discrete geometry (52-XX) 6 Geometry (51-XX) 5 General and overarching topics; collections (00-XX) 5 Mathematics education (97-XX) 4 Mathematical logic and foundations (03-XX) 4 Topological groups, Lie groups (22-XX) 4 Potential theory (31-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Classical thermodynamics, heat transfer (80-XX) 4 Astronomy and astrophysics (85-XX) 3 Group theory and generalizations (20-XX) 3 Sequences, series, summability (40-XX) 2 General algebraic systems (08-XX) 2 Nonassociative rings and algebras (17-XX) 2 Measure and integration (28-XX) 2 General topology (54-XX) 2 Algebraic topology (55-XX) 2 Manifolds and cell complexes (57-XX) 1 $$K$$-theory (19-XX)

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