FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation. - Nicholas J. Higham (ACM Trans. Math. Softw., 1988)

Algorithm 674: Fortran codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation. - Nicholas J. Higham (ACM Trans. Math. Softw., 1989)

Experience with a Matrix Norm Estimator. - Nicholas J. Higham (SIAM J. Sci. Comput., 1990)

Fast Polar Decomposition of an Arbitrary Matrix. - Nicholas J. Higham; Robert S. Schreiber (SIAM J. Sci. Comput., 1990)

Exploiting fast matrix multiplication within the level 3 BLAS. - Nicholas J. Higham (ACM Trans. Math. Softw., 1990)

Algorithm 694: a collection of test matrices in MATLAB. - Nicholas J. Higham (ACM Trans. Math. Softw., 1991)

Stability of a Method for Multiplying Complex Matrices with Three Real Matrix Multiplications. - Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 1992)

Backward Error and Condition of Structured Linear Systems. - Desmond J. Higham; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 1992)

Stability of block algorithms with fast level-3 BLAS. - James Demmel; Nicholas J. Higham (ACM Trans. Math. Softw., 1992)

Handbook of writing for the mathematical sciences. - Nicholas J. Higham (SIAM, 1993)

The Accuracy of Floating Point Summation. - Nicholas J. Higham (SIAM J. Sci. Comput., 1993)

Improved Error Bounds for Underdetermined System Solvers. - James Weldon Demmel; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 1993)

Optimization by Direct Search in Matrix Computations. - Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 1993)

A Parallel Algorithm for Computing the Polar Decomposition. - Nicholas J. Higham; Pythagoras Papadimitriou (Parallel Comput., 1994)

Stability of the Partitioned Inverse Method for Parallel Solution of Sparse Triangular Systems. - Nicholas J. Higham; Alex Pothen (SIAM J. Sci. Comput., 1994)

Stability of block LU factorization. - James Weldon Demmel; Nicholas J. Higham; Robert S. Schreiber (Numer. Linear Algebra Appl., 1995)

Matrix Powers in Finite Precision Arithmetic. - Nicholas J. Higham; Philip A. Knight (SIAM J. Matrix Anal. Appl., 1995)

Stability of Parallel Triangular System Solvers. - Nicholas J. Higham (SIAM J. Sci. Comput., 1995)

Accuracy and stability of numerical algorithms. - Nicholas J. Higham (SIAM, 1996)

Testing linear algebra software. - Nicholas J. Higham (Quality of Numerical Software, 1996)

Stable iterations for the matrix square root. - Nicholas J. Higham (Numer. Algorithms, 1997)

Stability of the Diagonal Pivoting Method with Partial Pivoting. - Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 1997)

Factorizing complex symmetric matrices with positive definite real and imaginary parts. - Nicholas J. Higham (Math. Comput., 1998)

Structured Backward Error and Condition of Generalized Eigenvalue Problems. - Desmond J. Higham; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 1998)

A Modified Cholesky Algorithm Based on a Symmetric Indefinite Factorization. - Sheung Hun Cheng; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 1998)

Row-Wise Backward Stable Elimination Methods for the Equality Constrained Least Squares Problem. - Anthony J. Cox; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 1999)

Matlab guide. - Desmond J. Higham; Nicholas J. Higham (SIAM, 2000)

A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra. - Nicholas J. Higham; Françoise Tisseur (SIAM J. Matrix Anal. Appl., 2000)

Parallel Implementation of a Block Algorithm for Matrix 1-Norm Estimation. - Sheung Hun Cheng; Nicholas J. Higham (Euro-Par, 2001)

Approximating the Logarithm of a Matrix to Specified Accuracy. - Sheung Hun Cheng; Nicholas J. Higham; Charles S. Kenney; Alan J. Laub (SIAM J. Matrix Anal. Appl., 2001)

Analysis of the Cholesky Method with Iterative Refinement for Solving the Symmetric Definite Generalized Eigenproblem. - Philip I. Davies; Nicholas J. Higham; Françoise Tisseur (SIAM J. Matrix Anal. Appl., 2001)

Evaluating Padé Approximants of the Matrix Logarithm. - Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 2001)

Solving a Quadratic Matrix Equation by Newton's Method with Exact Line Searches. - Nicholas J. Higham; Hyun-Min Kim (SIAM J. Matrix Anal. Appl., 2001)

Structured Pseudospectra for Polynomial Eigenvalue Problems, with Applications. - Françoise Tisseur; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 2001)

Accuracy and stability of numerical algorithms, Second Edition. - Nicholas J. Higham (SIAM, 2002)

