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Higham, Nicholas J. (b. 1961 d. 2024)

Author ID: higham.nicholas-j Recent zbMATH articles by "Higham, Nicholas J."
Published as: Higham, Nicholas J.; Higham, N. J.; Higham, Nicholas; Higham, Nick
Homepage: https://nhigham.com/
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all top 5

Co-Authors

54 single-authored
18 Tisseur, Françoise
10 Higham, Desmond J.
10 Mary, Theo A.
9 Al-Mohy, Awad H.
7 Fasi, Massimiliano
6 Mackey, D. Steven
6 Pranesh, Srikara
5 Cheng, Sheung Hun
5 Lin, Lijing
5 Relton, Samuel D.
4 Carson, Erin Claire
4 Cox, Anthony J.
4 Davies, Philip I.
4 Dongarra, Jack J.
4 Guo, Chun-Hua
3 Blanchard, Pierre
3 Demmel, James Weldon
3 Knight, Philip A.
3 Mackey, Niloufer
3 Strabić, Nataša
3 Tomov, Stanimire Z.
2 Abdelfattah, Ahmad
2 Aprahamian, Mary
2 Bojanczyk, Adam W.
2 Borsdorf, Rüdiger
2 Connolly, Michael P.
2 Gates, Mark
2 Gautschi, Walter
2 Haidar, Azzam
2 Kim, Hyunmin
2 Lettington, Matthew C.
2 Lopez, Florent
2 Luszczek, Piotr
2 Mehrmann, Volker
2 Mikaitis, Mantas
2 Nakatsukasa, Yuji
2 Papadimitriou, Pythagoras
2 Patel, Harikrishna
2 Schreiber, Robert S.
2 Sherwood, Dennis
2 Stewart, Gilbert Wright
2 Zounon, Mawussi
1 Amestoy, Patrick R.
1 Anzt, Hartwig
1 Bai, Zhaojun
1 Bayraktar, Harun H.
1 Benzi, Michele
1 Betcke, Timo
1 Bini, Dario Andrea
1 Björk, Åke
1 Boman, Erik G.
1 Braconnier, Thierry
1 Brezinski, Claude
1 Buttari, Alfredo
1 Chan, Raymond Hon-Fu
1 Cojean, Terry
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 Glendinning, Paul Alexander
1 Golub, Gene Howard
1 Grammont, Laurence
1 Greenbaum, Anne
1 Greif, Chen
1 Grigori, Laura
1 Grützmacher, Thomas
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 Elena
1 Kurzak, Jakub
1 Laffey, Thomas J.
1 Laub, Alan J.
1 L’Excellent, Jean-Yves
1 Li, Rencang
1 Li, Sherry Xin
1 Lindquist, Neil
1 Loe, Jennifer A.
1 Martin, Paul Andrew
1 Mehl, Christian
1 Meini, Beatrice
1 Nadukandi, Prashanth
1 Nayak, Pratik
1 Noferini, Vanni
1 O’Leary, Dianne P.
1 Pan, Jianxin
1 Pothen, Alex
1 Pranesh, Sri
1 Puerta, Ferran
...and 21 more Co-Authors

Publications by Year

Citations contained in zbMATH Open

171 Publications have been cited 6,023 times in 3,852 Documents Cited by Year
Accuracy and stability of numerical algorithms. 2nd ed. Zbl 1011.65010
Higham, Nicholas J.
844
2002
Functions of matrices. Theory and computation. Zbl 1167.15001
Higham, Nicholas J.
793
2008
Accuracy and stability of numerical algorithms. Zbl 0847.65010
Higham, Nicholas J.
320
1996
Computing the nearest correlation matrix – a problem from finance. Zbl 1006.65036
Higham, Nicholas J.
172
2002
Computing a nearest symmetric positive semidefinite matrix. Zbl 0649.65026
Higham, Nicholas J.
162
1988
Computing the action of the matrix exponential, with an application to exponential integrators. Zbl 1234.65028
Al-Mohy, Awad H.; Higham, Nicholas J.
147
2011
NLEVP, a collection of nonlinear eigenvalue problems. Zbl 1295.65140
Betcke, Timo; Higham, Nicholas J.; Mehrmann, Volker; Schröder, Christian; Tisseur, Françoise
141
2013
The scaling and squaring method for the matrix exponential revisited. Zbl 1081.65037
Higham, Nicholas J.
129
2005
The numerical stability of barycentric Lagrange interpolation. Zbl 1067.65016
Higham, Nicholas J.
111
2004
A new scaling and squaring algorithm for the matrix exponential. Zbl 1194.15021
Al-Mohy, Awad H.; Higham, Nicholas J.
