## Publications

### 2021

- M. P. Connolly, N. J. Higham and T. Mary. SIAM J. Sci. Comput., 43(1): A566-A585, 2021. (11 February 2021)
- PeerJ Comput. Sci., 7: e330, 2021. (10 February 2021)
- SIAM J. Matrix Anal. Appl., 42(1), 185–201. 2021. (02 February 2021)
- SIAM J. Sci. Comput., 43(1): A258-A277. 2021. (19 January 2021)

### 2020

- N. J. Higham and T. Mary. Sharper Probabilistic Backward Error Analysis for Basic Linear Algebra Kernels with Random Data, SIAM J. Sci. Comput., 42(5), A3427–A3446, 2020. (22 October 2020)
- A. Abdelfattah, S. Tomov and J. Dongarra. Matrix multiplication on batches of small matrices in half and half-complex precisions, Journal of Parallel and Distributed Computing, Volume 145, November 2020, Pages 188-201, 2020. (November 2020)
- N. J. Higham and X. Liu. A Multiprecision Derivative-Free Schur–Parlett Algorithm for Computing Matrix Functions, MIMS EPrint 2020.19, 2020. (07 September 2020)
- V. Coppé, D. Huybrechs, R. Matthysen and M. Webb. The AZ algorithm for least squares systems with a known incomplete generalized inverse, SIAM Journal on Matrix Analysis and Applications, 41(3), 1237-1259, 2020. (27 August 2020)
- P. Blanchard, D. J. Higham and N. J. Higham. Accurately Computing the Log-Sum-Exp and Softmax Functions, IMA J. Numer. Anal., 2020 (Advanced access). (19 August 2020)
- M. Fasi and N. J. Higham. Matrices with Tunable Infinity-Norm Condition Number and No Need for Pivoting in LU Factorization, MIMS EPrint 2020.17, 2020. (01 August 2020)
- M. Fasi, N. J. Higham, M. Mikaitis and S. Pranesh. Numerical Behavior of NVIDIA Tensor Cores, MIMS EPrint 2020.10, 2020. (17 July 2020)
- J. W. Pearson and S. Güttel . A spectral-in-time Newton-Krylov method for nonlinear PDE-constrained optimization, MIMS EPrint 2020.16, 2020. (16 July 2020)
- A. Abdelfattah et al. A Survey of Numerical Methods Utilizing Mixed Precision Arithmetic, ArXiv:2007.06674, 2020. (13 July 2020)
- Q. Cao, Y. Pei, K. Akbudak, A. Mikhalev, G. Bosilca, H. Ltaief, D. Keyes, and J. Dongarra. Extreme-scale task-based cholesky factorization toward climate and weather prediction applications, In Proceedings of the Platform for Advanced Scientific Computing Conference, pp. 1-11, 2020. (June 2020)
- A. Ayala, S. Tomov, A. Haidar, and J. Dongarra. heFFTe: Highly Efficient FFT for Exascale, International Conference on Computational Science (ICCS 2020), Amsterdam, Netherlands, 2020. (June 2020)
- A. Abdelfattah, S. Tomov, and J. Dongarra. Investigating the Benefit of FP16-enabled Mixed-precision Solvers for Symmetric Positive Definite Matrices using GPUs, International Conference on Computational Science (ICCS 2020), Amsterdam, Netherlands, Elsevier, 2020. (June 2020)
- S. Güttel and M.Schweitzer. A comparison of limited-memory Krylov methods for Stieltjes functions of Hermitian matrices, arXiv preprint arXiv:2006.05922, 2020. (11 June 2020)
- S. Elsworth and S. Güttel. ABBA: Adaptive Brownian bridge-based symbolic aggregation of time series, Data Mining and Knowledge Discovery, 34:1175–1200, 2020. (03 June 2020)
- S. Pranesh. Backward error and condition number of a generalized Sylvester equation, with application to the stochastic Galerkin method, Linear Algebra and its Applications, 594, 95-116, 2020. (01 June 2020)
- D. Zhong, P. Shamis, Q. Cao, G. Bosilca, and J. Dongarra. Using Arm Scalable Vector Extension to optimize Open MPI
**,**20th IEEE/ACM International Symposium on Cluster, Cloud and Internet Computing (CCGRID 2020), Melbourne, Australia, IEEE/ACM, 2020. (May 2020) - Y. Pei, Q. Cao, G. Bosilca, P. Luszczek, V. Eijkhout, and J. Dongarra. Communication Avoiding 2D Stencil Implementations over PaRSEC Task-Based Runtime, 21st IEEE International Workshop on Parallel and Distributed Scientific and Engineering Computing (PDSEC 2020), New Orleans, LA, IEEE, 2020. (May 2020)
- F. Lopez, E. Chow, S. Tomov, and J. Dongarra. Asynchronous SGD for DNN training on Shared-memory Parallel Architectures, Workshop on Scalable Deep Learning over Parallel And Distributed Infrastructures (ScaDL 2020), 2020. (May 2020)
- 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, SIAM Journal on Scientific Computing, 42(3), C124-C141, 2020. (27 May 2020)
- D. J. Higham, N. J. Higham and S. Pranesh. Random Matrices Generating Large Growth in LU Factorization with Pivoting, MIMS EPrint 2020.13, 2020. (14 May 2020)
- A. Haidar, H. Bayraktar, S. Tomov, J. Dongarra and N. J. Higham. Mixed-Precision Solution of Linear Systems Using Accelerator-Based Computing, Technical Report ICL-UT-20-05, Innovative Computing Laboratory, University of Tennessee, Knoxville, TN, USA, 2020. (May 2020)
