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

- Randomized Low Rank Matrix Approximation: Rounding Error Analysis and a Mixed Precision Algorithm (with M. P. Connolly and S. Pranesh). MIMS EPrint 2022.5, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, July 2022.
- Hamilton’s Discovery of the Quaternions and Creativity in Mathematics (with Dennis Sherwood). MIMS EPrint 2021.9, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, June 2022.
- Probabilistic Rounding Error Analysis of Householder QR Factorization (with M. P. Connolly), MIMS EPrint 2022.5, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, February 2022; revised August 2022.
- Matrix Multiplication in Multiword Arithmetic: Error Analysis and Application to GPU Tensor Cores (with M. Fasi, F. Lopez, T. Mary, and M. Mikaitis), MIMS EPrint 2022.3, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, January 2022. To appear in SIAM J. Sci. Comput.
- Combining Sparse Approximate Factorizations with Mixed Precision Iterative Refinement (with P. Amestoy, A. Buttari, J.-Y. L’Excellent, T. Mary, and B. Vieublé), MIMS EPrint 2022.2, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, January 2022.
- 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. To appear in SIAM J. Matrix Anal. Appl.
- Mixed Precision Algorithms in Numerical Linear Algebra (with T. Mary), Acta Numerica, 31:347–414, 2022.
- Stochastic Rounding: Implementation, Error Analysis and Applications (with M. Croci, M. Fasi, T. Mary, and M. Mikaitis), Roy. Soc. Open Sci., 9(3):1–25, 2022. Science News article about the paper.
- Anymatrix: An Extensible MATLAB Matrix Collection, (with M. Mikaitis), Numer. Algorithms, 90(3):1175–1196, 2021.
- 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), SIAM J. Matrix Anal. Appl., 43(1):233—256, 2022.
- 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; revised April 2022. 22 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), Amer. Math. Monthly, 129(5):454–465, 2022.
- 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.
- 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.
- Solving Block Low-Rank Linear Systems by LU Factorization is Numerically Stable (with T. Mary). IMA J. Numer. Anal., 42(2):951–980, 2021.

## Links

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