Papers

• A Parametrization of Structure-Preserving Transformations for Matrix Polynomials with S. Garvey and S. Wang., Linear Algebra Appl., 674:68-90,2023.
• Robust rational approximations of nonlinear eigenvalue problems (with Stefan Guettel and Gian Maria Negri Porzio), SIAM J. Sci. Comput., 44(4), A2439-A2463, 2022.
• Performance Evaluation of Mixed Precision Algorithms for Solving Sparse Linear Systems (with Mawussi Zounon, Nicholas J. Higham, Craig Lucas), PeerJ Computer Science., 8:e778(1-22), 2022.
• Min-Max Elementwise Backward Error for Roots of Polynomials and a Corresponding Backward Stable Root Finder (with Marc Van Barel). Linear Algebra Appl., 623: 454-477, 2021. doi: 10.1016/j.laa.2020.10.034
• The role of network topology, growth laws and mechanics in the dynamics of cell assemblies (with A. Erlich, G. W. Jones, D. E. Moulton,and A. Goriely). Proc. R. Soc. A 47620190523, 2020.
• Filtering Frequencies in a Shift-and-invert Lanczos Algorithm for the Dynamic Analysis of Structures (with Mante Zemaite and Ramaseshan Kannan). SIAM J. Sci. Comput., 41(3), B601-B624, 2019.
• The Structured Condition Number of a Differentiable Map Between Matrix Manifolds, with Applications (with Bahar Arslan and Vanni Noferini). SIAM. J. Matrix Anal. & Appl., 40(2), 774-799, 2019.
• Max-Balanced Hungarian Scalings Max-Balancing Hungarian Scalings (with James Hook, Jennifer Pestana, and Jonathan Hogg). SIAM. J. Matrix Anal. & Appl., 40(1), 320-346, 2019
• Compact two-sided Krylov metods for nonlinear eigenvalue problems (with Pieter Lietaert and Karl Meerbergen). SIAM J. Sci. Comput., 40(5),A2801-A2829, 2018.
• A max-plus approach to incomplete Cholesky factorization preconditioners (with James Hook, Jennifer Scott, and Jonathan Hogg). SIAM J. Sci. Comput., 40(4), A1987-A2004, 2018.
• Reduction of matrix polynomials to simpler forms (with Yuji Nakatsukasa, Leo Taslaman, and Ion Zaballa). SIAM. J. Matrix Anal. & Appl., 39(1), 148-177, 2018.
• Polynomial eigenvalue solver based on tropically scaled Lagrange linearization (with Marc Van Barel), Linear Algebra Appl., 542:186-208, 2018.
• The Nonlinear Eigenvalue Problem (with Stefan Guettel), Acta Numerica, 26:1-94, 2017.
• Incomplete LU preconditioner based on max-plus approximation of LU factorization (with James Hook) SIAM. J. Matrix Anal. & Appl., 38(4), 1160-1189, 2017.
• Improving the numerical stability of the Sakurai-Sugiura method for quadratic eigenvalue problems, (with Hongjia Chen, Yasuyuki Maeda, Akira Imakura, and Tetsuya Sakurai), JSIAM Letters Vol.9 (2017) pp.17-20, 2017.
• On the sign characteristics of Hermitian matrix polynomials (with Volker Mehrmann, Vanni Noferini and Hongguo Xu) Linear Algebra Appl., 511: 328-364, 2016.
• Efficient block preconditioning for a C1 finite element discretisation of the Dirichlet biharmonic problem (with Jennifer Pestana, Richard Muddle, Matthias Heil, and Milan Mihajlovic) SIAM J. Sci. Comput., 38(1), A325-A345, 2016.
• Polynomial Eigenvalue Problems: Theory, Computation, and Structure (with D. Steven Mackey and Niloufer Mackey) In: P. Benner et al. (eds). Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory. Springer International Publishing, Switzerland, pp. 319-348, 2015.
• Algorithms for Hessenberg-Triangular Reduction of Fiedler Linearization of Matrix Polynomials (with Lars Karlsson). SIAM J. Sci. Comput., 37(3), C384-C414, 2015.
• Tropical roots as approximations to eigenvalues of matrix polynomials (with Vanni Noferini and Meisam Sharify), SIAM. J. Matrix Anal. & Appl., 36(1), 138-157, 2015.
• Detecting the Causes of Ill-Conditioning in Structural Finite Element Models with Ramaseshan Kannan, Stephen Hendry and Nick Higham). Computers and Structures, 133:79-89, 2014. Published version.
• Triangularizing matrix polynomials (with Leo Taslaman and Ion Zaballa), Linear Algebra Appl. 439(7):1679-1699 2013.
• Finite and infinite elementary divisors of matrix polynomials: a global approach (with Ion Zaballa) MIMS EPrint 2012.78, August 2012.
