The Github repository njhigham-bib contains a BibTeX database of all my papers, books, EPrints, articles, etc. Direct links: njhigham.pdf, njhigham.bib (requires strings.bib).

A complete list of all my publications is available with links and BibTeX entries (via BibBase: may take a few seconds to load).

- Latest Papers
- Correlation matrices
- Eigenvalue problems
- Least squares problems
- Linear systems, condition estimation
- Matrix functions and nonlinear matrix equations
- Miscellaneous
- Articles and book reviews
- Links

## Latest Papers

- Computing the Square Root of a Low-Rank Perturbation of the Scaled Identity Matrix (with M. Fasi and X. Liu), MIMS EPrint 2022.1, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, January 2022.
- Mixed Precision Algorithms in Numerical Linear Algebra (With T. Mary), MIMS EPrint 2021.20, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, April 2021. To appear in Acta Numerica.
- Stochastic Rounding: Implementation, Error Analysis, and Applications (with M. Croci, M. Fasi, T. Mary, and M. Mikaitis), MIMS EPrint 2021.17, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, October 2021; revised January 2022.
- Anymatrix: An Extensible MATLAB Matrix Collection, (with M. Mikaitis), Numer. Algorithms, 2021; early view.
- Anymatrix: An Extensible MATLAB Matrix Collection. Users’ Guide (with M. Mikaitis). MIMS EPrint 2021.15, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, October 2021. 31 pp.
- Numerical Stability of Algorithms at Extreme Scale and Low Precisions MIMS EPrint 2021.14, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, September 2021.
- Arbitrary Precision Algorithms for Computing the Matrix Cosine and its Fréchet Derivative, (with A. H. Al-Mohy and X. Liu), MIMS EPrint 2021.23, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, August 2021; revised November 2021. To appear in SIAM J. Matrix Anal. Appl.
- Disseminating Research Through Articles and Blogs. Mathematics Today, 57(4):116–117, 2021. Also available as a page on the IMA website.
- A set of Batched Basic Linear Algebra Subprograms and LAPACK routines (with A. Abdelfattah, T. Costa, J. Dongarra, M. Gates, A. Haidar, S. Hammarling, J. Kurzak, P. Luszczek, S. Tomov, and M. Zounon). ACM Trans. Math. Software, 47(3):21:1–21:23, 2021.
- The Mathematics Of Floating-Point Arithmetic. LMS Newsletter, 493:35–41, 2021.
- Five-precision GMRES-based iterative refinement (with P. Amestoy, A. Buttari, J.-Y. L’Excellent, T. Mary, and B. Vieublé). MIMS EPrint 2021.5, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, April 2021. 21 pp.
- Integer Matrix Factorisations, Superalgebras and the Quadratic Form Obstruction (with M. C. Lettington and K. M. Schmidt). Linear Algebra Appl., 622:250–267, 2021.
- Optimizing and Factorizing the Wilson Matrix (with M. C. Lettington), MIMS EPrint 2021.3, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, February 2021. 12 pp. To appear in American Mathematical Monthly.
- Cover Image: Bohemian Matrices (with R. M. Corless, and S. E. Thornton). LMS Newsletter, 491:16, 2020.
- Completing the Matrix (with D. I. Georgescu). The Actuary, pages 24-27, November 2020.
- Performance Impact of Precision Reduction In Sparse Linear Systems Solvers (with M. Zounon, C. Lucas and F. Tisseur), PeerJ Comput. Sci., 8:e778(1–22), 2022.
- A Multiprecision Derivative-Free Schur-Parlett Algorithm for Computing Matrix Functions (with Xiaobo Liu), SIAM J. Matrix Anal. Appl., 42(3):1401–1422, 2021. Blog post.
- Matrices with Tunable Infinity-Norm Condition Number and No Need for Pivoting in LU Factorization (with M. Fasi). SIAM J. Matrix Anal. Appl. 42(1):417–435, 2021. Blog post.
- A Survey of Numerical Methods Utilizing Mixed Precision Arithmetic (with A. Abdelfattah et al.). Int. J. High Performance Computing Applications, 35(4):344–369, 2021.
- Mixed-Precision Iterative Refinement Using Tensor Cores on GPUs to Accelerate Solution of Linear Systems (with A. Haidar, H. Bayraktar, S. Tomov and J. Dongarra), Proc. Roy. Soc. London A, 476 (2243):20200110, 2020.
- Stochastic Rounding and Its Probabilistic Backward Error Analysis (with M. P. Connolly and and T. Mary), SIAM J. Sci. Comput., 43(1):A566–A585, 2021. Blog post.
- Numerical Behavior of NVIDIA Tensor Cores (with M. Fasi), M. Mikaitis, and S. Pranesh), PeerJ Comput. Sci. 7:e330(1–19), 2021. Blog post.
- Generating Extreme-Scale Matrices with Specified Singular Values or Condition Numbers (with M. Fasi), SIAM J. Sci. Comput., 43(1):A663–A684, 2021.
- Random Matrices Generating Large Growth in LU Factorization with Pivoting (with D. J. Higham and S. Pranesh), SIAM J. Matrix Anal. Appl., 42(1):185–201, 2021.
- A Catalogue of Software for Matrix Functions. Version 3.0 (with Edvin Hopkins), MIMS EPrint 2020.7, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, March 2020. 24 pp.
- Three-Precision GMRES-based Iterative Refinement for Least Squares Problems (with E. Carson and S. Pranesh). SIAM J. Sci. Comput., 42(6):A4063-A4083, 2020.
- Sharper Probabilistic Backward Error Analysis for Basic Linear Algebra Kernels With Random Data (with T. Mary). SIAM J. Sci. Comput., 42(5):A3427-A3446, 2020. Blog post.
- Numerical Algorithms for High-Performance Computational Science (with J. Dongarra and L. Grigori). Phil. Trans. R. Soc. A, 378(2166):1-18, 2020.
- Exploiting Lower Precision Arithmetic in Solving Symmetric Positive Definite Linear Systems and Least Squares Problems (with S. Pranesh). SIAM J. Sci. Comput., 43(1):A258–A277, 2021.
- Mixed Precision Block Fused Multiply-Add: Error Analysis and Application to GPU Tensor Coress (with P. Blanchard, F. Lopez, T. Mary and S. Pranesh). SIAM J. Sci. Comput., 42(3):C124-C141, 2020.
- Accurately Computing the Log-Sum-Exp and Softmax Functions (with P. Blanchard and D. J. Higham). IMA J. Numer. Anal., 1–20, 2020 (Advanced access).
- Solving Block Low-Rank Linear Systems by LU Factorization is Numerically Stable (with T. Mary). IMA J. Numer. Anal., 1–30. 2021 (Advanced access).

## Links

- Citations on Google Scholar.
- Researcher ID profile
- List of publications on MathSciNet (requires subscription).
- Citations on MathSciNet (requires subscription).