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Higham, Nicholas J.

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Published as: Higham, Nicholas J.; Higham, N. J.; Higham, Nicholas; Higham, Nick
Homepage: https://nhigham.com/
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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.

Publications by Year

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.
685
2002
Functions of matrices. Theory and computation. Zbl 1167.15001
Higham, Nicholas J.
586
2008
Accuracy and stability of numerical algorithms. Zbl 0847.65010
Higham, Nicholas J.
302
1996
Computing the nearest correlation matrix – a problem from finance. Zbl 1006.65036
Higham, Nicholas J.
148
2002
Computing a nearest symmetric positive semidefinite matrix. Zbl 0649.65026
Higham, Nicholas J.
134
1988
Computing the action of the matrix exponential, with an application to exponential integrators. Zbl 1234.65028
Al-Mohy, Awad H.; Higham, Nicholas J.
115
2011
The scaling and squaring method for the matrix exponential revisited. Zbl 1081.65037
Higham, Nicholas J.
107
2005
NLEVP, a collection of nonlinear eigenvalue problems. Zbl 1295.65140
Betcke, Timo; Higham, Nicholas J.; Mehrmann, Volker; Schröder, Christian; Tisseur, Françoise
101
2013
The numerical stability of barycentric Lagrange interpolation. Zbl 1067.65016
Higham, Nicholas J.
88
2004
Computing the polar decomposition - with applications. Zbl 0607.65014
Higham, Nicholas J.
79
1986
A new scaling and squaring algorithm for the matrix exponential. Zbl 1194.15021
Al-Mohy, Awad H.; Higham, Nicholas J.
73
2010
Computing \(A^\alpha, \log(A)\), and related matrix functions by contour integrals. Zbl 1176.65053
Hale, Nicholas; Higham, Nicholas J.; Trefethen, Lloyd N.
68
2008
Matrix nearness problems and applications. Zbl 0681.65029
Higham, N. J.
61
1989
Computing real square roots of a real matrix. Zbl 0625.65032
Higham, Nicholas J.
56
1987
Symmetric linearizations for matrix polynomials. Zbl 1137.15006
Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise
55
2006
The scaling and squaring method for the matrix exponential revisited. Zbl 1178.65040
Higham, Nicholas J.
51
2009
Structured pseudospectra for polynomial eigenvalue problems, with applications. Zbl 0996.65042
Tisseur, Françoise; Higham, Nicholas J.
50
2001
Structured backward error and condition of generalized eigenvalue problems. Zbl 0935.65032
Higham, Desmond J.; Higham, Nicholas J.
49
1998
A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra. Zbl 0959.65061
Higham, Nicholas J.; Tisseur, Françoise
46
2000
Bounds for eigenvalues of matrix polynomials. Zbl 1055.15030
Higham, Nicholas J.; Tisseur, Françoise
46
2003
A Schur-Parlett algorithm for computing matrix functions. Zbl 1052.65031
Davies, Philip I.; Higham, Nicholas J.
43
2003
Newton’s method for the matrix square root. Zbl 0614.65045
Higham, Nicholas J.
42
1986
Backward error and condition of structured linear systems. Zbl 0747.65028
Higham, Desmond J.; Higham, Nicholas J.
42
1992
The conditioning of linearizations of matrix polynomials. Zbl 1131.65034
Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise
42
2006
Numerical analysis of a quadratic matrix equation. Zbl 0966.65040
Higham, Nicholas J.; Kim, Hyun-Min
41
2000
Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042
Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise
41
2008
Iterative solution of a nonsymmetric algebraic Riccati equation. Zbl 1146.65035
Guo, Chun-Hua; Higham, Nicholas J.
39
2008
\(J\)-orthogonal matrices: Properties and generation. Zbl 1034.65026
Higham, Nicholas J.
37
2003
A survey of condition number estimation for triangular matrices. Zbl 0635.65049
Higham, Nicholas J.
36
1987
Computing matrix functions. Zbl 1242.65090
Higham, Nicholas J.; Al-Mohy, Awad H.
35
2010
A survey of componentwise perturbation theory in numerical linear algebra. Zbl 0815.65062
Higham, Nicholas J.
34
1994
Error analysis of the Björck-Pereyra algorithms for solving Vandermonde systems. Zbl 0595.65029
Higham, Nicholas J.