98
2010
Computing the polar decomposition - with applications. Zbl 0607.65014
Higham, Nicholas J.
87
1986
Computing \(A^\alpha, \log(A)\), and related matrix functions by contour integrals. Zbl 1176.65053
Hale, Nicholas; Higham, Nicholas J.; Trefethen, Lloyd N.
79
2008
Symmetric linearizations for matrix polynomials. Zbl 1137.15006
Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise
73
2006
Matrix nearness problems and applications. Zbl 0681.65029
Higham, N. J.
71
1989
Computing real square roots of a real matrix. Zbl 0625.65032
Higham, Nicholas J.
62
1987
The scaling and squaring method for the matrix exponential revisited. Zbl 1178.65040
Higham, Nicholas J.
58
2009
Bounds for eigenvalues of matrix polynomials. Zbl 1055.15030
Higham, Nicholas J.; Tisseur, Françoise
56
2003
A Schur-Parlett algorithm for computing matrix functions. Zbl 1052.65031
Davies, Philip I.; Higham, Nicholas J.
54
2003
Structured pseudospectra for polynomial eigenvalue problems, with applications. Zbl 0996.65042
Tisseur, Françoise; Higham, Nicholas J.
53
2001
Structured backward error and condition of generalized eigenvalue problems. Zbl 0935.65032
Higham, Desmond J.; Higham, Nicholas J.
52
1998
A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra. Zbl 0959.65061
Higham, Nicholas J.; Tisseur, Françoise
51
2000
Newton’s method for the matrix square root. Zbl 0614.65045
Higham, Nicholas J.
49
1986
The conditioning of linearizations of matrix polynomials. Zbl 1131.65034
Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise
48
2006
Iterative solution of a nonsymmetric algebraic Riccati equation. Zbl 1146.65035
Guo, Chun-Hua; Higham, Nicholas J.
46
2007
Numerical analysis of a quadratic matrix equation. Zbl 0966.65040
Higham, Nicholas J.; Kim, Hyun-Min
46
2000
Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042
Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise
46
2008
\(J\)-orthogonal matrices: Properties and generation. Zbl 1034.65026
Higham, Nicholas J.
45
2003
Backward error and condition of structured linear systems. Zbl 0747.65028
Higham, Desmond J.; Higham, Nicholas J.
44
1992
The accuracy of floating point summation. Zbl 0788.65053
Higham, Nicholas J.
40
1993
A survey of condition number estimation for triangular matrices. Zbl 0635.65049
Higham, Nicholas J.
39
1987
Computing matrix functions. Zbl 1242.65090
Higham, Nicholas J.; Al-Mohy, Awad H.
39
2010
A survey of componentwise perturbation theory in numerical linear algebra. Zbl 0815.65062
Higham, Nicholas J.
37
1994
Stable iterations for the matrix square root. Zbl 0884.65035
Higham, Nicholas J.
37
1997
FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimations. Zbl 0665.65043
Higham, Nicholas J.
36
1988
Accelerating the solution of linear systems by iterative refinement in three precisions. Zbl 1453.65067
Carson, Erin; Higham, Nicholas J.
34
2018
Solving a quadratic matrix equation by newton’s method with exact line searches. Zbl 1017.65038
Higham, Nicholas J.; Kim, Hyun-Min
34
2001
Algorithms for the matrix \(p\)th root. Zbl 1103.65046
Bini, Dario A.; Higham, Nicholas; Meini, Beatrice
34
2005
Error analysis of the Björck-Pereyra algorithms for solving Vandermonde systems. Zbl 0595.65029
Higham, Nicholas J.
34
1987
The symmetric Procrustes problem. Zbl 0641.65034
Higham, Nicholas J.
32
1988
A preconditioned Newton algorithm for the nearest correlation matrix. Zbl 1188.65055
Borsdorf, Rüdiger; Higham, Nicholas J.
32
2010
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.
32
2002
Perturbation theory and backward error for \(AX - XB = C\). Zbl 0781.65034
Higham, Nicholas J.
31
1993
A Schur-Newton method for the matrix \(p\)th root and its inverse. Zbl 1128.65030
Guo, Chun-Hua; Higham, Nicholas J.
30
2006
A Schur-Padé algorithm for fractional powers of a matrix. Zbl 1242.65091
Higham, Nicholas J.; Lin, Lijing
29
2011
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.
29
2009
Solving the indefinite least squares problem by hyperbolic QR factorization. Zbl 1036.65035
Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna
29
2003
The matrix sign decomposition and its relation to the polar decomposition. Zbl 0816.15012
Higham, Nicholas J.
