# Publications

This is a list of publications available through the MIMS EPrint Server. It is not a complete list of publications for each person and in some cases content might be restricted for copyright reasons. Please get in touch with the relevant Group member for further information.

A recent list of books produced by the Numerical Analysis Group and some recent dissertations are also available.

## Browse by author

### A. H. Al-Mohy

Awad H. Al-Mohy and Nicholas J. Higham, Computing the Fréchet Derivative of the Matrix Exponential, with an application to Condition Number Estimation, SIAM Journal On Matrix Analysis and Applications., 30, (2009).

Awad H. Al-Mohy and Nicholas J. Higham, The Complex Step Approximation to the Fréchet Derivative of a Matrix Function, Numerical Algorithms, 53, (2010).

Awad H. Al-Mohy and Nicholas J. Higham, A New Scaling and Squaring Algorithm for the Matrix Exponential, SIAM Journal On Matrix Analysis and Applications., 31, (2009).

Nicholas J. Higham and Awad H. Al-Mohy, Computing Matrix Functions, Acta Numerica, 19, (2010).

Awad H. Al-Mohy, Algorithms for the Matrix Exponential and its Fr\'echet Derivative, (2010).

Awad H. Al-Mohy and Nicholas J. Higham, Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators, SIAM Journal on Scientific Computing, 33, (2011).

Awad H. Al-Mohy, A More Accurate Briggs Method for the Logarithm, preprint, (2011).

Awad H. Al-Mohy and Nicholas J. Higham, Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm, SIAM Journal on Scientific Computing, 34, (2012).

Awad H. Al-Mohy, Nicholas J. Higham and Samuel D. Relton, Computing the Frechet Derivative of the Matrix Logarithm and Estimating the Condition Number, SIAM J. Sci. Comput., 35, (2013).

Awad H. Al-Mohy, Nicholas J. Higham and Samuel D. Relton, New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously, preprint, (2014).

### C. T. H. Baker

C. T. H. Baker, C. A. H. Paul and H. Tian, Differential algebraic equations with after-effect, Journal of Computational and Applied Mathematics, 140, (2002).

C. T. H. Baker, G. A. Bocharov, C. A. H. Paul and F. A. Rihan, Computational modelling with functional differential equations: identification, selection and sensitivity, Applied Numerical Mathematics, 53, (2005).

C. T. H. Baker, G. A. Bocharov, J. M. Ford, P. M. Lumb, S. J. Norton, C. A. H. Paul, T. Junt, P. Krebs and B. Ludewig, Computational approahes to parameter estimation and model selection in immunology, Journal of Computational and Applied Mathematics, 184, (2005).

C. T. H. Baker and C. A. H. Paul, Discontinuous solutions of neutral delay differential equations, Applied Numerical Mathematics, 56, (2006).

Christopher Baker and Yihong Song, Periodic solutions of discrete Volterra equations, Mathematics and Computers in Simulation, 64, (2004).

### A. Bespalov

Alexei Bespalov and Norbert Heuer, Natural hp-BEM for the electric field integral equation with singular solutions, preprint, (2010).

Alexei Bespalov, Catherine E. Powell and David Silvester, A priori error analysis of stochastic Galerkin mixed approximations of elliptic PDEs with random data, SIAM Journal on Numerical Analysis, 50, (2012).

David Silvester, Alexei Bespalov and Catherine E. Powell, A framework for the development of implicit solvers for incompressible flow problems, preprint, (2011).

Alex Bespalov, Catherine E. Powell and David Silvester, Energy norm a posteriori error estimation for parametric operator equations, SIAM Journal on Scientific Computing, 36, (2014).

### T. Betcke

Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder and Françoise Tisseur, NLEVP: A Collection of Nonlinear Eigenvalue Problems, preprint, (2008).

Timo Betcke, The Generalized Singular Value Decomposition and the Method of Particular Solutions, SIAM J. Sci. Comp., 30, (2008).

Alex H. Barnett and Timo Betcke, Quantum mushroom billiards, Chaos, 17, (2007).

T. Betcke, Optimal scaling of generalized and polynomial eigenvalue problems, preprint, (2007).

A. H. Barnett and T. Betcke, Stability and Convergence of the Method of Fundamental Solutions for Helmholtz problems on analytic domains, Journal of Computational Physics, 227, (2008).

Timo Betcke and Daniel Kressner, Perturbation, Computation and Refinement of Invariant Subspaces for Matrix Polynomials, preprint, (2009).

Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder and Françoise Tisseur, NLEVP: A Collection of Nonlinear Eigenvalue Problems, preprint, (2010).

Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder and Françoise Tisseur, NLEVP: A Collection of Nonlinear Eigenvalue Problems. Users' Guide, preprint, (2010).

Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder and Françoise Tisseur, NLEVP: A Collection of Nonlinear Eigenvalue Problems, preprint, (2011).

Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder and Françoise Tisseur, NLEVP: A Collection of Nonlinear Eigenvalue Problems. Users' Guide, preprint, (2011).

Timo Betcke and Lloyd N. Trefethen, Reviving the Method of Particular Solutions, SIAM Review, 47, (2005).