33
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.
32
1988
Stable iterations for the matrix square root. Zbl 0884.65035
Higham, Nicholas J.
32
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.
30
2002
The accuracy of floating point summation. Zbl 0788.65053
Higham, Nicholas J.
30
1993
A Schur-Newton method for the matrix \(p\)th root and its inverse. Zbl 1128.65030
Guo, Chun-Hua; Higham, Nicholas J.
29
2006
Solving a quadratic matrix equation by newton’s method with exact line searches. Zbl 1017.65038
Higham, Nicholas J.; Kim, Hyun-Min
28
2001
The symmetric Procrustes problem. Zbl 0641.65034
Higham, Nicholas J.
27
1988
More on pseudospectra for polynomial eigenvalue problems and applications in control theory. Zbl 1004.65046
Higham, Nicholas J.; Tisseur, Françoise
27
2002
The matrix sign decomposition and its relation to the polar decomposition. Zbl 0816.15012
Higham, Nicholas J.
26
1994
A Schur-Padé algorithm for fractional powers of a matrix. Zbl 1242.65091
Higham, Nicholas J.; Lin, Lijing
26
2011
A preconditioned Newton algorithm for the nearest correlation matrix. Zbl 1188.65055
Borsdorf, Rüdiger; Higham, Nicholas J.
26
2010
Algorithms for the matrix \(p\)th root. Zbl 1103.65046
Bini, Dario A.; Higham, Nicholas; Meine, Beatrice
26
2005
Stability analysis of algorithms for solving confluent Vandermonde-like systems. Zbl 0724.65025
Higham, Nicholas J.
25
1990
Perturbation theory and backward error for \(AX - XB = C\). Zbl 0781.65034
Higham, Nicholas J.
25
1993
An improved Schur-Padé algorithm for fractional powers of a matrix and their Fréchet derivatives. Zbl 1279.65050
Higham, Nicholas J.; Lin, Lijing
25
2013
Stability of block. Zbl 0834.65010
Demmel, James W.; Higham, Nicholas J.; Schreiber, Robert S.
24
1995
Efficient algorithms for the matrix cosine and sine. Zbl 1084.65039
Hargreaves, Gareth I.; Higham, Nicholas J.
24
2005
Solving the indefinite least squares problem by hyperbolic QR factorization. Zbl 1036.65035
Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna
24
2003
Fast solution of Vandermonde-like systems involving orthogonal polynomials. Zbl 0666.65025
Higham, Nicholas J.
23
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
23
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.
23
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.
22
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.
22
2013
Factorizing complex symmetric matrices with positive definite real and imaginary parts. Zbl 0909.65016
Higham, Nicholas J.
21
1998
Accelerating the solution of linear systems by iterative refinement in three precisions. Zbl 1453.65067
Carson, Erin; Higham, Nicholas J.
21
2018
Numerically stable generation of correlation matrices and their factors. Zbl 0969.65036
Davies, Philip I.; Higham, Nicholas J.
20
2000
Computing the field of values and pseudospectra using the Lanczos method with continuation. Zbl 0861.65033
Braconnier, Thierry; Higham, Nicholas J.
19
1996
A modified Cholesky algorithm based on a symmetric indefinite factorization. Zbl 0949.65022
Cheng, Sheung Hun; Higham, Nicholas J.
19
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.
18
2015
Exploiting fast matrix multiplication within the level 3 BLAS. Zbl 0900.65118
Higham, Nicholas J.
18
1990
Algorithm 694: A collection of test matrices in MATLAB. Zbl 0900.65120
Higham, Nicholas J.
18
1991
Detecting and solving hyperbolic quadratic eigenvalue problems. Zbl 1180.65042
Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise
17
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
17
2004
Large growth factors in Gaussian elimination with pivoting. Zbl 0681.65012
Higham, Nicholas J.; Higham, Desmond J.
17
1989
An improved arc algorithm for detecting definite Hermitian pairs. Zbl 1202.65054
Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise
17
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.
17
2017
Estimating the matrix \(p\)-norm. Zbl 0741.65040
Higham, Nicholas J.
