## Publications

### 2020

- E.Carson, N. J. Higham and S. Pranesh. Three-Precision GMRES-based Iterative Refinement for Least Squares Problems, MIMS EPrint 2020.5, 2020. (03 February 2020)
- N. J. Higham and T. Mary. Sharper Probabilistic Backward Error Analysis for Basic Linear Algebra Kernels With Random Data, MIMS EPrint 2020.4, 2020. (21 January 2020)
- J. Dongarra, N. J. Higham and L. Grigori. Numerical Algorithms for High-Performance Computational Science, Phil. Trans. R. Soc. A, 378(2166):1-18, 2020. (20 January 2020)
- F. Tisseur and M. Van Barel. Min-Max Elementwise Backward Error for Roots of Polynomials and a Corresponding Backward Stable Root Finder, arXiv:2001.05281, 2020. (15 January 2020)
- M. Mikaitis. Stochastic Rounding: Algorithms and Hardware Accelerator, arXiv:2001.01501, 2020. (06 January 2020)
- M. Mikaitis. Issues with rounding in the GCC implementation of the ISO 18037:2008 standard fixed-point arithmetic, arXiv:2001.01496, 2020. (06 January 2020)

### 2019

- N. J. Higham and S. Pranesh. Exploiting Lower Precision Arithmetic in Solving Symmetric Positive Definite Linear Systems and Least Squares Problems, MIMS EPrint 2019.20, 2019. (06 November 2019)
- P. Blanchard, F. Lopez, N. J. Higham, T. May and S. Pranesh. Mixed Precision Block Fused Multiply-Add: Error Analysis and Application to GPU Tensor Cores, MIMS EPrint 2019.18, 2019. (22 February 2020)
- N. J. Higham and T. Mary. A New Approach to Probabilistic Rounding Error Analysis, SIAM J. Sci. Comput., 41(5):A2815-A2835, 2019. (12 September 2019)
- N. J. Higham and T. Mary. Solving Block Low-Rank Linear Systems by LU Factorization is Numerically Stable, MIMS EPrint 2019.15, 2019. (09 September 2019)
- P. Blanchard, D. J. Higham and N. J. Higham. Accurate Computation of the Log-Sum-Exp and Softmax Functions, MIMS EPrint 2019.16, 2019. (31 January 2020)
- S. Pranesh. Backward error and condition number of a generalized Sylvester equation, with application to the stochastic Galerkin method, MIMS EPrint 2019.13, 2019. (19 June 2019)
- J. Dongarra, M. Gates, A. Haidar, J. Kurzak, P. Luszczek, P. Wu, I. Yamazaki, A. Yarkhan, M. Abalenkovs, N. Bagherpour, S. Hammarling, J. Šístek, D. Stevens, M. Zounon, and S. Relton. PLASMA: Parallel Linear Algebra Software for Multicore Using OpenMP, ACM Transactions on Mathematical Software (TOMS), 45(2), 16, 2019. (06 June 2019)
- S. Elsworth and S. Güttel. ABBA: Adaptive Brownian bridge-based symbolic aggregation of time series, MIMS 2019.11, 2019. (28 May 2019)
- Bridging the Gap between Flat and Hierarchical Low-rank Matrix Formats: the Multilevel Block Low-Rank Format, SIAM J. Sci. Comput., 41(3):A1414-A1442, 2019. (02 May 2019)
- A. Erlich, G. W. Jones, F. Tisseur, D. E. Moulton and A. Goriely. The role of network topology, growth laws and mechanics in the dynamics of cell assemblies, arXiv:1904.11161, 2019. (25 April 2019)
- P. Blanchard, N. J. Higham and T. Mary. A Class of Fast and Accurate Summation Algorithms, MIMS EPrint 2019.6, 2019. To appear in SIAM J. Sci. Comput. (22 February 2020)
- M. Fasi. Optimality of the Paterson-Stockmeyer methods for evaluating matrix polynomials and rational functions, Linear Algebra Appl., 574:182–200, 2019.
- Performance and Scalability of the Block Low-Rank Multifrontal Factorization on Multicore Architectures, ACM Trans. Math. Software, 45(1):2:1-2:26, 2019. (28 March 2019)
- N. J. Higham and S. Pranesh. Simulating Low Precision Floating-Point Arithmetic, MIMS EPrint 2019.4, 2019. (20 March 2019)
- L. Wang, F. Tisseur, G. Strang and B. K. P. Horn. Stability analysis of a chain of non-identical vehicles under bilateral cruise control, MIMS EPrint 2018.3, 2019. (17 March 2019)
- J. Hook, J. Pestana, F. Tisseur and J. Hogg. Max-Balanced Hungarian Scalings, SIAM J. Matrix Anal. Appl., 40(1), 320–346, 2019. (26 February 2019)
- H. Anzt, J. Dongarra, G. Flegar, N. J. Higham and E. S. Quintana-Orti. Adaptive Precision in Block-Jacobi Preconditioning for Iterative Sparse Linear System Solvers, Concurrency Computat.: Pract. Exper, 31(6), e4460, 2019 (18 February 2019)
- S. Elsworth and S. Güttel. The block rational Arnoldi method, MIMS 2019.2, 2019. (17 February 2019)
- C. Jeannerod, T. Mary, C. Pernet and D. Roche. Exploiting Fast Matrix Arithmetic in Block Low-Rank Factorizations, MIMS EPrint 2019.1, 2019. (03 February 2019)
- N. J. Higham and T. Mary. A new preconditioner that exploits low-rank approximations to factorization error, SIAM J. Sci. Comput., 41(1), A59-A82, 2019. (02 January 2019)