Computing the Matrix Cosine. - Nicholas J. Higham; Matthew I. Smith (Numer. Algorithms, 2003)

Solving the Indefinite Least Squares Problem by Hyperbolic QR Factorization. - Adam W. Bojanczyk; Nicholas J. Higham; Harikrishna Patel (SIAM J. Matrix Anal. Appl., 2003)

A Schur-Parlett Algorithm for Computing Matrix Functions. - Philip I. Davies; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 2003)

J-Orthogonal Matrices: Properties and Generation. - Nicholas J. Higham (SIAM Rev., 2003)

Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups. - Nicholas J. Higham; D. Steven Mackey; Niloufer Mackey; Françoise Tisseur (SIAM J. Matrix Anal. Appl., 2004)

Matlab guide, Second Edition. - Desmond J. Higham; Nicholas J. Higham (SIAM, 2005)

Algorithms for the matrix pth root. - Dario Andrea Bini; Nicholas J. Higham; Beatrice Meini (Numer. Algorithms, 2005)

Efficient algorithms for the matrix cosine and sine. - Gareth I. Hargreaves; Nicholas J. Higham (Numer. Algorithms, 2005)

The Scaling and Squaring Method for the Matrix Exponential Revisited. - Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 2005)

Functions Preserving Matrix Groups and Iterations for the Matrix Square Root. - Nicholas J. Higham; D. Steven Mackey; Niloufer Mackey; Françoise Tisseur (SIAM J. Matrix Anal. Appl., 2005)

LAPACK-Style Codes for Pivoted Cholesky and QR Updating. - Sven Hammarling; Nicholas J. Higham; Craig Lucas (PARA, 2006)

A Schur-Newton Method for the Matrix lowercase{ boldmathp}th Root and its Inverse. - Chun-Hua Guo; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 2006)

Symmetric Linearizations for Matrix Polynomials. - Nicholas J. Higham; D. Steven Mackey; Niloufer Mackey; Françoise Tisseur (SIAM J. Matrix Anal. Appl., 2006)

The Conditioning of Linearizations of Matrix Polynomials. - Nicholas J. Higham; D. Steven Mackey; Françoise Tisseur (SIAM J. Matrix Anal. Appl., 2006)

Commentary. - Nicholas J. Higham (Milestones in Matrix Computation, 2007)

Iterative Solution of a Nonsymmetric Algebraic Riccati Equation. - Chun-Hua Guo; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 2007)

Backward Error of Polynomial Eigenproblems Solved by Linearization. - Nicholas J. Higham; Ren-Cang Li; Françoise Tisseur (SIAM J. Matrix Anal. Appl., 2007)

Functions of matrices - theory and computation. - Nicholas J. Higham (SIAM, 2008)

Computing the Fréchet Derivative of the Matrix Exponential, with an Application to Condition Number Estimation. - Awad H. Al-Mohy; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 2008)

Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems. - Chun-Hua Guo; Nicholas J. Higham; Françoise Tisseur (SIAM J. Matrix Anal. Appl., 2008)

Computing AAlpha, log(A), and Related Matrix Functions by Contour Integrals. - Nicholas Hale; Nicholas J. Higham; Lloyd N. Trefethen (SIAM J. Numer. Anal., 2008)

Developing a High-Performance Computing/Numerical Analysis Roadmap. - Anne E. Trefethen; Nicholas J. Higham; Iain S. Duff; Peter V. Coveney (Int. J. High Perform. Comput. Appl., 2009)

A New Scaling and Squaring Algorithm for the Matrix Exponential. - Awad H. Al-Mohy; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 2009)

An Improved Arc Algorithm for Detecting Definite Hermitian Pairs. - Chun-Hua Guo; Nicholas J. Higham; Françoise Tisseur (SIAM J. Matrix Anal. Appl., 2009)

Definite Matrix Polynomials and their Linearization by Definite Pencils. - Nicholas J. Higham; D. Steven Mackey; Françoise Tisseur (SIAM J. Matrix Anal. Appl., 2009)

Computing matrix functions. - Nicholas J. Higham; Awad H. Al-Mohy (Acta Numer., 2010)

The complex step approximation to the Fréchet derivative of a matrix function. - Awad H. Al-Mohy; Nicholas J. Higham (Numer. Algorithms, 2010)

Computing a Nearest Correlation Matrix with Factor Structure. - Rüdiger Borsdorf; Nicholas J. Higham; Marcos Raydan (SIAM J. Matrix Anal. Appl., 2010)