16
1992
A framework for analyzing nonlinear eigenproblems and parametrized linear systems. Zbl 1288.65049
Grammont, Laurence; Higham, Nicholas J.; Tisseur, Françoise
16
2011
Componentwise perturbation theory for linear systems with multiple right- hand sides. Zbl 0801.65043
Higham, Desmond J.; Higham, Nicholas J.
16
1992
Improved inverse scaling and squaring algorithms for the matrix logarithm. Zbl 1252.15027
Al-Mohy, Awad H.; Higham, Nicholas J.
16
2012
A new approach to probabilistic rounding error analysis. Zbl 07123205
Higham, Nicholas J.; Mary, Theo
16
2019
Anderson acceleration of the alternating projections method for computing the nearest correlation matrix. Zbl 1347.65074
Higham, Nicholas J.; Strabić, Nataša
15
2016
The complex step approximation to the Fréchet derivative of a matrix function. Zbl 1188.65054
Al-Mohy, Awad H.; Higham, Nicholas J.
15
2010
Bounding the error in Gaussian elimination for tridiagonal systems. Zbl 0716.65025
Higham, Nicholas J.
15
1990
Analysis of the Cholesky decomposition of a semi-definite matrix. Zbl 0721.65014
Higham, Nicholas J.
15
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.
15
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.
15
1999
Matlab guide. 2nd ed. Zbl 1067.68180
Higham, Desmond J; Higham, Nicholas J.
14
2005
Definite matrix polynomials and their linearization by definite pencils. Zbl 1232.65059
Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise
14
2009
Improved error bounds for undetermined system solvers. Zbl 0770.65025
Demmel, James W.; Higham, Nicholas J.
14
1993
Experience with a matrix norm estimator. Zbl 0752.65036
Higham, Nicholas J.
14
1990
Computing the matrix cosine. Zbl 1033.65027
Higham, Nicholas J.; Smith, Matthew I.
14
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.
13
2013
Stability of methods for matrix inversion. Zbl 0748.65021
Du Croz, Jeremy J.; Higham, Nicholas J.
13
1992
Efficient algorithms for computing the condition number of a tridiagonal matrix. Zbl 0599.65026
Higham, Nicholas J.
13
1986
Stability of block algorithms with fast level-3 BLAS. Zbl 0892.65016
Demmel, James W.; Higham, Nicholas J.
13
1992
On \(p\)th roots of stochastic matrices. Zbl 1223.15042
Higham, Nicholas J.; Lin, Lijing
12
2011
Stability of the diagonal pivoting method with partial pivoting. Zbl 0884.65024
Higham, Nicholas J.
12
1997
Iterative refinement enhances the stability of \(QR\) factorization methods for solving linear equations. Zbl 0736.65016
Higham, Nicholas J.
12
1991
Computing a nearest correlation matrix with factor structure. Zbl 1213.65022
Borsdorf, Rüdiger; Higham, Nicholas J.; Raydan, Marcos
12
2010
Matlab guide. Zbl 0953.68642
Higham, Desmond J.; Higham, Nicholas J.
11
2000
Computing \(f(A)b\) for matrix functions \(f\). Zbl 1117.65319
Davies, Philip I.; Higham, Nicholas J.
11
2005
Fast polar decomposition of an arbitrary matrix. Zbl 0711.65024
Higham, Nicholas J.; Schreiber, Robert S.
11
1990
The canonical generalized polar decomposition. Zbl 1222.15018
Higham, Nicholas J.; Mehl, Christian; Tisseur, Françoise
11
2010
Finite precision behavior of stationary iteration for solving singular systems. Zbl 0787.65021
Higham, Nicholas J.; Knight, Philip A.
11
1993
Iterative refinement for linear systems and LAPACK. Zbl 0887.65034
Higham, Nicholas J.
11
1997
Stability of Householder QR factorization for weighted least squares problems. Zbl 0903.65036
Cox, A. J.; Higham, N. J.
11
1998
The equality constrained indefinite least squares problem: Theory and algorithms. Zbl 1050.65035
Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna
11
2003
Arbitrary precision algorithms for computing the matrix cosine and its Fréchet derivative. Zbl 07487115
Al-Mohy, Awad H.; Higham, Nicholas J.; Liu, Xiaobo
1
2022
Optimizing and factorizing the Wilson matrix. Zbl 07525560
Higham, Nicholas J.; Lettington, Matthew C.