29
1994
More on pseudospectra for polynomial eigenvalue problems and applications in control theory. Zbl 1004.65046
Higham, Nicholas J.; Tisseur, Françoise
29
2002
An improved Schur-Padé algorithm for fractional powers of a matrix and their Fréchet derivatives. Zbl 1279.65050
Higham, Nicholas J.; Lin, Lijing
29
2013
Functions preserving matrix groups and iterations for the matrix square root. Zbl 1079.65053
Higham, Nicholas J.; Mackey, D. Steven; Mackey, Niloufer; Tisseur, Françoise
28
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.
28
2001
A new approach to probabilistic rounding error analysis. Zbl 07123205
Higham, Nicholas J.; Mary, Theo
28
2019
Stability of block. Zbl 0834.65010
Demmel, James W.; Higham, Nicholas J.; Schreiber, Robert S.
27
1995
Efficient algorithms for the matrix cosine and sine. Zbl 1084.65039
Hargreaves, Gareth I.; Higham, Nicholas J.
27
2005
Stability analysis of algorithms for solving confluent Vandermonde-like systems. Zbl 0724.65025
Higham, Nicholas J.
27
1990
Numerically stable generation of correlation matrices and their factors. Zbl 0969.65036
Davies, Philip I.; Higham, Nicholas J.
26
2000
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.
26
2017
Fast solution of Vandermonde-like systems involving orthogonal polynomials. Zbl 0666.65025
Higham, Nicholas J.
25
1988
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.
25
2013
A modified Cholesky algorithm based on a symmetric indefinite factorization. Zbl 0949.65022
Cheng, Sheung Hun; Higham, Nicholas J.
23
1998
Factorizing complex symmetric matrices with positive definite real and imaginary parts. Zbl 0909.65016
Higham, Nicholas J.
23
1998
Improved inverse scaling and squaring algorithms for the matrix logarithm. Zbl 1252.15027
Al-Mohy, Awad H.; Higham, Nicholas J.
23
2012
Matlab guide. 2nd ed. Zbl 1067.68180
Higham, Desmond J; Higham, Nicholas J.
21
2005
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.
21
2015
Anderson acceleration of the alternating projections method for computing the nearest correlation matrix. Zbl 1347.65074
Higham, Nicholas J.; Strabić, Nataša
21
2016
Large growth factors in Gaussian elimination with pivoting. Zbl 0681.65012
Higham, Nicholas J.; Higham, Desmond J.
20
1989
Exploiting fast matrix multiplication within the level 3 BLAS. Zbl 0900.65118
Higham, Nicholas J.
19
1990
Computing the field of values and pseudospectra using the Lanczos method with continuation. Zbl 0861.65033
Braconnier, Thierry; Higham, Nicholas J.
19
1996
On \(p\)th roots of stochastic matrices. Zbl 1223.15042
Higham, Nicholas J.; Lin, Lijing
19
2011
Detecting and solving hyperbolic quadratic eigenvalue problems. Zbl 1180.65042
Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise
18
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
18
2004
Estimating the matrix \(p\)-norm. Zbl 0741.65040
Higham, Nicholas J.
18
1992
Algorithm 694: A collection of test matrices in MATLAB. Zbl 0900.65120
Higham, Nicholas J.
18
1991
Squeezing a matrix into half precision, with an application to solving Linear systems. Zbl 1420.65017
Higham, Nicholas J.; Pranesh, Srikara; Zounon, Mawussi
18
2019
The complex step approximation to the Fréchet derivative of a matrix function. Zbl 1188.65054
Al-Mohy, Awad H.; Higham, Nicholas J.
17
2010
Computing the matrix cosine. Zbl 1033.65027
Higham, Nicholas J.; Smith, Matthew I.
17
2003
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.
17
1999
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.
17
2008
Analysis of the Cholesky decomposition of a semi-definite matrix. Zbl 0721.65014
Higham, Nicholas J.
17
1990
A framework for analyzing nonlinear eigenproblems and parametrized linear systems. Zbl 1288.65049
Grammont, Laurence; Higham, Nicholas J.; Tisseur, Françoise
17
2011
An improved arc algorithm for detecting definite Hermitian pairs. Zbl 1202.65054
Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise
17
2010
Definite matrix polynomials and their linearization by definite pencils. Zbl 1232.65059
Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise
16
2009
Iterative refinement enhances the stability of \(QR\) factorization methods for solving linear equations. Zbl 0736.65016
Higham, Nicholas J.
16
1991
Componentwise perturbation theory for linear systems with multiple right- hand sides. Zbl 0801.65043
Higham, Desmond J.; Higham, Nicholas J.
16
1992
Iterative refinement for linear systems and LAPACK. Zbl 0887.65034
Higham, Nicholas J.