The Canonical Generalized Polar Decomposition. - Nicholas J. Higham; Christian Mehl; Françoise Tisseur (SIAM J. Matrix Anal. Appl., 2010)

A Schur-Padé Algorithm for Fractional Powers of a Matrix. - Nicholas J. Higham; Lijing Lin (SIAM J. Matrix Anal. Appl., 2011)

Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators. - Awad H. Al-Mohy; Nicholas J. Higham (SIAM J. Sci. Comput., 2011)

Blocked Schur Algorithms for Computing the Matrix Square Root. - Edvin Deadman; Nicholas J. Higham; Rui Ralha (PARA, 2012)

Backward Stability of Iterations for Computing the Polar Decomposition. - Yuji Nakatsukasa; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 2012)

Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm. - Awad H. Al-Mohy; Nicholas J. Higham (SIAM J. Sci. Comput., 2012)

An Improved Schur-Padé Algorithm for Fractional Powers of a Matrix and Their Fréchet Derivatives. - Nicholas J. Higham; Lijing Lin (SIAM J. Matrix Anal. Appl., 2013)

Computing the Fréchet Derivative of the Matrix Logarithm and Estimating the Condition Number. - Awad H. Al-Mohy; Nicholas J. Higham; Samuel D. Relton (SIAM J. Sci. Comput., 2013)

Stable and Efficient Spectral Divide and Conquer Algorithms for the Symmetric Eigenvalue Decomposition and the SVD. - Yuji Nakatsukasa; Nicholas J. Higham (SIAM J. Sci. Comput., 2013)

NLEVP: A Collection of Nonlinear Eigenvalue Problems. - Timo Betcke; Nicholas J. Higham; Volker Mehrmann; Christian Schröder; Françoise Tisseur (ACM Trans. Math. Softw., 2013)

Reducing the influence of tiny normwise relative errors on performance profiles. - Nicholas J. Dingle; Nicholas J. Higham (ACM Trans. Math. Softw., 2013)

Covariance structure regularization via entropy loss function. - Lijing Lin; Nicholas J. Higham; Jianxin Pan (Comput. Stat. Data Anal., 2014)

Performance analysis of asynchronous Jacobi's method implemented in MPI, SHMEM and OpenMP. - Iain Bethune; J. Mark Bull; Nicholas J. Dingle; Nicholas J. Higham (Int. J. High Perform. Comput. Appl., 2014)

The Matrix Unwinding Function, with an Application to Computing the Matrix Exponential. - Mary Aprahamian; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 2014)

Higher Order Fréchet Derivatives of Matrix Functions and the Level-2 Condition Number. - Nicholas J. Higham; Samuel D. Relton (SIAM J. Matrix Anal. Appl., 2014)

Estimating the Condition Number of the Fréchet Derivative of a Matrix Function. - Nicholas J. Higham; Samuel D. Relton (SIAM J. Sci. Comput., 2014)

An Algorithm for the Matrix Lambert W Function. - Massimiliano Fasi; Nicholas J. Higham; Bruno Iannazzo (SIAM J. Matrix Anal. Appl., 2015)

New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously. - Awad H. Al-Mohy; Nicholas J. Higham; Samuel D. Relton (SIAM J. Sci. Comput., 2015)

Matching exponential-based and resolvent-based centrality measures. - Mary Aprahamian; Desmond J. Higham; Nicholas J. Higham (J. Complex Networks, 2016)

An algorithm to compute the polar decomposition of a 3 × 3 matrix. - Nicholas J. Higham; Vanni Noferini (Numer. Algorithms, 2016)

Anderson acceleration of the alternating projections method for computing the nearest correlation matrix. - Nicholas J. Higham; Natasa Strabic (Numer. Algorithms, 2016)

Matrix Depot: an extensible test matrix collection for Julia. - Weijian Zhang; Nicholas J. Higham (PeerJ Comput. Sci., 2016)

Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms. - Mary Aprahamian; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 2016)

Bounds for the Distance to the Nearest Correlation Matrix. - Nicholas J. Higham; Natasa Strabic (SIAM J. Matrix Anal. Appl., 2016)

Restoring Definiteness via Shrinking, with an Application to Correlation Matrices with a Fixed Block. - Nicholas J. Higham; Natasa Strabic; Vedran Sego (SIAM Rev., 2016)

Estimating the Largest Elements of a Matrix. - Nicholas J. Higham; Samuel D. Relton (SIAM J. Sci. Comput., 2016)

Testing Matrix Function Algorithms Using Identities. - Edvin Deadman; Nicholas J. Higham (ACM Trans. Math. Softw., 2016)

The Rise of Multiprecision Arithmetic. - Nicholas John Higham (ARITH, 2017)