- M. P. Connolly, N. J. Higham and and T. Mary. Stochastic Rounding and Its Probabilistic Backward Error Analysis, MIMS EPrint 2020.12, 2020. (10 August 2020)
- P. Beckman, J. Dongarra, N. Ferrier, G. Fox, T. Moore, D. Reed and M. Beck. Harnessing the Computing Continuum for Programming Our World, Fog Computing: Theory and Practice, 215-230, 2020. (25 April 2020)
- S. Elsworth and S. Güttel. The block rational Arnoldi method, SIAM Journal on Matrix Analysis and Applications, 41(2), 365-388, 2020. (09 April 2020)
- M. Fasi and M. Mikaitis. Algorithms for stochastically rounded elementary arithmetic operations in IEEE 754 floating-point arithmetic, MIMS EPrint 2020.9, 2020. (01 April 2020)
- M. Fasi and N. Higham. Generating Extreme-Scale Matrices with Specified Singular Values or Condition Numbers, MIMS EPrint 2020.8, 2020. (27 March 2020)
- N. Higham and E. Hopkins. A Catalogue of Software for Matrix Functions. Version 3.0, MIMS EPrint 2020.7, 2020. (27 March 2020)
- I. V. Gosea and S. Güttel. Algorithms for the rational approximation of matrix-valued functions, arXiv preprint arXiv:2003.06410, 2020. (13 March 2020)
- S. Elsworth and S. Güttel. Time Series Forecasting Using LSTM Networks: A Symbolic Approach, arXiv preprint arXiv:2003.05672, 2020. (12 March 2020)
- H. Anzt, T. Cojean, C. Yen-Chen, J. Dongarra, G. Flegar, P. Nayak, S. Tomov, Y. M. Tsai and Wang, W. Load-balancing sparse matrix vector product kernels on gpus,
*A*CM Transactions on Parallel Computing (TOPC),*7*(1), 1-26, 2020. (March 2020) - E.Carson, N. J. Higham and S. Pranesh. Three-Precision GMRES-based Iterative Refinement for Least Squares Problems, MIMS EPrint 2020.5, 2020. (21 June 2020)
- P. Blanchard, N. J. Higham and T. Mary. A Class of Fast and Accurate Summation Algorithms, SIAM J. Sci. Comput., 42(3):A1541-A1557, 2020. (07 May 2020)
- Y. Lu, I. Yamazaki, F. Ino, Y. Matsushita, S. Tomov and J. Dongarra. Reducing the amount of out‐of‐core data access for GPU‐accelerated randomized SVD, Concurrency and Computation: Practice and Experience, e5754, 2020. (13 April 2020)
- E Poupard, WP Heath and S Güttel. A Hamiltonian Decomposition for Fast Interior-Point Solvers in Model Predictive Control, MIMS EPrint 2020.6, 2020. (18 February 2020)
- S. Güttel, D. Kressner and K. Lund. Limited-memory polynomial methods for large-scale matrix functions, arXiv preprint arXiv:2002.01682. (08 June 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, 2020 IEEE 27th Symposium on Computer Arithmetic (ARITH), Portland, OR, USA, pp. 129-132, 2020. (06 January 2020)
- K. Wong, S. Tomov and J. Dongarra. (2020). Project-Based Research and Training in High Performance Data Sciences, Data Analytics, and Machine Learning, The Journal of Computational Science Education,
*11*(1), 2020. (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. (09 July 2020)
- B. Arslan, V. Noferini and F. Tisseur. The Structured Condition Number of a Differentiable Map Between Matrix Manifolds, with Applications, SIAM. J. Matrix Anal. & Appl., 40(2), 774-799, 2019. (25 June 2019)
- N. J. Higham. Error Analysis For Standard and GMRES-Based Iterative Refinement in Two and Three-Precisions, MIMS EPrint 2019.19, 2019. (03 Dec 2019)
- 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. (07 September 2020)
- 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)
- 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)
- 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, SIAM J. Sci. Comput., 41(5):C585-C602, 2019. (29 October 2019)
- N. J.Higham, S. Pranesh and M. Zounon. Squeezing a Matrix Into Half Precision, with an Application to Solving Linear Systems, SIAM J. Sci. Comput., 41(4), A2536-A2551, 2019. (01 August 2019)
- M. Zemaite, F. Tisseur and R. Kannan. Filtering Frequencies in a Shift-and-invert Lanczos Algorithm for the Dynamic Analysis of Structures, SIAM J. Sci. Comput., 41(3), B601-B624, 2019. (25 June 2019)
- N. J. Higham, G. M. Negri Porzio and F. Tisseur. An Updated Set of Nonlinear Eigenvalue Problems, MIMS EPrint 2019.5, 2019. (26 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)
- C. Jeannerod, T. Mary, C. Pernet and D. Roche. Improving the Complexity of Block Low-Rank Factorizations with Fast Matrix Arithmetic, SIAM Journal on Matrix Analysis and Applications, 40(4), 1478-1496, 2019. (26 November 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. (02 January 2019)