16
1997
Simulating low precision floating-point arithmetic. Zbl 07124603
Higham, Nicholas J.; Pranesh, Srikara
16
2019
Bounding the error in Gaussian elimination for tridiagonal systems. Zbl 0716.65025
Higham, Nicholas J.
15
1990
Improved error bounds for undetermined system solvers. Zbl 0770.65025
Demmel, James W.; Higham, Nicholas J.
15
1993
Stable and efficient spectral divide and conquer algorithms for the symmetric eigenvalue decomposition and the SVD. Zbl 1326.65049
Nakatsukasa, Yuji; Higham, Nicholas J.
15
2013
The canonical generalized polar decomposition. Zbl 1222.15018
Higham, Nicholas J.; Mehl, Christian; Tisseur, Françoise
15
2010
The equality constrained indefinite least squares problem: Theory and algorithms. Zbl 1050.65035
Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna
14
2003
Experience with a matrix norm estimator. Zbl 0752.65036
Higham, Nicholas J.
14
1990
Stability of methods for matrix inversion. Zbl 0748.65021
Du Croz, Jeremy J.; Higham, Nicholas J.
14
1992
An algorithm for the matrix Lambert \(W\) function. Zbl 1317.65116
Fasi, Massimiliano; Higham, Nicholas J.; Iannazzo, Bruno
14
2015
Computing a nearest correlation matrix with factor structure. Zbl 1213.65022
Borsdorf, Rüdiger; Higham, Nicholas J.; Raydan, Marcos
13
2010
Efficient algorithms for computing the condition number of a tridiagonal matrix. Zbl 0599.65026
Higham, Nicholas J.
13
1986
Fast polar decomposition of an arbitrary matrix. Zbl 0711.65024
Higham, Nicholas J.; Schreiber, Robert S.
13
1990
Stability of block algorithms with fast level-3 BLAS. Zbl 0892.65016
Demmel, James W.; Higham, Nicholas J.
13
1992
The Princeton companion to applied mathematics. Zbl 1327.00002
13
2015
The accuracy of solutions to triangular systems. Zbl 0683.65029
Higham, Nicholas J.
12
1989
Probabilistic rounding error analysis of Householder QR factorization. Zbl 1520.65019
Connolly, Michael P.; Higham, Nicholas J.
1
2023
Matrix multiplication in multiword arithmetic: error analysis and application to GPU tensor cores. Zbl 1511.65040
Fasi, Massimiliano; Higham, Nicholas J.; Lopez, Florent; Mary, Theo; Mikaitis, Mantas
1
2023
Mixed precision algorithms in numerical linear algebra. Zbl 1512.65081
Higham, Nicholas J.; Mary, Theo
7
2022
Solving block low-rank linear systems by LU factorization is numerically stable. Zbl 1511.65024
Higham, Nicholas J.; Mary, Theo
4
2022
Anymatrix: an extensible MATLAB matrix collection. Zbl 1492.65002
Higham, Nicholas J.; Mikaitis, Mantas
4
2022
Arbitrary precision algorithms for computing the matrix cosine and its Fréchet derivative. Zbl 1508.65044
Al-Mohy, Awad H.; Higham, Nicholas J.; Liu, Xiaobo
3
2022
Optimizing and factorizing the Wilson matrix. Zbl 1489.15012
Higham, Nicholas J.; Lettington, Matthew C.
1
2022
Stochastic rounding and its probabilistic backward error analysis. Zbl 1462.65050
Connolly, Michael P.; Higham, Nicholas J.; Mary, Theo
11
2021
A multiprecision derivative-free Schur-Parlett algorithm for computing matrix functions. Zbl 1476.65067
Higham, Nicholas J.; Liu, Xiaobo
7
2021
Exploiting lower precision arithmetic in solving symmetric positive definite linear systems and least squares problems. Zbl 1467.65023
Higham, Nicholas J.; Pranesh, Srikara
6
2021
Random matrices generating large growth in LU factorization with pivoting. Zbl 1459.65036
Higham, Desmond J.; Higham, Nicholas J.; Pranesh, Srikara
5
2021
Accurately computing the log-sum-exp and softmax functions. Zbl 1509.65019
Blanchard, Pierre; Higham, Desmond J.; Higham, Nicholas J.
4
2021
Generating extreme-scale matrices with specified singular values or condition number. Zbl 1462.65041
Fasi, Massimiliano; Higham, Nicholas J.
2
2021
Matrices with tunable infinity-norm condition number and no need for pivoting in LU factorization. Zbl 1467.65035
Fasi, Massimiliano; Higham, Nicholas J.