1
2022
Exploiting lower precision arithmetic in solving symmetric positive definite linear systems and least squares problems. Zbl 1467.65023
Higham, Nicholas J.; Pranesh, Srikara
4
2021
A multiprecision derivative-free Schur-Parlett algorithm for computing matrix functions. Zbl 1476.65067
Higham, Nicholas J.; Liu, Xiaobo
4
2021
Integer matrix factorisations, superalgebras and the quadratic form obstruction. Zbl 1467.15009
Higham, Nicholas J.; Lettington, Matthew C.; Schmidt, Karl Michael
2
2021
Random matrices generating large growth in LU factorization with pivoting. Zbl 1459.65036
Higham, Desmond J.; Higham, Nicholas J.; Pranesh, Srikara
1
2021
Stochastic rounding and its probabilistic backward error analysis. Zbl 1462.65050
Connolly, Michael P.; Higham, Nicholas J.; Mary, Theo
1
2021
Generating extreme-scale matrices with specified singular values or condition number. Zbl 1462.65041
Fasi, Massimiliano; Higham, Nicholas J.
1
2021
Matrices with tunable infinity-norm condition number and no need for pivoting in LU factorization. Zbl 1467.65035
Fasi, Massimiliano; Higham, Nicholas J.
1
2021
Accurately computing the log-sum-exp and softmax functions. Zbl 07528305
Blanchard, Pierre; Higham, Desmond J.; Higham, Nicholas J.
1
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
6
2020
Three-precision GMRES-based iterative refinement for least squares problems. Zbl 1461.65032
Carson, Erin; Higham, Nicholas J.; Pranesh, Srikara
3
2020
A class of fast and accurate summation algorithms. Zbl 1471.65035
Blanchard, Pierre; Higham, Nicholas J.; Mary, Theo
2
2020
Sharper probabilistic backward error analysis for basic linear algebra kernels with random data. Zbl 1452.65090
Higham, Nicholas J.; Mary, Theo
2
2020
Numerical algorithms for high-performance computational science. Zbl 1462.65231
Dongarra, Jack; Grigori, Laura; Higham, Nicholas J.
2
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.
1
2020
A new approach to probabilistic rounding error analysis. Zbl 07123205
Higham, Nicholas J.; Mary, Theo
16
2019
Squeezing a matrix into half precision, with an application to solving Linear systems. Zbl 1420.65017
Higham, Nicholas J.; Pranesh, Srikara; Zounon, Mawussi
11
2019
Simulating low precision floating-point arithmetic. Zbl 07124603
Higham, Nicholas J.; Pranesh, Srikara
9
2019
A new preconditioner that exploits low-rank approximations to factorization error. Zbl 1408.65013
Higham, Nicholas J.; Mary, Theo
6
2019
An arbitrary precision scaling and squaring algorithm for the matrix exponential. Zbl 1437.65033
Fasi, Massimiliano; Higham, Nicholas J.
2
2019
Accelerating the solution of linear systems by iterative refinement in three precisions. Zbl 1453.65067
Carson, Erin; Higham, Nicholas J.
21
2018
Multiprecision algorithms for computing the matrix logarithm. Zbl 1390.15073
Fasi, Massimiliano; Higham, Nicholas J.
5
2018
Computing the wave-kernel matrix functions. Zbl 1403.65020
Nadukandi, Prashanth; Higham, Nicholas J.
3
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.
17
2017
Matlab guide. 3rd revised and updated edition. Zbl 1357.68001
Higham, Desmond J; Higham, Nicholas J.
7
2017
Computing the action of trigonometric and hyperbolic matrix functions. Zbl 1365.65135
Higham, Nicholas J.; Kandolf, Peter
7
2017
Anderson acceleration of the alternating projections method for computing the nearest correlation matrix. Zbl 1347.65074
Higham, Nicholas J.; Strabić, Nataša
15
2016
Matrix inverse trigonometric and inverse hyperbolic functions: theory and algorithms. Zbl 1388.15012
Aprahamian, Mary; Higham, Nicholas J.
9
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
7
2016
Estimating the largest elements of a matrix. Zbl 1352.65132
Higham, Nicholas J.; Relton, Samuel D.