### 2018

- M. Fasi and N. J. Higham. An Arbitrary Precision Scaling and Squaring Algorithm for the Matrix Exponential, MIMS EPrint 2018.36, 2018. (25 November 2018)
- A.Haidar, S. Tomov, J. Dongarra and N. J. Higham. Harnessing GPU Tensor Cores for Fast FP16 Arithmetic to Speed up Mixed-Precision Iterative Refinement Solvers, In Proceedings of the International Conference for High Performance Computing, Networking, Storage, and Analysis (p. 47), IEEE Press, 2018. (11 November 2018)
- S. Elsworth and S. Güttel. Conversions between barycentric, RKFUN, and Newton representations of rational interpolants, MIMS EPrint 2017.40, 2018. (4 October 2018)
- M. Fasi and B. Iannazzo. Computing Primary Solutions of Equations Involving Primary Matrix Functions, Linear Algebra and its Applications, 560, 17-42, 2018. (18 September 2018)
- P. Lietaert, K. Meerbergen and F. Tisseur. Compact Two-Sided Krylov Methods for Nonlinear Eigenvalue Problems, SIAM J. Sci. Comput., 40(5), A2801-A2829, 2018. (4 September 2018)
- C. Qiu, S. Güttel, X. Ren, C. Yin, U. Liu, B. Zhang and G.Egbert. A block rational Krylov method for three-dimensional time-domain marine controlled-source electromagnetic modelinga Search A block rational Krylov method for three-dimensional time-domain marine controlled-source electromagnetic modeling, MIMS EPrint 2018.22, 2018. (19 August 2018)
- P. Nadukandi and N. J. Higham. Computing the wave-kernel matrix functions,,
*SIAM J. Sci. Comput.*, 40(6), A4060–A4082, 2019. (6 December 2018) - A. Haidar, A. Abdelfattah, M. Zounon, P. Wu, S. Pranesh, S. Tomov, and J. Dongarra. The Design of Fast and Energy-Efficient Linear Solvers: On the Potential of Half-Precision Arithmetic and Iterative Refinement Techniques, In
*International Conference on Computational Science*, pp. 586-600. Springer, Cham, 2018. (12 June 2048) - M. Zemaite, F. Tisseur and R. Kannan. Filtering Frequencies in a Shift-and-invert Lanczos Algorithm for the Dynamic Analysis of Structures, MIMS EPrint 2018.17, 2018. (25 May 2018)
- W. Zhang, J. Deakin N. J. Higham and S. Wang Etymo: A New Discovery Engine for AI Research, in Companion Proceedings of the Web Conference 2018, International World Wide Web Conferences Steering Committee, pp. 227-230, 2018. (23 April 2018)
- T. Kinyanjui, J. Middleton, S. Güttel, J. Cassell, J. Ross and T. House. Scabies in residential care homes: Modelling, inference and interventions for well-connected population sub-units, PLoS Computational Biology, 14(3):1–24,2018. (26 March 2018)
- M. Fasi and N. J. Higham. Multiprecision Algorithms for Computing The Matrix Logarithm, SIAM J. Matrix Anal. Appl., 39(1):472-491, 2018. (17 March 2018)
- M. Fasi and N. J. Higham. Multiprecision Algorithms for Computing the Matrix Logarithm, SIAM J. Matrix Anal. Appl., 39(1), 472–491, 2018. 15 March 2018)
- E. Carson and N, J. Higham, Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions, SIAM J. Sci. Comput., 40(2), A817–A847, 2018. (15 March 2018)
- D. I. Georgescu, G. W. Peter and N. J. Higham. Explicit Solutions to Correlation Matrix Completion Problems, with an Application to Risk Management and Insurance, Roy. Soc. Open Sci., 5(3):1-11, 2018. (1 March 2018)
- I. Yamazaki, J. Kurzak, P. Wu, M. Zounon, and J. Dongarra. Symmetric Indefinite Linear Solver Using OpenMP Task on Multicore Architectures, IEEE Trans. Parallel Distrib. Syst. 29(8): 1879-1892, 2018. (23 February 2018)
- M. Fasi and B. Iannazzo. Computing the weighted geometric mean of two large-scale matrices and its inverse times a vector (with B. Iannazzo). SIAM J. Matrix Anal. Appl., 39(1):178-203, 2018. (01 February 2018)
- Y. Makatsukasa, L. Taslaman, F. Tisseur and I. Zaballa. Reduction of Matrix Polynomials to Simpler Forms, SIAM. J. Matrix Anal. & Appl., 39(1), 148-177, 2018. (30 January 2018)