Optimized Batched Linear Algebra for Modern Architectures. - Jack J. Dongarra; Sven Hammarling; Nicholas J. Higham; Samuel D. Relton; Mawussi Zounon (Euro-Par, 2017)

The Design and Performance of Batched BLAS on Modern High-Performance Computing Systems. - Jack J. Dongarra; Sven Hammarling; Nicholas J. Higham; Samuel D. Relton; Pedro Valero-Lara; Mawussi Zounon (ICCS, 2017)

A New Analysis of Iterative Refinement and Its Application to Accurate Solution of Ill-Conditioned Sparse Linear Systems. - Erin C. Carson; Nicholas J. Higham (SIAM J. Sci. Comput., 2017)

Computing the Action of Trigonometric and Hyperbolic Matrix Functions. - Nicholas J. Higham; Peter Kandolf (SIAM J. Sci. Comput., 2017)

Harnessing GPU tensor cores for fast FP16 arithmetic to speed up mixed-precision iterative refinement solvers. - Azzam Haidar; Stanimire Tomov; Jack J. Dongarra; Nicholas J. Higham (SC, 2018)

Etymo: A New Discovery Engine for AI Research. - Weijian Zhang; Jonathan Deakin; Nicholas J. Higham; Shuaiqiang Wang (WWW (Companion Volume), 2018)

Multiprecision Algorithms for Computing the Matrix Logarithm. - Massimiliano Fasi; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 2018)

Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions. - Erin C. Carson; Nicholas J. Higham (SIAM J. Sci. Comput., 2018)

Computing the Wave-Kernel Matrix Functions. - Prashanth Nadukandi; Nicholas J. Higham (SIAM J. Sci. Comput., 2018)

Adaptive precision in block-Jacobi preconditioning for iterative sparse linear system solvers. - Hartwig Anzt; Jack J. Dongarra; Goran Flegar; Nicholas J. Higham; Enrique S. Quintana-Ortí (Concurr. Comput. Pract. Exp., 2019)

Accurate Computation of the Log-Sum-Exp and Softmax Functions. - Pierre Blanchard; Desmond J. Higham; Nicholas J. Higham (CoRR, 2019)

An Arbitrary Precision Scaling and Squaring Algorithm for the Matrix Exponential. - Massimiliano Fasi; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 2019)

A New Preconditioner that Exploits Low-Rank Approximations to Factorization Error. - Nicholas J. Higham; Théo Mary (SIAM J. Sci. Comput., 2019)

A New Approach to Probabilistic Rounding Error Analysis. - Nicholas J. Higham; Théo Mary (SIAM J. Sci. Comput., 2019)

Simulating Low Precision Floating-Point Arithmetic. - Nicholas J. Higham; Srikara Pranesh (SIAM J. Sci. Comput., 2019)

Squeezing a Matrix into Half Precision, with an Application to Solving Linear Systems. - Nicholas J. Higham; Srikara Pranesh; Mawussi Zounon (SIAM J. Sci. Comput., 2019)

A Survey of Numerical Methods Utilizing Mixed Precision Arithmetic. - Ahmad Abdelfattah; Hartwig Anzt; Erik G. Boman; Erin C. Carson; Terry Cojean; Jack J. Dongarra; Mark Gates; Thomas Grützmacher; Nicholas J. Higham; Xiaoye Sherry Li; Neil Lindquist; Yang Liu 179; et al. (CoRR, 2020)

Mixed Precision Block Fused Multiply-Add: Error Analysis and Application to GPU Tensor Cores. - Pierre Blanchard; Nicholas J. Higham; Florent Lopez; Théo Mary; Srikara Pranesh (SIAM J. Sci. Comput., 2020)

A Class of Fast and Accurate Summation Algorithms. - Pierre Blanchard; Nicholas J. Higham; Théo Mary (SIAM J. Sci. Comput., 2020)

Three-Precision GMRES-Based Iterative Refinement for Least Squares Problems. - Erin C. Carson; Nicholas J. Higham; Srikara Pranesh (SIAM J. Sci. Comput., 2020)

Sharper Probabilistic Backward Error Analysis for Basic Linear Algebra Kernels with Random Data. - Nicholas J. Higham; Théo Mary (SIAM J. Sci. Comput., 2020)

A survey of numerical linear algebra methods utilizing mixed-precision arithmetic. - Ahmad Abdelfattah; Hartwig Anzt; Erik G. Boman; Erin C. Carson; Terry Cojean; Jack J. Dongarra; Alyson Fox; Mark Gates; Nicholas J. Higham; Xiaoye S. Li; Jennifer A. Loe; Piotr Luszczek; et al. (Int. J. High Perform. Comput. Appl., 2021)