3
2016
Bounds for the distance to the nearest correlation matrix. Zbl 1347.65075
Higham, Nicholas J.; Strabić, Nataša
2
2016
Testing matrix function algorithms using identities. Zbl 1347.65087
Deadman, Edvin; Higham, Nicholas J.
2
2016
An algorithm to compute the polar decomposition of a \(3 \times 3\) matrix. Zbl 1353.65020
Higham, Nicholas J.; Noferini, Vanni
2
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.
18
2015
An algorithm for the matrix Lambert \(W\) function. Zbl 1317.65116
Fasi, Massimiliano; Higham, Nicholas J.; Iannazzo, Bruno
10
2015
The Princeton companion to applied mathematics. Zbl 1327.00002
4
2015
Matrix functions: a short course. Zbl 1332.15021
Higham, Nicholas J.; Lin, Lijing
1
2015
Higher order Fréchet derivatives of matrix functions and the level-2 condition number. Zbl 1308.65066
Higham, Nicholas J.; Relton, Samuel D.
7
2014
The matrix unwinding function, with an application to computing the matrix exponential. Zbl 1300.65024
Aprahamian, Mary; Higham, Nicholas J.
6
2014
Covariance structure regularization via entropy loss function. Zbl 06983908
Lin, Lijing; Higham, Nicholas J.; Pan, Jianxin
5
2014
Estimating the condition number of the Fréchet derivative of a matrix function. Zbl 1377.65054
Higham, Nicholas J.; Relton, Samuel D.
3
2014
NLEVP, a collection of nonlinear eigenvalue problems. Zbl 1295.65140
Betcke, Timo; Higham, Nicholas J.; Mehrmann, Volker; Schröder, Christian; Tisseur, Françoise
101
2013
An improved Schur-Padé algorithm for fractional powers of a matrix and their Fréchet derivatives. Zbl 1279.65050
Higham, Nicholas J.; Lin, Lijing
25
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.
22
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.
13
2013
Reducing the influence of tiny normwise relative errors on performance profiles. Zbl 1298.65086
Dingle, Nicholas J.; Higham, Nicholas J.
6
2013
Improved inverse scaling and squaring algorithms for the matrix logarithm. Zbl 1252.15027
Al-Mohy, Awad H.; Higham, Nicholas J.
16
2012
Backward stability of iterations for computing the polar decomposition. Zbl 1252.65083
Nakatsukasa, Yuji; Higham, Nicholas J.
7
2012
Computing the action of the matrix exponential, with an application to exponential integrators. Zbl 1234.65028
Al-Mohy, Awad H.; Higham, Nicholas J.
115
2011
A Schur-Padé algorithm for fractional powers of a matrix. Zbl 1242.65091
Higham, Nicholas J.; Lin, Lijing
26
2011
A framework for analyzing nonlinear eigenproblems and parametrized linear systems. Zbl 1288.65049
Grammont, Laurence; Higham, Nicholas J.; Tisseur, Françoise
16
2011
On \(p\)th roots of stochastic matrices. Zbl 1223.15042
Higham, Nicholas J.; Lin, Lijing
12
2011
A new scaling and squaring algorithm for the matrix exponential. Zbl 1194.15021
Al-Mohy, Awad H.; Higham, Nicholas J.
73
2010
Computing matrix functions. Zbl 1242.65090
Higham, Nicholas J.; Al-Mohy, Awad H.
35
2010
A preconditioned Newton algorithm for the nearest correlation matrix. Zbl 1188.65055
Borsdorf, Rüdiger; Higham, Nicholas J.
26
2010
An improved arc algorithm for detecting definite Hermitian pairs. Zbl 1202.65054
Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise
17
2010
The complex step approximation to the Fréchet derivative of a matrix function. Zbl 1188.65054
Al-Mohy, Awad H.; Higham, Nicholas J.
15
2010
Computing a nearest correlation matrix with factor structure. Zbl 1213.65022
Borsdorf, Rüdiger; Higham, Nicholas J.; Raydan, Marcos
12
2010
The canonical generalized polar decomposition. Zbl 1222.15018
Higham, Nicholas J.; Mehl, Christian; Tisseur, Françoise
11
2010
The scaling and squaring method for the matrix exponential revisited. Zbl 1178.65040
Higham, Nicholas J.