### 2017

- E. Carson and N. J. Higham. A new analysis of iterative refinement and its application to accurate solution of ill-conditioned sparse linear systems, SIAM J. Sci. Comput., 39(6):A2834-A2856, 2017. (6 December 2017)
- B. Arslan, V. Noferini and F. Tisseur. The Structured Condition Number of a Differentiable Map Between Matrix Manifolds, with Applications, MIMS EPrint 2017.36, 2017. (8 November 2017)
- M. Berljafa and S. Güttel. Parallelization of the rational Arnoldi algorithm, SIAM J. Sci. Comput., 39(5):S197–S221, 2017. (8 November 2017)
- J. Hogg, J. Hook, J. Scott and F. Tisseur. A max-plus approach to incomplete Cholesky factorization preconditioners, MIMS EPrint 2016.59, 2016. (8 November 2017)
- S. Güttel and F. Tisseur. The Nonlinear Eigenvalue Problem, MIMS EPrint 2017.7, 2017. (20 October 2017)
- S. Hammarling. Second Workshop on Batched, Reproducible, and Reduced Precision BLAS, MIMS 2017.14, 2017.
- J. Hook and F. Tisseur. Incomplete LU Preconditioner Based on Max-Plus Approximation of LU Factorization, SIAM. J. Matrix Anal. & Appl., 38(4), 1160-1189, 2017. (19 October 2017)
- S. Güttel and J. W. Pearson. A rational deferred correction approach to parabolic optimal control problems, IMA Journal of Numerical Analysis,
*38*(4), 1861-1892, 2017. (8 November 2017) - M.J Gander, S. Güttel and M. Petcu. A nonlinear ParaExp algorithm, MIMS EPrint 2017.17. (21 January 2018).
- M. Berljafa and S. Güttel. The RKFIT algorithm for nonlinear rational approximation, SIAM J. Sci. Comput., 39(5):A2049–A2071, 2017. (8 November 2017)
- H. Chen, Y. Maeda, A. Imakura, T. Sakurai and F. Tisseur. Improving the numerical stability of the Sakurai-Sugiura method for quadratic eigenvalue problems, JSIAM Letters Vol.9 (2017) pp.17-20, 2017. (24 March 2017)

### 2016

- M. Van Barel and F. Tisseur. Polynomial eigenvalue solver based on tropically scaled Lagrange linearization, MIMS EPrint 2016.61, 2016. (8 November 2017)
- V. Druskin, S. Güttel and L. Knizhnerman. Compressing variable-coefficient exterior Helmholtz problems via RKFIT, MIMS EPrint 2016.53, 2016.
- V. Mehrmann, V. Noferini, F. Tisseur and H. Xu. On the sign characteristics of Hermitian matrix polynomials, Linear Algebra Appl., 511: 328-364, 2016. (14 September 2016)
- V. Druskin, S. Güttel and L. Knizhnerman. Near-optimal perfectly matched layers for indefinite Helmholtz problems, SIAM Rev., 58(1):90–116, 2016. (20 October 2017)
- S. Güttel and Y. Nakatsukasa. Scaled and squared subdiagonal Padé approximation for the matrix exponential, SIAM J. Matrix Anal. Appl., 37(1):145–170, 2016.
- S. Hammarling. Workshop on batched, reproducible, and reduced precision BLAS. MIMS EPrint 2016.41, 2016. (20 October 2017)
- J. Dongarra, I Duff, M. Gates, A. Haidar, S. Hammarling, N. J. Higham, J. Hogg, P. ValeroLara, S. Relton, S. Tomov, and M. Zounon. A proposed API for batched basic linear algebra subprograms. MIMS EPrint 2016.25, 2016. (08 November 2017)
- J.Pestana, R. Muddle, M. Heil, F. Tisseur and M. Mihajlovic. Efficient block preconditioning for a C1 finite element discretisation of the Dirichlet biharmonic problem, SIAM J. Sci. Comput., 38(1), A325-A345, 2016. (08 November 2017)