• Triangularizing Quadratic Matrix Polynomials (with Ion Zaballa) SIAM. J. Matrix Anal. & Appl., 34(2), 312-337, 2013.
• An Algorithm for the Complete Solution of Quadratic Eigenvalue Problems with Sven Hammarling and Chris Munro, ACM Transactions on Mathematical Software, 39(3), pp18:1-18:19, 2013.
• NLEVP: A Collection of Nonlinear Eigenvalue Problems (with Timo Betcke, Nick Higham, Volker Mehrmann and Christian Schroder), ACM Transactions on Mathematical Software, 39(2), pp7:1-7:28, 2013.
• Standard Triples of Structured Matrix Polynomials (with Maha Al-Ammari), Linear Algebra Appl., 437(3):817-834, 2012.
• Hermitian Matrix Polynomials with Real Eigenvalues of Definite Type. Part I: Classification (with Maha Al-Ammari). Linear Algebra Appl., 436(10):3954-3973, 2012.
• Hermitian Quadratic Matrix Polynomials: Solvents and Inverse Problems (with Peter Lancaster). Linear Algebra Appl., 436(10):4017-4026, 2012.
• A Framework for Analyzing Nonlinear Eigenproblems and Parametrized Linear Systems (with Laurence Grammont and Nick Higham ). Linear Algebra Appl., 435: 623-640, 2011.
• Deflating Quadratic Matrix Polynomials with Structure Preserving Transformations (with Seamus D. Garvey and Christopher Munro). Linear Algebra Appl., 435: 464-479, 2011.
• The Canonical Generalized Polar Decomposition (with Nick Higham and Christian Mehl), SIAM J. Matrix Anal. Appl. 31(4): 2163-2180, 2010.
• An Improved Arc Algorithm for Detecting Definite Hermitian Pairs (with Chun-Hua Guo and Nick Higham, SIAM J. Matrix Anal. Appl. 31(3), 1131-1151, 2009.
• Definite Matrix Polynomials and their Linearization by Definite Pencils (with Nick Higham and D. Steven Mackey), SIAM J. Matrix Anal. Appl. 31(2), 478-502, 2009.
• Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems (with Chun-Hua Guo and Nick Higham), SIAM J. Matrix Anal. Appl., 30(4):1593-1613, 2009.
• On the Definition of Two Natural Classes of Scalar Product. (With D. Steven Mackey and Niloufer Mackey, MIMS EPrint 2007.64, April 2007 (revised February 2009).
• Scaling, Sensitivity and Stability in the Numerical Solution of Quadratic Eigenvalue Problems (With Nick Higham, D. Steven Mackey, Seamus D. Garvey), MIMS EPrint 2006.406, November 2006. Internat. J. Numer. Methods Eng., 73(3):344-360, 2008. Published version.
• Structured Mapping Problems for Matrices Associated with Scalar Products Part I: Lie and Jordan Algebras (With D. Steven Mackey and Niloufer Mackey, SIAM J. Matrix Anal. Appl., 29(4):1389-1410, 2008.
• Backward Error of Polynomial Eigenproblems Solved by Linearization (With Nick Higham and Ren-Cang Li), SIAM J. Matrix Anal. Appl., 29(4):1218-1241, 2007.
• Symmetric Linearizations for Matrix Polynomials (With Nick Higham), D. Steven Mackey and Niloufer Mackey, SIAM J. Matrix Anal. Appl., 29(1):143-159, 2006.
• Structured Condition Numbers and Backward Errors in Scalar Product Spaces (with Stef Graillat). Electronic Journal of Linear Algebra (15):159-177, 2006.
• Structured Eigenvalue Condition Numbers (with Michael Karow and Daniel Kressner), SIAM J. Matrix Anal. Appl. 28(4):1052-1068, 2006.
• The Conditioning of Linearizations of Matrix Polynomials (with Nick Higham and D. Steven Mackey), SIAM J. Matrix Anal. Appl. 28(4):1005-1028, 2006.
• Structured Factorizations in Scalar Product Spaces, (with D. S. Mackey and N. Mackey) SIAM J. Matrix Anal. Appl., 27(3):821-850, 2006.
• Functions Preserving Matrix Groups and Iterations for the Matrix Square Root (With Nick Higham, D. Steven Mackey and Niloufer Mackey, SIAM J. Matrix Anal. Appl. 26(3):849-877, 2005.
• The Ehrlich-Aberth Method for the Nonsymmetric Tridiagonal Eigenvalue Problem (With Dario A. Bini and Luca Gemignani). SIAM J. Matrix Anal. Appl. 27(1):153-175, 2005.
• Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups (With Nick Higham, D. Steven Mackey and Niloufer Mackey). SIAM J. Matrix Anal. Appl. 25(4):1178-1192, 2004.