T. Betcke and L. N. Trefethen, Computations of Eigenvalue Avoidance in Planar Domains, PAMM, Proceedings in Applied Mathematics and Mechanics, 4, (2004).

Lloyd N. Trefethen and Timo Betcke, Computed eigenmodes of planar regions, AMS Contemporary Mathematics.

Timo Betcke and Heinrich Voss, A Jacobi-Davidson type projection method for nonlinear eigenvalue problems, Future Generation Computer Systems, 20, (2004).

Timo Betcke, A GSVD formulation of a domain decomposition method for planar eigenvalue problems, IMA Journal of Numerical Analysis.

### Y. Chahlaoui

Younes Chahlaoui and Paul Van Dooren, Benchmark examples for model reduction of linear time invariant dynamical systems..

Younes Chahlaoui and Paul Van Dooren, Model reduction of time-varying systems., (2006).

Younes Chahlaoui, Kyle A Gallivan, Antoine Vandendorpe and Paul Van Dooren, Model Reduction of Second-Order Systems., (2006).

Younes Chahlaoui, Kyle A Gallivan and Paul Van Dooren, An incremental method for computing dominant singular subspaces, (2001).

Younes Chahlaoui, Kyle A Gallivan and Paul Van Dooren, The Hinfinity-norm calculation for large sparse systems., (2004).

Younes Chahlaoui, Damien Lemonnier, Antoine Vandendorpe and Paul Van Dooren, Second Order Structure Preserving Balanced Truncation., (2004).

Younes Chahlaoui, Damien Lemonnier, Antoine Vandendorpe and Paul Van Dooren, Second Order Balanced Truncation., Linear Algebra and its Applications, 415, (2004).

Younes Chahlaoui and Paul Van Dooren, Recursive Gramian and Hankel map approximation of large dynamical systems., (2003).

Younes Chahlaoui and Paul Van Dooren, Recursive low rank Hankel approximation and model reduction., (2003).

Younes Chahlaoui, Kyle A Gallivan and Paul Van Dooren, Recursive calculation of dominant singular subspaces., SIAM Journal on Matrix Analysis and Applications (SIMAX), 25, (2003).

Younes Chahlaoui, Damien Lemonnier, Karl Meerbergen, Antoine Vandendorpe and Paul Van Dooren, Model reduction of second order systems, (2002).

Younes Chahlaoui and Paul Van Dooren, Estimating Gramians of large-scale time-varying systems., (2002).

Younes Chahlaoui and Paul Van Dooren, A collection of benchmark examples for model reduction of linear time invariant dynamical systems., (2002).

Younes Chahlaoui, Low-rank approximation and model reduction., (2003).

Y Chahlaoui, K.A Gallivan and P Van Dooren, Calculating the $\mathcal{H}_{\infty}$-Norm of Large Sparse Systems via Chandrasekhar Iterations and Extrapolations, (2007).

Younes Chahlaoui and Paul Van Dooren, First/second order transformation system. Tentative proof, preprint, (2008).

Younes Chahlaoui, Model reduction of switched dynamical systems, (2009).

Younes Chahlaoui, Françoise Tisseur and Paul Van Dooren, A new approach for MOR of second order Dynamical Systems, (2009).

Younes Chahlaoui, A posteriori error bounds for discrete balanced truncation, Linear Algebra and Its Applications, special number in honor of the 65th anniversary of Dan Sorensen in 2011..

Younès Chahlaoui, Two efficient SVD/Krylov algorithms for model order reduction of large scale systems, Electronic Transactions On Numerical Analysis (ETNA), 38, (2011).

Younes Chahlaoui, PVDâ€™s contributions to numerical methods in systems and control, (2011).

Younes Chahlaoui, Model Order Reduction or How to make everything as simple as possible but not simpler, (2011).

Younes Chahlaoui, Gramian based model reduction of switched dynamical systems, (2011).

Younes Chahlaoui, An interview with Paul Van Dooren, preprint, (2011).

Younes Chahlaoui and Margarita Korovina, CICADA Collection, preprint, (2014).

### E. Deadman

E Deadman, Outer Boundary Conditions in Numerical Relativity, (2009).

E Deadman and J.M. Stewart, Numerical Relativity and Asymptotic Flatness, Classical and Quantum Gravity, 26, (2009).

Edvin Deadman, Nicholas J. Higham and Rui Ralha, Blocked Schur Algorithms for Computing the Matrix Square Root, Lecture Notes in Computer Science, 7782, (2013).

Nicholas J. Higham and Edvin Deadman, A Catalogue of Software for Matrix Functions. Version 1.0, preprint, (2014).

Edvin Deadman and Nicholas J. Higham, Testing matrix function algorithms using identities, preprint, (2014).

Edvin Deadman, Estimating the Condition Number of f(A)b, preprint, (2014).

### N. Dingle

Bruno R. C. Magalhaes, Nicholas J. Dingle and William J. Knottenbelt, GPU-enabled steady-state solution of large Markov models, (2010).

M.C. Guenther, N.J. Dingle, J.T. Bradley and W.J. Knottenbelt, Passage-time Computation and Aggregation Strategies for Large Semi-Markov Processes, Performance Evaluation, (2010).