2
2021
Integer matrix factorisations, superalgebras and the quadratic form obstruction. Zbl 1467.15009
Higham, Nicholas J.; Lettington, Matthew C.; Schmidt, Karl Michael
2
2021
A set of batched basic linear algebra subprograms and LAPACK routines. Zbl 07467952
Abdelfattah, Ahmad; Costa, Timothy; Dongarra, Jack; Gates, Mark; Haidar, Azzam; Hammarling, Sven; Higham, Nicholas J.; Kurzak, Jakub; Luszczek, Piotr; Tomov, Stanimire; Zounon, Mawussi
2
2021
The mathematics of floating-point arithmetic. Zbl 1477.65276
Higham, Nicholas J.
1
2021
Sharper probabilistic backward error analysis for basic linear algebra kernels with random data. Zbl 1452.65090
Higham, Nicholas J.; Mary, Theo
11
2020
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
9
2020
Three-precision GMRES-based iterative refinement for least squares problems. Zbl 1461.65032
Carson, Erin; Higham, Nicholas J.; Pranesh, Srikara
9
2020
A class of fast and accurate summation algorithms. Zbl 1471.65035
Blanchard, Pierre; Higham, Nicholas J.; Mary, Theo
9
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.
6
2020
Numerical algorithms for high-performance computational science. Zbl 1462.65231
Dongarra, Jack; Grigori, Laura; Higham, Nicholas J.
4
2020
A new approach to probabilistic rounding error analysis. Zbl 07123205
Higham, Nicholas J.; Mary, Theo
28
2019
Squeezing a matrix into half precision, with an application to solving Linear systems. Zbl 1420.65017
Higham, Nicholas J.; Pranesh, Srikara; Zounon, Mawussi
18
2019
Simulating low precision floating-point arithmetic. Zbl 07124603
Higham, Nicholas J.; Pranesh, Srikara
16
2019
A new preconditioner that exploits low-rank approximations to factorization error. Zbl 1408.65013
Higham, Nicholas J.; Mary, Theo
12
2019
An arbitrary precision scaling and squaring algorithm for the matrix exponential. Zbl 1437.65033
Fasi, Massimiliano; Higham, Nicholas J.
6
2019
Accelerating the solution of linear systems by iterative refinement in three precisions. Zbl 1453.65067
Carson, Erin; Higham, Nicholas J.
34
2018
Multiprecision algorithms for computing the matrix logarithm. Zbl 1390.15073
Fasi, Massimiliano; Higham, Nicholas J.
8
2018
Computing the wave-kernel matrix functions. Zbl 1403.65020
Nadukandi, Prashanth; Higham, Nicholas J.
5
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.
26
2017
Matlab guide. 3rd revised and updated edition. Zbl 1357.68001
Higham, Desmond J; Higham, Nicholas J.
9
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
21
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
11
2016
Matrix inverse trigonometric and inverse hyperbolic functions: theory and algorithms. Zbl 1388.15012
Aprahamian, Mary; Higham, Nicholas J.
10
2016
Testing matrix function algorithms using identities. Zbl 1347.65087
Deadman, Edvin; Higham, Nicholas J.
5
2016
An algorithm to compute the polar decomposition of a \(3 \times 3\) matrix. Zbl 1353.65020
Higham, Nicholas J.; Noferini, Vanni
4
2016
Estimating the largest elements of a matrix. Zbl 1352.65132
Higham, Nicholas J.; Relton, Samuel D.
4
2016
Bounds for the distance to the nearest correlation matrix. Zbl 1347.65075
Higham, Nicholas J.; Strabić, Nataša
3
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.
21
2015
An algorithm for the matrix Lambert \(W\) function. Zbl 1317.65116
Fasi, Massimiliano; Higham, Nicholas J.; Iannazzo, Bruno
14
2015
The Princeton companion to applied mathematics. Zbl 1327.00002
13
2015
Matrix functions: a short course. Zbl 1332.15021
Higham, Nicholas J.; Lin, Lijing
2
2015
Higher order Fréchet derivatives of matrix functions and the level-2 condition number. Zbl 1308.65066
Higham, Nicholas J.; Relton, Samuel D.
11
2014
Covariance structure regularization via entropy loss function. Zbl 1506.62109
Lin, Lijing; Higham, Nicholas J.; Pan, Jianxin
10
2014
The matrix unwinding function, with an application to computing the matrix exponential. Zbl 1300.65024
Aprahamian, Mary; Higham, Nicholas J.
9
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
141
2013
An improved Schur-Padé algorithm for fractional powers of a matrix and their Fréchet derivatives. Zbl 1279.65050
Higham, Nicholas J.; Lin, Lijing
29
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.
25
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.
15
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.
23
2012
Backward stability of iterations for computing the polar decomposition. Zbl 1252.65083
Nakatsukasa, Yuji; Higham, Nicholas J.