• G-Refectors: Analogues of Householder Transformations in Scalar Product Spaces , (with D. S. Mackey and N. Mackey) Linear Algebra Appl. 385: 187-213, 2004.
• Structured Tools for Structured Matrices , (with D. S. Mackey and N. Mackey) Electronic Journal of Linear Algebra, (10):106-145, 2003.
• Tridiagonal-diagonal Reduction of Symmetric Indefinite Pairs , SIAM J. Matrix Anal. Appl. 26(1):215-232, 2004.
• Simultaneous Tridiagonalization of Two Symmetric Matrices , (with S. D. Garvey, M. I. Friswell, J. E. T. Penny and U. Prells) Int. J. Numer. Meth. Engng.,57(12):1643-1660, 2003.
• A Chart of Backward Errors and Condition Numbers for Singly and Doubly Structured Eigenvalue Problems, SIAM J. Matrix Anal. Appl., 24(3):877-897, 2003.
• Implicit Gamma Theorems (I): Pseudoroots and Pseudospectra (with Jean-Pierre Dedieu, Myong-Hi Kim and Michael Shub), Found. Comput. Math. 3:1-31, 2003.
• Detecting a Definite Hermitian Pair and a Hyperbolic or Elliptic Quadratic Eigenvalue Problem, and Associated Nearness Problems (with Nick Higham and Paul Van Dooren), Linear Algebra Appl., 351-352:455-474, 2002.
• More on Pseudospectra for Polynomial Eigenvalue Problems and Applications in Control Theory (with Nick Higham), Linear Algebra Appl., 351-352:435-453, 2002.
• Perturbation Theory for Homogeneous Polynomial Eigenvalue Problems (with Jean-Pierre Dedieu), Linear Algebra Appl., 358:71-94, 2003.
• Bounds for Eigenvalues of Matrix Polynomials (with Nick Higham), Linear Algebra Appl., 358:5-22, 2003.
• The Quadratic Eigenvalue Problem (with Karl Meerbergen), SIAM Review, (43)2:235-286,2001.
• Analysis of the Cholesky Method with Iterqative Refinement for Solving the Symmetric Definite Generalized Eigenproblem (with Philip Davies and Nick Higham), SIAM J. Matrix Anal. Appl., 23(2):472-493, 2001.
• Structured Pseudospectra for Polynomial Eigenvalue Problems, with Applications (with Nick Higham), SIAM J. Matrix Anal. Appl., 23(1):187-208, 2001.
• Stability of Structured Hamiltonian Eigensolvers SIAM J. Matrix Anal. Appl., 23(1): 103-125, 2001.
• Newton's Method in Floating Point Arithmetic and Iterative Refinement of Generalized Eigenvalue Problems SIAM J. Matrix Anal. Appl., 22(4): 1038-1057, 2001.
• A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra (With Nick Higham). SIAM J. Matrix Anal. Appl., 21(4): 1185-1201, 2000.
• Backward Error and Condition of Polynomial Eigenvalue Problems Linear Algebra Appl., 309(1-3):339-361, 2000.
• A Parallel Divide and Conquer Algorithm for the Symmetric Eigenvalue Problem on Distributed Memory Architectures. (With Jack Dongarra). SIAM J. Sci. Comput., 20(6): 2223-2236, 1999.
• Parallel Implementation of a Symmetric Eigensolver Based on the Yau and Lu Method (with S. Domas), Lecture Notes in Computer Science 1215, pp.140-153, 1997.
• Parallel Implementation of the Yau and Lu Method for Eigenvalue Computation, Int. Journal of Supercomputer Appl. and High Performance Comp., 11(3), pp.197-204, 1997.
• PVM Precise Eigenvalue Computations (with M. Ahues and A. Largillier), in J. Dongarra, M. Gengler, B. Tourancheau, X. Vigouroux, editors, EuroPVM'95, volume 5 of Parallelisme, Reseaux et Repartition, pp. 253-258, Hermes, Paris, 1995.

Technical Reports

• Stability analysis of a chain of non-identical vehicles under bilateral cruise control (with Liang Wang, Gilbert Strang and Berthold K. P. Horn). MIMS EPrint 2019.3, March 2019.
• Parallelizing the Divide and Conquer Algorithm for the Symmetric Tridiagonal Eigenvalue Problem on Distributed Memory Architectures (With Jack Dongarra). NA Report No. 317, March 1998.
• Backward Stability of the QR Algorithm TR 239, UMR 5585 Lyon Saint-Etienne, October 1996.
• Methodes numeriques pour le calcul d'elements spectraux, Ph.D thesis, May 1997, University of Saint-Etienne, France.
• A New Deflation Criterion for the QR Algorithm. LAPACK Working Note 122, March 1997.