A.M. Mason, N.J. Dingle, W.J. Knottenbelt, D. Bell, W. Buchanan and C. Theummler, Modelling infection spread using location tracking, International Journal of Healthcare Technology and Management, 11, (2010).

Nicholas Dingle, GPU-based solution of Continuous Time Markov Chains using CUSP, preprint, (2011).

Nicholas Dingle, HydraMP: Exploiting shared memory parallelism in HYDRA with OpenMP, (2011).

Iain Bethune, J. Mark Bull, Nicholas J. Dingle and Nicholas J. Higham, Performance analysis of asynchronous Jacobi's method implemented in MPI, SHMEM and OpenMP, preprint, (2012).

Nicholas J. Dingle, William J. Knottenbelt and Demetris Spanias, On the (Page)Ranking of Professional Tennis Players, (2012).

Nikolaus Huber, Fabian Brosig, Nicholas Dingle, Kaustubh Joshi and Samuel Kounev, Providing Dependability and Performance in the Cloud: Case Studies, (2012).

Nicholas J. Dingle and Nicholas J. Higham, Reducing the Influence of Tiny Normwise Relative Errors on Performance Profiles, preprint, (2011).

Nicholas J. Dingle, Inexact Sparse Matrix-Vector Products in the Calculation of Passage Time Distributions in Large Semi-Markov Models, preprint, (2013).

Iain Bethune, J. Mark Bull, Nicholas J. Dingle and Nicholas J. Higham, Investigating the Performance of Asynchronous Jacobi's Method for Solving Systems of Linear Equations, To appear in International Journal of High Performance Computing Applications.

James Hook and Nick Dingle, Performance Analysis of Asynchronous Parallel Jacobi, preprint, (2013).

Robert Andrew and Nicholas J. Dingle, Implementing QR Factorization Updating Algorithms on GPUs, Parallel Computing, 4, (2014).

### J. Dongarra

Jakub Kurzak, Alfredo Buttari, Piotr Luszczek and Jack Dongarra, The PlayStation 3 for High Performance Scientific Computing, preprint, (2008).

Marc Baboulin, Jack Dongarra and Stanimire Tomov, Some Issues in Dense Linear Algebra for Multicore and Special Purpose Architectures, preprint, (2009).

George Bosilca, Remi Delmas, Jack Dongarra and Julien Langou, Algorithmic Based Fault Tolerance Applied to High Performance Computing, preprint, (2009).

Jack Dongarra and Julien Langou, The Problem with the Linpack Benchmark 1.0 Matrix Generator, preprint, (2009).

Hatem Ltaief, Jakub Kurzak and Jack Dongarra, Parallel Band Two-Sided Matrix Bidiagonalization for Multicore Architectures, preprint, (2009).

Hatem Ltaief, Jakub Kurzak and Jack Dongarra, Parallel Block Hessenberg Reduction using Algorithms-By-Tiles for Multicore Architectures Revisited, preprint, (2009).

Stanimire Tomov, Jack Dongarra and Marc Baboulin, Towards Dense Linear Algebra for Hybrid GPU Accelerated Manycore Systems, preprint, (2009).

Yinan Li, Jack Dongarra and Stanimire Tomov, A Note on Auto-tuning GEMM for GPUs, preprint, (2009).

Alfredo Buttari, Jack Dongarra and Jakub Kurzak, Limitations of the PlayStation 3 for High Performance Cluster Computing, preprint, (2007).

Alfredo Buttari, Jack Dongarra, Jakub Kurzak, Piotr Luszczek and Stanimire Tomov, Using Mixed Precision for Sparse Matrix Computations to Enhance the Performance while Achieving 64-bit Accuracy, preprint, (2007).

Jakub Kurzak, Alfredo Buttari and Jack Dongarra, Solving Systems of Linear Equations on the CELL Processor Using Cholesky Factorization, preprint, (2007).

Marc Baboulin, Jack Dongarra, Serge Gratton and Julien Langou, Computing the Conditioning of the Components of a Linear Least Squares Solution, preprint, (2007).

Alfredo Buttari, Julien Langou, Jakub Kurzak and Jack Dongarra, A Class of Parallel Tiled Linear Algebra Algorithms for Multicore Architectures, preprint, (2007).

Jack Dongarra, G Golub, C Moler and K Moore, Netlib and NA-Net: building a scientific computing community, preprint, (2007).

Alfredo Buttari, Jack Dongarra, Julie Langou, Julien Langou, Piotr Luszczek and Jakub Kurzak, Mixed Precision Iterative Refinement Techniques for the Solution of Dense Linear Systems, preprint, (2007).

G Bosilca, Z Chen, J Dongarra and J Langou, Recovery Patterns for Iterative Methods in a Parallel Unstable Environment, preprint, (2007).

Jack Dongarra and Piotr Luszczek, How Elegant Code Evolves with Hardware: The Case of Gaussian Elimination, preprint, (2007).

F Tisseur and J Dongarra, A Parallel Divide and Conquer Algorithm for the Symmetric Eigenvalue Problem on Distributed Memory Architectures, SIAM Journal on Scientific Computing, 20.

### S. Güttel

Stefan Güttel and Leonid Knizhnerman, A black-box rational Arnoldi variant for Cauchy-Stieltjes matrix functions, preprint, (2012).