10
2012
Computing the action of the matrix exponential, with an application to exponential integrators. Zbl 1234.65028
Al-Mohy, Awad H.; Higham, Nicholas J.
147
2011
A Schur-Padé algorithm for fractional powers of a matrix. Zbl 1242.65091
Higham, Nicholas J.; Lin, Lijing
29
2011
On \(p\)th roots of stochastic matrices. Zbl 1223.15042
Higham, Nicholas J.; Lin, Lijing
19
2011
A framework for analyzing nonlinear eigenproblems and parametrized linear systems. Zbl 1288.65049
Grammont, Laurence; Higham, Nicholas J.; Tisseur, Françoise
17
2011
A new scaling and squaring algorithm for the matrix exponential. Zbl 1194.15021
Al-Mohy, Awad H.; Higham, Nicholas J.
98
2010
Computing matrix functions. Zbl 1242.65090
Higham, Nicholas J.; Al-Mohy, Awad H.
39
2010
A preconditioned Newton algorithm for the nearest correlation matrix. Zbl 1188.65055
Borsdorf, Rüdiger; Higham, Nicholas J.
32
2010
The complex step approximation to the Fréchet derivative of a matrix function. Zbl 1188.65054
Al-Mohy, Awad H.; Higham, Nicholas J.
17
2010
An improved arc algorithm for detecting definite Hermitian pairs. Zbl 1202.65054
Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise
17
2010
The canonical generalized polar decomposition. Zbl 1222.15018
Higham, Nicholas J.; Mehl, Christian; Tisseur, Françoise
15
2010
Computing a nearest correlation matrix with factor structure. Zbl 1213.65022
Borsdorf, Rüdiger; Higham, Nicholas J.; Raydan, Marcos
13
2010
The scaling and squaring method for the matrix exponential revisited. Zbl 1178.65040
Higham, Nicholas J.
58
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.
29
2009
Detecting and solving hyperbolic quadratic eigenvalue problems. Zbl 1180.65042
Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise
18
2009
Definite matrix polynomials and their linearization by definite pencils. Zbl 1232.65059
Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise
16
2009
Functions of matrices. Theory and computation. Zbl 1167.15001
Higham, Nicholas J.
793
2008
Computing \(A^\alpha, \log(A)\), and related matrix functions by contour integrals. Zbl 1176.65053
Hale, Nicholas; Higham, Nicholas J.; Trefethen, Lloyd N.
79
2008
Backward error of polynomial eigenproblems solved by linearization. Zbl 1159.65042
Higham, Nicholas J.; Li, Ren-Cang; Tisseur, Françoise
46
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.
17
2008
Iterative solution of a nonsymmetric algebraic Riccati equation. Zbl 1146.65035
Guo, Chun-Hua; Higham, Nicholas J.
46
2007
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
73
2006
The conditioning of linearizations of matrix polynomials. Zbl 1131.65034
Higham, Nicholas J.; Mackey, D. Steven; Tisseur, Françoise
48
2006
A Schur-Newton method for the matrix \(p\)th root and its inverse. Zbl 1128.65030
Guo, Chun-Hua; Higham, Nicholas J.
30
2006
The scaling and squaring method for the matrix exponential revisited. Zbl 1081.65037
Higham, Nicholas J.
129
2005
Algorithms for the matrix \(p\)th root. Zbl 1103.65046
Bini, Dario A.; Higham, Nicholas; Meini, Beatrice
34
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
28
2005
Efficient algorithms for the matrix cosine and sine. Zbl 1084.65039
Hargreaves, Gareth I.; Higham, Nicholas J.
27
2005
Matlab guide. 2nd ed. Zbl 1067.68180
Higham, Desmond J; Higham, Nicholas J.
21
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.
111
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
18
2004
Bounds for eigenvalues of matrix polynomials. Zbl 1055.15030
Higham, Nicholas J.; Tisseur, Françoise
56
2003
A Schur-Parlett algorithm for computing matrix functions. Zbl 1052.65031
Davies, Philip I.; Higham, Nicholas J.
54
2003
\(J\)-orthogonal matrices: Properties and generation. Zbl 1034.65026
Higham, Nicholas J.
45
2003
Solving the indefinite least squares problem by hyperbolic QR factorization. Zbl 1036.65035
Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna
29
2003
Computing the matrix cosine. Zbl 1033.65027
Higham, Nicholas J.; Smith, Matthew I.
17
2003
The equality constrained indefinite least squares problem: Theory and algorithms. Zbl 1050.65035
Bojanczyk, Adam; Higham, Nicholas J.; Patel, Harikrishna
14
2003
Accuracy and stability of numerical algorithms. 2nd ed. Zbl 1011.65010
Higham, Nicholas J.