Numerical behavior of NVIDIA tensor cores. - Massimiliano Fasi; Nicholas J. Higham; Mantas Mikaitis; Srikara Pranesh (PeerJ Comput. Sci., 2021)

Matrices with Tunable Infinity-Norm Condition Number and No Need for Pivoting in LU Factorization. - Massimiliano Fasi; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 2021)

Random Matrices Generating Large Growth in LU Factorization with Pivoting. - Desmond J. Higham; Nicholas J. Higham; Srikara Pranesh (SIAM J. Matrix Anal. Appl., 2021)

A Multiprecision Derivative-Free Schur-Parlett Algorithm for Computing Matrix Functions. - Nicholas J. Higham; Xiaobo Liu (SIAM J. Matrix Anal. Appl., 2021)

Stochastic Rounding and Its Probabilistic Backward Error Analysis. - Michael P. Connolly; Nicholas J. Higham; Théo Mary (SIAM J. Sci. Comput., 2021)

Generating Extreme-Scale Matrices With Specified Singular Values or Condition Number. - Massimiliano Fasi; Nicholas J. Higham (SIAM J. Sci. Comput., 2021)

Exploiting Lower Precision Arithmetic in Solving Symmetric Positive Definite Linear Systems and Least Squares Problems. - Nicholas J. Higham; Srikara Pranesh (SIAM J. Sci. Comput., 2021)

A Set of Batched Basic Linear Algebra Subprograms and LAPACK Routines. - Ahmad Abdelfattah; Timothy B. Costa; Jack J. Dongarra; Mark Gates; Azzam Haidar; Sven Hammarling; Nicholas J. Higham; Jakub Kurzak; Piotr Luszczek; Stanimire Tomov; Mawussi Zounon (ACM Trans. Math. Softw., 2021)

The Influence and Contribution of Jack Dongarra to Numerical Linear Algebra. - Sven Hammarling; Nicholas J. Higham (Comput. Sci. Eng., 2022)

Anymatrix: an extensible MATLAB matrix collection. - Nicholas J. Higham; Mantas Mikaitis (Numer. Algorithms, 2022)

Performance impact of precision reduction in sparse linear systems solvers. - Mawussi Zounon; Nicholas J. Higham; Craig Lucas; Françoise Tisseur (PeerJ Comput. Sci., 2022)

Arbitrary Precision Algorithms for Computing the Matrix Cosine and its Fréchet Derivative. - Awad H. Al-Mohy; Nicholas J. Higham; Xiaobo Liu (SIAM J. Matrix Anal. Appl., 2022)

Optimizing and Factorizing the Wilson Matrix. - Nicholas J. Higham; Matthew C. Lettington (Am. Math. Mon., 2022)

Mixed precision algorithms in numerical linear algebra. - Nicholas J. Higham; Théo Mary (Acta Numer., 2022)

The Power of Bidiagonal Matrices. - Nicholas J. Higham (CoRR, 2023)

Matrix Multiplication in Multiword Arithmetic: Error Analysis and Application to GPU Tensor Cores. - Massimiliano Fasi; Nicholas J. Higham; Florent Lopez; Théo Mary; Mantas Mikaitis (SIAM J. Sci. Comput., 2023)

Computing the Square Root of a Low-Rank Perturbation of the Scaled Identity Matrix. - Massimiliano Fasi; Nicholas J. Higham; Xiaobo Liu (SIAM J. Matrix Anal. Appl., 2023)

Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement. - Patrick Amestoy; Alfredo Buttari; Nicholas J. Higham; Jean-Yves L'Excellent; Théo Mary; Bastien Vieuble (ACM Trans. Math. Softw., 2023)

Probabilistic Rounding Error Analysis of Householder QR Factorization. - Michael P. Connolly; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 2023)

Five-Precision GMRES-Based Iterative Refinement. - Patrick Amestoy; Alfredo Buttari; Nicholas J. Higham; Jean-Yves L'Excellent; Théo Mary; Bastien Vieuble (SIAM J. Matrix Anal. Appl., 2024)

Computing accurate eigenvalues using a mixed-precision Jacobi algorithm. - Nicholas J. Higham; Françoise Tisseur; Marcus Webb; Zhengbo Zhou (CoRR, 2025)

Mixed-precision algorithms for solving the Sylvester matrix equation. - Andrii Dmytryshyn; Massimiliano Fasi; Nicholas J. Higham; Xiaobo Liu (CoRR, 2025)