Stefan Güttel and Georges Klein, Efficient high-order rational integration and deferred correction with equispaced data, preprint, (2013).

Stefan Güttel, Roel Van Beeumen, Karl Meerbergen and Wim Michiels, NLEIGS: A class of robust fully rational Krylov methods for nonlinear eigenvalue problems, preprint, (2013).

Elias Jarlebring and Stefan Güttel, A spatially adaptive iterative method for a class of nonlinear operator eigenproblems, preprint, (2012).

Stefan Güttel and Jen Pestana, Some observations on weighted GMRES, preprint, (2013).

Vladimir Druskin, Stefan Güttel and Leonid Knizhnerman, Near-optimal perfectly matched layers for indefinite Helmholtz problems, preprint, (2013).

Andreas Frommer, Stefan Güttel and Marcel Schweitzer, Efficient and stable Arnoldi restarts for matrix functions based on quadrature, preprint, (2013).

Ralph-Uwe Börner, Oliver G. Ernst and Stefan Güttel, Three-Dimensional Transient Electromagnetic Modeling Using Rational Krylov Methods, preprint, (2014).

Stefan Güttel, Eric Polizzi, Peter Tang and Gautier Viaud, Zolotarev quadrature rules and load balancing for the FEAST eigensolver, preprint, (2014).

### S. J. Hammarling

Sven Hammarling, An Introduction to the Quality of Computed Solutions, (2005).

S. J. Hammarling, Latent Roots and Latent Vectors, (1970).

M.F. Anjos, S. Hammarling and C.C. Paige, Solving the Generalized Symmetric Eigenvalue Problem, Unpublished, (1992).

Sven Hammarling, The Singular Value Decomposition in Multivariate Statistics, ACM Signum Newsletter, 20, (1985).

Sven Hammarling, A Survey of Numerical Aspects of Plane Rotations, Middlesex Polytechnic Report, Maths, (1977).

Sven Hammarling and Craig Lucas, Updating the QR factorization and the least squares problem, preprint, (2008).

Nicholas J. Higham, Analysis of the Cholesky Decomposition of a Semi-definite Matrix, (1990).

Sven Hammarling, Christopher J. Munro and Francoise Tisseur, An Algorithm for the Complete Solution of Quadratic Eigenvalue Problems, preprint, (2011).

G. W. Howell, J. W. Demmel, C. T. Fulton, S. Hammarling and K. Marmol, Cache Efficient Bidiagonalization Using BLAS 2.5 Operators, preprint.

Sven Hammarling, Nicholas J. Higham and Craig Lucas, LAPACK-Style Codes for Pivoted Cholesky and QR Updating, preprint.

### N. J. Higham

Nicholas J. Higham, An Interview with Gene Golub, preprint, (2008).

Nicholas J. Higham, Functions of Matrices: Theory and Computation, (2008).

Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder and Françoise Tisseur, NLEVP: A Collection of Nonlinear Eigenvalue Problems, preprint, (2008).

Philip I. Davies, Nicholas J. Higham and Françoise Tisseur, Analysis of the Cholesky Method with Iterative Refinement for Solving the Symmetric Definite Generalized Eigenproblem, SIAM Journal on Matrix Analysis and Applications, 23, (2001).

Nicholas Hale, Nicholas J. Higham and Lloyd N. Trefethen, Computing $A^\alpha$, $\log(A)$ and Related Matrix Functions by Contour Integrals, SIAM Journal on Numerical Analysis, 46, (2008).

Nicholas J. Higham, Analysis of the Cholesky Decomposition of a Semi-definite Matrix, (1990).

Nicholas J. Higham and G. W. Stewart, Numerical Linear Algebra in Statistical Computing, (1987).

Nicholas J. Higham, Cholesky Factorization, preprint, (2008).

Rudiger Borsdorf and Nicholas J. Higham, A Preconditioned Newton Algorithm for the Nearest Correlation Matrix, IMA Journal of Numerical Analysis, 30, (2008).

Chun-Hua Guo, Nicholas J. Higham and Françoise Tisseur, Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems, SIAM Journal On Matrix Analysis and Applications., 30, (2009).

Awad H. Al-Mohy and Nicholas J. Higham, Computing the Fréchet Derivative of the Matrix Exponential, with an application to Condition Number Estimation, SIAM Journal On Matrix Analysis and Applications., 30, (2009).

Gareth I. Hargreaves and Nicholas J. Higham, Efficient Algorithms for the Matrix Cosine and Sine, Numerical Algorithms, 40, (2005).

James W. Demmel, Nicholas J. Higham and Robert S. Schreiber, Stability of Block LU Factorization, Numerical Linear Algebra with Applications, Vol. 2, (1995).

Nicholas J. Higham, D. Steven Mackey and Françoise Tisseur, Definite Matrix Polynomials and their Linearization by Definite Pencils, SIAM Journal on Matrix Analysis and Applications, 31, (2009).

Chun-Hua Guo, Nicholas J. Higham and Françoise Tisseur, An Improved Arc Algorithm for Detecting Definite Hermitian Pairs, SIAM Journal On Matrix Analysis and Applications., 31, (2009).