844
2002
Computing the nearest correlation matrix – a problem from finance. Zbl 1006.65036
Higham, Nicholas J.
172
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.
32
2002
More on pseudospectra for polynomial eigenvalue problems and applications in control theory. Zbl 1004.65046
Higham, Nicholas J.; Tisseur, Françoise
29
2002
Structured pseudospectra for polynomial eigenvalue problems, with applications. Zbl 0996.65042
Tisseur, Françoise; Higham, Nicholas J.
53
2001
...and 71 more Documents
all top 5

Cited by 4,989 Authors

63 Higham, Nicholas J.
59 Wei, Yimin
39 Peña, Juan Manuel
37 Kressner, Daniel
36 Dopico, Froilán M.
29 Rump, Siegfried Michael
28 Nakatsukasa, Yuji
28 Reichel, Lothar
26 Miyajima, Shinya
26 Tisseur, Françoise
24 Li, Rencang
24 Mehrmann, Volker
24 Noferini, Vanni
24 Van Dooren, Paul M.
23 Bini, Dario Andrea
23 Diao, Huaian
22 Ibáñez González, Jacinto Javier
22 Li, Hanyu
21 Benner, Peter
21 Ogita, Takeshi
19 Defez, Emilio
19 Soleymani, Fazlollah
18 Benzi, Michele
18 Sastre, Jorge
17 Melman, Aaron
17 Simoncini, Valeria
16 Corless, Robert Malcolm
15 Graillat, Stef
15 Iannazzo, Bruno
15 Jarlebring, Elias
15 Meini, Beatrice
15 Poloni, Federico Giovanni
15 Rozložník, Miroslav
15 Vabishchevich, Pëtr Nikolaevich
14 Alonso, Pedro
14 Cardoso, João R.
14 Delgado, Jorge F. M.
14 Liu, Qiaohua
14 Mackey, D. Steven
14 Robol, Leonardo
14 Wu, Xinyuan
13 Faßbender, Heike
13 Li, Wen
13 Marco García, Ana
13 Oishi, Shin’ichi
12 Fasi, Massimiliano
12 Guo, Chun-Hua
12 Güttel, Stefan
12 Hu, Xiyan
12 Kulikov, Gennady Yur’evich
12 Martínez, José-Javier
12 Mary, Theo A.
12 Noschese, Silvia
12 Pérez, Javier J.
12 Schweitzer, Marcel
11 Caliari, Marco
11 Frommer, Andreas
11 Gemignani, Luca
11 Gratton, Serge
11 Kim, Hyunmin
11 Massei, Stefano
11 Mitrouli, Marilena
11 Ostermann, Alexander
11 Ozaki, Katsuhisa
11 Psarrakos, Panayiotis J.
11 Sadkane, Miloud
11 Smoktunowicz, Alicja
11 Szyld, Daniel B.
11 Wang, Shaoxin
10 Barrio, Roberto
10 Bochev, M. A.
10 Cucker, Felipe
10 de Terán, Fernando
10 Estrada, Ernesto
10 Lin, Wen-Wei
10 Liu, Xinguo
10 Neff, Patrizio
10 Olshevsky, Vadim
10 Raydan, Marcos
10 Vandebril, Raf
10 Wei, Musheng
10 Yang, Hu
10 Ziętak, Krystyna
9 Alam, Rafikul
9 Dongarra, Jack J.
9 Drmač, Zlatko
9 Duan, Xuefeng
9 Higham, Desmond J.
9 Jeannerod, Claude-Pierre
9 Liao, Anping
9 Mehl, Christian
9 Pan, Victor Yakovlevich
9 Shen, Chungen
9 Stanimirović, Predrag S.
9 Wang, Weiguo
9 Zhang, Lei
8 Arrigo, Francesca
8 Bueno, María Isabel
8 Carson, Erin Claire
8 Chu, Moody T.
...and 4,889 more Authors
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Cited in 497 Serials

434 Linear Algebra and its Applications
265 Journal of Computational and Applied Mathematics
161 SIAM Journal on Matrix Analysis and Applications
147 Numerical Algorithms
138 Applied Mathematics and Computation
129 SIAM Journal on Scientific Computing
119 BIT
89 Journal of Computational Physics
76 Numerical Linear Algebra with Applications
74 Computers & Mathematics with Applications
73 Applied Numerical Mathematics
68 Numerische Mathematik
67 Mathematics of Computation
58 Linear and Multilinear Algebra
44 Journal of Scientific Computing
40 Calcolo
38 Computer Methods in Applied Mechanics and Engineering
34 International Journal of Computer Mathematics
33 Computer Physics Communications
32 ELA. The Electronic Journal of Linear Algebra
30 Applied Mathematics Letters
27 Mathematical Programming. Series A. Series B
26 ETNA. Electronic Transactions on Numerical Analysis
25 Automatica
25 Japan Journal of Industrial and Applied Mathematics
23 Mathematics and Computers in Simulation
23 Computational and Applied Mathematics
22 Journal of Mathematical Analysis and Applications
22 Advances in Computational Mathematics
21 Journal of Optimization Theory and Applications
21 SIAM Journal on Optimization
21 Computational Optimization and Applications
20 SIAM Journal on Numerical Analysis
19 Theoretical Computer Science
19 SIAM Review
18 ACM Transactions on Mathematical Software
15 Applied Mathematical Modelling
14 Computing
14 Journal of Multivariate Analysis
14 Journal of Complexity