51
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.
22
2009
Detecting and solving hyperbolic quadratic eigenvalue problems. Zbl 1180.65042
Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise
17
2009
Definite matrix polynomials and their linearization by definite pencils. Zbl 1232.65059
Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise
14
2009
Functions of matrices. Theory and computation. Zbl 1167.15001
Higham, Nicholas J.
586
2008
Computing \(A^\alpha, \log(A)\), and related matrix functions by contour integrals. Zbl 1176.65053
Hale, Nicholas; Higham, Nicholas J.; Trefethen, Lloyd N.
68
2008
Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042
Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise
41
2008
Iterative solution of a nonsymmetric algebraic Riccati equation. Zbl 1146.65035
Guo, Chun-Hua; Higham, Nicholas J.
39
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.
15
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.
7
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.
1
2007
Symmetric linearizations for matrix polynomials. Zbl 1137.15006
Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise
55
2006
The conditioning of linearizations of matrix polynomials. Zbl 1131.65034
Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise
42
2006
A Schur-Newton method for the matrix \(p\)th root and its inverse. Zbl 1128.65030
Guo, Chun-Hua; Higham, Nicholas J.
29
2006
The scaling and squaring method for the matrix exponential revisited. Zbl 1081.65037
Higham, Nicholas J.
107
2005
Algorithms for the matrix \(p\)th root. Zbl 1103.65046
Bini, Dario A.; Higham, Nicholas; Meine, Beatrice
26
2005
Efficient algorithms for the matrix cosine and sine. Zbl 1084.65039
Hargreaves, Gareth I.; Higham, Nicholas J.
24
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
23
2005
Matlab guide. 2nd ed. Zbl 1067.68180
Higham, Desmond J; Higham, Nicholas J.
14
2005
Computing \(f(A)b\) for matrix functions \(f\). Zbl 1117.65319
Davies, Philip I.; Higham, Nicholas J.
11
2005
The numerical stability of barycentric Lagrange interpolation. Zbl 1067.65016
Higham, Nicholas J.
88
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
17
2004
Bounds for eigenvalues of matrix polynomials. Zbl 1055.15030
Higham, Nicholas J.; Tisseur, Françoise
46
2003
A Schur-Parlett algorithm for computing matrix functions. Zbl 1052.65031
Davies, Philip I.; Higham, Nicholas J.
43
2003
\(J\)-orthogonal matrices: Properties and generation. Zbl 1034.65026
Higham, Nicholas J.
37
2003
Solving the indefinite least squares problem by hyperbolic QR factorization. Zbl 1036.65035
Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna
24
2003
Computing the matrix cosine. Zbl 1033.65027
Higham, Nicholas J.; Smith, Matthew I.
14
2003
The equality constrained indefinite least squares problem: Theory and algorithms. Zbl 1050.65035
Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna
11
2003
Accuracy and stability of numerical algorithms. 2nd ed. Zbl 1011.65010
Higham, Nicholas J.
685
2002
Computing the nearest correlation matrix – a problem from finance. Zbl 1006.65036
Higham, Nicholas J.
148
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.
30
2002
More on pseudospectra for polynomial eigenvalue problems and applications in control theory. Zbl 1004.65046
Higham, Nicholas J.; Tisseur, Françoise
27
2002
Structured pseudospectra for polynomial eigenvalue problems, with applications. Zbl 0996.65042
Tisseur, Françoise; Higham, Nicholas J.
50
2001
Solving a quadratic matrix equation by newton’s method with exact line searches. Zbl 1017.65038
Higham, Nicholas J.; Kim, Hyun-Min
28
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.
23
2001
Evaluating Padé approximants of the matrix logarithm. Zbl 0989.65054
Higham, Nicholas J.
9
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
4
2001
A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra. Zbl 0959.65061
Higham, Nicholas J.; Tisseur, Françoise
46
2000
Numerical analysis of a quadratic matrix equation. Zbl 0966.65040
Higham, Nicholas J.; Kim, Hyun-Min
41
2000
Numerically stable generation of correlation matrices and their factors. Zbl 0969.65036
Davies, Philip I.; Higham, Nicholas J.
20
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
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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)
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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)
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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)
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5 Mathematics education (97-XX)
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1 \(K\)-theory (19-XX)

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