Anne Trefethen, Nicholas J. Higham, Iain Duff and Peter Coveney, Developing a High-Performance Computing/Numerical Analysis Roadmap, International Journal of High Performance Computing Applications, 23, (2009).

Anne Trefethen, Nicholas J. Higham, Iain Duff and Peter Coveney, Applications/Algorithms Roadmapping Activity. First Stage Final Report, preprint, (2009).

Nicholas J. Higham, The Scaling and Squaring Method for the Matrix Exponential Revisited, SIAM Review, 51, (2009).

Awad H. Al-Mohy and Nicholas J. Higham, The Complex Step Approximation to the Fréchet Derivative of a Matrix Function, Numerical Algorithms, 53, (2010).

Laurence Grammont, Nicholas J. Higham and Françoise Tisseur, A Framework for Analyzing Nonlinear Eigenproblems and Parametrized Linear Systems, Linear Algebra and its Applications, 435, (2011).

Nicholas J. Higham and Lijing Lin, On $p$th Roots of Stochastic Matrices, Linear Algebra and its Applications, 435, (2011).

Awad H. Al-Mohy and Nicholas J. Higham, A New Scaling and Squaring Algorithm for the Matrix Exponential, SIAM Journal On Matrix Analysis and Applications., 31, (2009).

Nicholas J. Higham and Awad H. Al-Mohy, Computing Matrix Functions, Acta Numerica, 19, (2010).

Nicholas J. Higham, Christian Mehl and Françoise Tisseur, The Canonical Generalized Polar Decomposition, SIAM Journal On Matrix Analysis and Applications, 31, (2010).

Rüdiger Borsdorf, Nicholas J. Higham and Marcos Raydan, Computing a Nearest Correlation Matrix with Factor Structure, SIAM Journal on Matrix Analysis and Applications, 31, (2010).

Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder and Françoise Tisseur, NLEVP: A Collection of Nonlinear Eigenvalue Problems, preprint, (2010).

Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder and Françoise Tisseur, NLEVP: A Collection of Nonlinear Eigenvalue Problems. Users' Guide, preprint, (2010).

Philip I. Davies and Nicholas J. Higham, A Schur--Parlett Algorithm for Computing Matrix Functions, SIAM Journal On Matrix Analysis and Applications, 25, (2003).

Nicholas J. Higham, Gaussian Elimination, Wiley Interdisciplinary Reviews: Computational Statistics, 3, (2011).

Awad H. Al-Mohy and Nicholas J. Higham, Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators, SIAM Journal on Scientific Computing, 33, (2011).

Nicholas J. Higham and Lijing Lin, A Schur--Pad\'e Algorithm for Fractional Powers of a Matrix, SIAM J. on Matrix Analysis and Applications, 32, (2011).

Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder and Françoise Tisseur, NLEVP: A Collection of Nonlinear Eigenvalue Problems, preprint, (2011).

Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder and Françoise Tisseur, NLEVP: A Collection of Nonlinear Eigenvalue Problems. Users' Guide, preprint, (2011).

Nicholas J. Higham, Commentary on Selected Papers by Gene Golub on Matrix Factorizations and Applications, (2007).

Iain Bethune, J. Mark Bull, Nicholas J. Dingle and Nicholas J. Higham, Performance analysis of asynchronous Jacobi's method implemented in MPI, SHMEM and OpenMP, preprint, (2012).

Yuji Nakatsukasa and Nicholas J. Higham, Backward stability of iterations for computing the polar decomposition, SIAM Journal on Matrix Analysis and Applications, 33, (2012).

Awad H. Al-Mohy and Nicholas J. Higham, Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm, SIAM Journal on Scientific Computing, 34, (2012).

Nicholas J. Dingle and Nicholas J. Higham, Reducing the Influence of Tiny Normwise Relative Errors on Performance Profiles, preprint, (2011).

Yuji Nakatsukasa and Nicholas J. Higham, Stable and Efficient Spectral Divide and Conquer Algorithms for the Symmetric Eigenvalue Decomposition and the SVD, SIAM J. Sci. Comput., 35, (2013).

Edvin Deadman, Nicholas J. Higham and Rui Ralha, Blocked Schur Algorithms for Computing the Matrix Square Root, Lecture Notes in Computer Science, 7782, (2013).

Iain Bethune, J. Mark Bull, Nicholas J. Dingle and Nicholas J. Higham, Investigating the Performance of Asynchronous Jacobi's Method for Solving Systems of Linear Equations, To appear in International Journal of High Performance Computing Applications.

Ramaseshan Kannan, Stephen Hendry, Nicholas J. Higham and Francoise Tisseur, Detecting the Causes of Ill-Conditioning in Structural Finite Element Models, preprint, (2013).

Awad H. Al-Mohy, Nicholas J. Higham and Samuel D. Relton, Computing the Frechet Derivative of the Matrix Logarithm and Estimating the Condition Number, SIAM J. Sci. Comput., 35, (2013).

Nicholas J. Higham and Lijing Lin, An Improved Schur--Pade Algorithm for Fractional Powers of a Matrix and their Frechet Derivatives, SIAM. J. Matrix Anal. & Appl., 34, (2013).