14 Optimization Methods & Software
13 Journal of the Franklin Institute
12 Mathematical and Computer Modelling
12 Abstract and Applied Analysis
12 Special Matrices
11 Journal of Symbolic Computation
11 Computational Statistics
11 Journal of Applied Mathematics and Computing
10 International Journal of Control
10 International Journal for Numerical Methods in Engineering
10 Systems & Control Letters
10 Computational Statistics and Data Analysis
10 Mathematical Problems in Engineering
10 Quantitative Finance
10 Foundations of Computational Mathematics
10 Acta Numerica
10 Operators and Matrices
10 JSIAM Letters
9 Computer Aided Geometric Design
9 Communications in Nonlinear Science and Numerical Simulation
8 Journal of Mathematical Physics
8 Journal of Approximation Theory
8 Neural Computation
8 Communications in Statistics. Simulation and Computation
8 European Journal of Operational Research
8 Journal of Mathematical Imaging and Vision
8 Applied and Computational Harmonic Analysis
8 Engineering Analysis with Boundary Elements
8 Lobachevskii Journal of Mathematics
8 Journal of Applied Mathematics
8 Communications in Computational Physics
8 The Annals of Applied Statistics
8 Journal of Computational and Graphical Statistics
8 Statistics and Computing
8 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
7 Inverse Problems
7 GAMM-Mitteilungen
6 Statistics & Probability Letters
6 Operations Research Letters
6 Optimization
6 Computational Mechanics
6 Applications of Mathematics
6 Journal of Global Optimization
6 Journal of Statistical Computation and Simulation
6 Advances in Applied Clifford Algebras
6 Journal of Mathematical Chemistry
6 Nonlinear Dynamics
6 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
6 Methodology and Computing in Applied Probability
6 Stochastic Models
6 Mediterranean Journal of Mathematics
6 Optimization Letters
6 Mathematical Programming Computation
5 Mathematical Methods in the Applied Sciences
5 Kybernetika
5 Numerical Functional Analysis and Optimization
5 Proceedings of the American Mathematical Society
5 Results in Mathematics
5 Annals of Operations Research
5 Computational Mathematics and Mathematical Physics
...and 397 more Serials
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Cited in 61 Fields

2,641 Numerical analysis (65-XX)
1,337 Linear and multilinear algebra; matrix theory (15-XX)
313 Operations research, mathematical programming (90-XX)
237 Statistics (62-XX)
217 Partial differential equations (35-XX)
191 Systems theory; control (93-XX)
185 Computer science (68-XX)
172 Ordinary differential equations (34-XX)
159 Operator theory (47-XX)
143 Approximations and expansions (41-XX)
139 Probability theory and stochastic processes (60-XX)
86 Fluid mechanics (76-XX)
85 Calculus of variations and optimal control; optimization (49-XX)
84 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
83 Mechanics of deformable solids (74-XX)
81 Combinatorics (05-XX)
75 Quantum theory (81-XX)
69 Biology and other natural sciences (92-XX)
64 Real functions (26-XX)
61 Special functions (33-XX)
59 Dynamical systems and ergodic theory (37-XX)
52 Information and communication theory, circuits (94-XX)
51 Functions of a complex variable (30-XX)
43 Harmonic analysis on Euclidean spaces (42-XX)
39 Mechanics of particles and systems (70-XX)
38 Number theory (11-XX)
37 Differential geometry (53-XX)
36 Statistical mechanics, structure of matter (82-XX)
28 Field theory and polynomials (12-XX)
27 Integral equations (45-XX)
26 Optics, electromagnetic theory (78-XX)
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15 Relativity and gravitational theory (83-XX)
10 Associative rings and algebras (16-XX)
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6 General and overarching topics; collections (00-XX)
5 Mathematical logic and foundations (03-XX)
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3 Mathematics education (97-XX)
2 General algebraic systems (08-XX)
2 General topology (54-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 \(K\)-theory (19-XX)

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