### 2018

- M. Fasi and N. J. Higham. An Arbitrary Precision Scaling and Squaring Algorithm for the Matrix Exponential, SIAM J. Matrix Anal. Appl., 40(4):1233-1256, 2019. (01 October 2019)
- 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, Linear Algebra Appl., 576:246–257, 2019. (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 modeling, Geophysical Journal International, 218(1), 100-114, 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)
- J. Hogg, J. Hook, J. Scott and F. Tisseur. A max-plus approach to incomplete Cholesky factorization preconditioners, SIAM J. Sci. Comput., 40(4), A1987-A2004, 2018. (03 July 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 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)
- M. Van Barel and F. Tisseur. Polynomial eigenvalue solver based on tropically scaled Lagrange linearization, Linear Algebra Appl., 542:186-208, 2018. (01 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. Peters 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)
- D. I. Georgescu and N. J. Higham. Completing Correlation Matrices, 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)
- Y. Nakatsukasa, 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)
- S. Güttel and F. Tisseur. The Nonlinear Eigenvalue Problem, Acta Numerica, 26:1-94, 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. (08 November 2017) - M. J. Gander, S. Güttel and M. Petcu. A nonlinear ParaExp algorithm. In International Conference on Domain Decomposition Methods (pp. 261-270). Springer, Cham. (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)
*Procedia Computer Science*, 108: 495-504, 2017. (June 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

*Nuclear Science and Engineering*, 184(4): 561-574, 2016. (December 2016)- V. Druskin, S. Güttel and L. Knizhnerman. Compressing variable-coefficient exterior Helmholtz problems via RKFIT, MIMS EPrint 2016.53, 2016.
*SIAM J. Matrix Anal. Appl.*, 37(4): 1453-1477, 2016. (11 October 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)
- E. Deadman and N. J. Higham. Testing matrix function algorithms using identities,
*ACM Transactions on Mathematical Software (TOMS)*,*42*(1), 1-15, 2016. (January 2016)