Nicholas J. Higham, Matrix Computations in Basic on a Microcomputer, preprint, (2013).

Nicholas J. Higham and Lin Lijing, Matrix Functions: A Short Course, preprint, (2013).

Nicholas J. Higham, Numerical Conditioning, (2014).

Nicholas J. Higham and Samuel D. Relton, Estimating the Condition Number of the Frechet Derivative of a Matrix Function, preprint, (2013).

Mary Aprahamian and Nicholas J. Higham, The Matrix Unwinding Function, with an Application to Computing the Matrix Exponential, SIAM Journal on Matrix Analysis and Applications, 35, (2014).

Lijing Lin, Nicholas J. Higham and Jianxin Pan, Covariance Structure Regularization via Entropy Loss Function, Computational Statistics & Data Analysis, 72, (2014).

Nicholas J. Higham and Edvin Deadman, A Catalogue of Software for Matrix Functions. Version 1.0, preprint, (2014).

Nicholas J. Higham, Functions of Matrices, (2014).

Edvin Deadman and Nicholas J. Higham, Testing matrix function algorithms using identities, preprint, (2014).

Nicholas J. Higham, Sylvester's Influence on Applied Mathematics, Mathematics Today, 50, (2014).

Awad H. Al-Mohy, Nicholas J. Higham and Samuel D. Relton, New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously, preprint, (2014).

Nicholas J. Higham and Samuel D. Relton, Higher Order Frechet Derivatives of Matrix Functions and the Level-2 Condition Number, SIAM Journal on Matrix Analysis and Applications, 35, (2014).

Nicholas J. Higham, $J$-Orthogonal Matrices: Properties and Generation, SIAM Review, 45, (2003).

Nicholas J. Higham, Computing the Nearest Correlation Matrix---A Problem from Finance, IMA Journal of Numerical Analysis, 22, (2002).

Nicholas J. Higham, Accuracy and Stability of Numerical Algorithms, (2002).

Nicholas J. Higham, Review of ``Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators'', by Lloyd N. Trefethen and Mark Embree. Princeton University Press, Princeton, NJ, USA, 2005. , Bull. Amer. Math. Soc., 44, (2007).

Nicholas J. Higham, Functions of Matrices, (2006).

Nicholas J Higham, The numerical stability of barycentric Lagrange interpolation, IMA Journal of Numerical Analysis, 24, (2004).

Nicholas J Higham and Hyun-Min Kim, Numerical analysis of a quadratic matrix equation, IMA Journal of Numerical Analysis, 20, (2000).

Adam Bojanczyk, Nicholas J Higham and Harikrishna Patel, Solving the indefinite least squares problem by hyperbolic QR factorization, SIAM Journal On Matrix Analysis And Applications, 24, (2003).

Sheung Hun Cheng, Nicholas J Higham, Charles S Kenney and Alan J Laub, Approximating the logarithm of a matrix to specified accuracy, SIAM Journal On Matrix Analysis And Applications, 22, (2001).

Nicholas J Higham and Hyun-Min Kim, Solving a quadratic matrix equation by Newton's method with exact line searches, SIAM Journal On Matrix Analysis And Applications, 23, (2001).

Françoise Tisseur and Nicholas J. Higham, Structured pseudospectra for polynomial eigenvalue problems, with applications, SIAM Journal On Matrix Analysis And Applications, 23, (2001).

Nicholas J. Higham and Françoise Tisseur, A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra, SIAM Journal On Matrix Analysis And Applications, 21, (2000).

Philip I. Davies and Nicholas J. Higham, Numerically stable generation of correlation matrices and their factors, BIT Numerical Mathematics, 40, (2000).

Nicholas J. Higham, QR factorization with complete pivoting and accurate computation of the SVD, Elsevier, Linear Algebra and its Applications, 309, (2000).

Nicholas J. Higham and Françoise Tisseur, More on pseudospectra for polynomial eigenvalue problems and applications in control theory, Elsevier, Linear Algebra and its Applications, 351-352, (2002).

Nicholas J. Higham, Françoise Tisseur and Paul M. Van Dooren, Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems, Elsevier, Linear Algebra and its Applications, 351-352, (2002).

Nicholas J. Higham, Estimating the matrix p-norm, Numerische Mathematik, 62, (1992).

Nicholas J. Higham and Pythagoras Papadimitriou, A parallel algorithm for computing the polar decomposition, Elsevier, Parallel Computing, 20, (1994).

Anthony J. Cox and Nicholas J. Higham, Backward error bounds for constrained least squares problems, BIT Numerical Mathematics, 39, (1999).

Anthony J. Cox and Nicholas J. Higham, Accuracy and stability of the null space method for solving the equality constrained least squares problem, BIT Numerical Mathematics, 39, (1999).

Thierry Braconnier and Nicholas J. Higham, Computing the field of values and pseudospectra using the Lanczos method with continuation, BIT Numerical Mathematics, 36:3, (1996).

Nicholas J. Higham, Perturbation Theory and Backward Error for $AX-XB=C$, BIT Numerical Mathematics, 33, (1993).

Nicholas J. Higham, Iterative refinement enhances the stability of QR factorization methods for solving linear equations, BIT Numerical Mathematics, 31, (1991).

Nicholas J. Higham, The symmetric Procrustes problem, BIT Numerical Mathematics, 28, (1988).

Nicholas J. Higham, Factorizing complex symmetric matrices with positive definite real and imaginary parts, Mathematics of Computation, 67, (1998).

Nicholas J. Higham, Stability of parallel triangular system solvers, SIAM Journal on Scientific Computing, 16, (1995).

Nicholas J. Higham, Experience with a Matrix Norm Estimator, SIAM Journal on Scientific and Statistical Computing, 11, (1990).

Nicholas J. Higham and Robert S. Schreiber, Fast polar decomposition of an arbitrary matrix, SIAM Journal on Scientific and Statistical Computing, 11, (1990).

Nicholas J. Higham and Alex Pothen, Stability of the partitioned inverse method for parallel solution of sparse triangular systems, SIAM Journal on Scientific Computing, 15, (1994).

Sheung Hun Cheng and Nicholas J. Higham, A modified Cholesky algorithm based on a symmetric indefinite factorization, SIAM Journal On Matrix Analysis And Applications, 19, (1998).

Desmond J. Higham and Nicholas J. Higham, Structured backward error and condition of generalized eigenvalue problems, SIAM Journal On Matrix Analysis And Applications, 20, (1998).

Nicholas J. Higham, Stability of the diagonal pivoting method with partial pivoting, SIAM Journal On Matrix Analysis And Applications, 18, (1997).

Nicholas J. Higham and Philip A. Knight, Matrix powers in finite precision arithmetic, SIAM Journal On Matrix Analysis And Applications, 16, (1995).

Nicholas J. Higham, Optimization by direct search in matrix computations, SIAM Journal On Matrix Analysis And Applications, 14, (1993).

Desmond J. Higham and Nicholas J. Higham, Backward error and condition of structured linear systems, SIAM Journal On Matrix Analysis And Applications, 13, (1992).

Nicholas J. Higham, Stability of a method for multiplying complex matrices with three real matrix multiplications, SIAM Journal On Matrix Analysis And Applications, 13, (1992).

James W. Demmel and Nicholas J. Higham, Improved error bounds for underdetermined system solvers, SIAM Journal On Matrix Analysis And Applications, 14, (1993).

Anthony J. Cox and Nicholas J. Higham, Row-wise backward stable elimination methods for the equality constrained least squares problem, SIAM Journal On Matrix Analysis And Applications, 21, (1999).

Nicholas J. Higham, Bounding the error in Gaussian elimination for tridiagonal systems, SIAM Journal On Matrix Analysis And Applications, 11, (1990).

Nicholas J. Higham, Stability analysis of algorithms for solving confluent Vandermonde-like systems, SIAM Journal On Matrix Analysis And Applications, 11, (1990).

Nicholas J. Higham and Desmond J. Higham, Large growth factors in Gaussian elimination with pivoting, SIAM Journal On Matrix Analysis And Applications, 10, (1989).

Sheung Hun Cheng and Nicholas J. Higham, The nearest definite pair for the Hermitian generalized eigenvalue problem, Linear Algebra and its Applications, 302-303, (1999).

Nicholas J. Higham and Sheung Hun Cheng, Modifying the interia of matrices arising in optimization, Linear Algebra and its Applications, 275-276, (1998).

Nicholas J. Higham and Philip A. Knight, Finite precision behavior of stationary iteration for solving singular systems, Linear Algebra and its Applications, 192, (1993).

Nicholas J. Higham, The matrix sign decomposition and its relation to the polar decomposition, Linear Algebra and its Applications, 212-213, (1994).

Desmond J. Higham and Nicholas J. Higham, Componentwise perturbation theory for linear systems with multiple right-hand sides, Linear Algebra and its Applications, 174, (1992).

Nicholas J. Higham, Computing a nearest symmetric positive semidefinite matrix, Linear Algebra and its Applications, 103, (1988).

Nicholas J. Higham, Computing real square roots of a real matrix, Linear Algebra and its Applications, 88-89, (1987).

Nicholas J. Higham, Exploiting fast matrix multiplication within the level 3 BLAS, ACM Transactions on Mathematical Software, 16, (1990).

Nicholas J. Higham, FORTRAN codes for estimating the one-norm of a real or complex matrix, with appliations to condition estimation, ACM Transactions on Mathematical Software, 14, (1988).

Nicholas J. Higham, Stable iterations for the matrix square root, Numerical Algorithms, 15, (1997).

Nicholas J. Higham, Newton's method for the matrix square root, Mathematics of Computation, 46, (1986).

Nicholas J. Higham, An Interview with Peter Lancaster, preprint.

Nicholas J. Higham, The Scaling and Squaring Method for the Matrix Exponential Revisited, SIAM Journal On Matrix Analysis and Applications, 26, (2005).

Dario A. Bini, Nicholas J. Higham and Beatrice Meini, Algorithms for the Matrix p'th Root, Numerical Algorithms, 39, (2005).

Nicholas J. Higham, D. Steven Mackey, Niloufer Mackey and Françoise Tisseur, Functions Preserving Matrix Groups and Iterations for the Matrix Square Root, SIAM Journal On Matrix Analysis and Applications, 26, (2005).

Chun-Hua Guo and Nicholas J. Higham, A Schur-Newton Method for the Matrix p'th Root and its Inverse, SIAM Journal On Matrix Analysis and Applications, 28, (2006).

Nicholas J. Higham, D. Steven Mackey, Niloufer Mackey and Françoise Tisseur, Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups, SIAM Journal On Matrix Analysis and Applications, 25, (2004).

Nicholas J. Higham, A Survey of Componentwise Perturbation Theory, (1994).

Nicholas J. Higham, Mihail Konstantinov, Volker Mehrmann and Petko Petkov, The Sensitivity of Computational Control Problems, IEEE Control Systems Magazine, 24, (2004).

Nicholas J. Higham, D. Steven Mackey and Françoise Tisseur, The Conditioning of Linearizations of Matrix Polynomials, SIAM J. Matrix Anal. Appl., 28, (2006).

Nicholas J. Higham, D. Steven Mackey, Niloufer Mackey and Françoise Tisseur, Symmetric Linearizations for Matrix Polynomials, SIAM Journal on Matrix Analysis and Applications, 29, (2006).

Sven Hammarling, Nicholas J. Higham and Craig Lucas, LAPACK-Style Codes for Pivoted Cholesky and QR Updating, preprint.

Nicholas J. Higham, Efficient Algorithms for Computing the Condition Number of a Tridiagonal Matrix, SIAM Journal of Scientific and Statistical Computing, 7, (1986).

Nicholas J. Higham, Computing the Polar Decomposition---with Applications, SIAM Journal of Scientific and Statistical Computing, 7, (1986).

Nicholas J. Higham, A Survey of Condition Number Estimation for Triangular Matrices, SIAM Review, 29, (1987).

Nicholas J. Higham, Algorithm 694: A Collection of Test Matrices in MATLAB, ACM Transactions on Mathematical Software, 17, (1991).

James W. Demmel and Nicholas J. Higham, Stability of Block Algorithms with Fast Level-3 BLAS, ACM Transactions on Mathematical Software, 18, (1992).

Chun-Hua Guo and Nicholas J. Higham, Iterative Solution of a Nonsymmetric Algebraic Riccati Equation, SIAM Journal On Matrix Analysis and Applications., 29, (2007).

Nicholas J. Higham, Recent Developments in Dense Numerical Linear Algebra, (1997).

Robert M. Corless, Hui Ding, Nicholas J. Higham and David J. Jeffrey, The Solution of S exp(S) = A is Not Always the Lambert W Function of A, (2007).

Nicholas J. Higham, Cayley, Sylvester, and Early Matrix Theory, Linear Algebra Appl., 428, (2008).

Philip I. Davies and Nicholas J. Higham, Computing $f(A)b$ for Matrix Functions $f$, (2005).

Nicholas J. Higham, Ren-Cang Li and Françoise Tisseur, Backward Error of Polynomial Eigenproblems Solved by Linearization, SIAM Journal on Matrix Analysis and Applications, 29, (2007).

Nicholas J. Higham, D. Steven Mackey, Françoise Tisseur and Seamus D. Garvey, Scaling, Sensitivity and Stability in the Numerical Solution of Quadratic Eigenvalue Problems , International Journal for Numerical Methods in Engineering, 73, (2008).

### J. Hook

James Hook and Dave Broomhead, Stochastic production trees as products of i.i.d. componentwise exponential max-plus matrices, preprint, (2011).

J Hook, Products of random Max-plus matrices, preprint, (2011).

JL Hook, Topics in Dynamical Systems, (2012).

JL Hook, Smoothing non-smooth systems with low-pass filters, preprint, (2013).

J Hook, Critical path statistics of max-plus linear systems with Gaussian noise, preprint, (2012).

James Hook and Nick Dingle, Performance Analysis of Asynchronous Parallel Jacobi, preprint, (2013).

James Hook and Françoise Tisseur, Tropical Eigenvalues, preprint, (2014).

James Hook, Max-Plus Singular Values, preprint, (2014).

### A. Khabou

Simplice Donfack, Laura Grigori and Amal Khabou, Avoiding communication through a multilevel LU factorization, Euro-Par 2012 Parallel Processing, 7484, (2012).

Amal Khabou, James W. Demmel, Laura Grigori and Ming Gu, LU FACTORIZATION WITH PANEL RANK REVEALING PIVOTING AND ITS COMMUNICATION AVOIDING VERSION, SIAM Journal on Matrix Analysis and Applications, Volume 34, (2013).

Laura Grigori, Mathias Jacquelin and Amal Khabou, Performance predictions of multilevel communication optimal LU and QR factorizations on hierarchical platforms, preprint, (2013).

### P. Lancaster

Erich Bohl, Ryan Hamilton and Peter Lancaster, Phylogenetic Trees Predicted by an Irreversible Markov Process, preprint, (2008).

Peter Lancaster and Françoise Tisseur, Hermitian Quadratic Matrix Polynomials: Solvents and Inverse Problems, preprint, (2010).

Peter Lancaster and Panayiotis Psarrakos, A Note on Weak and Strong Linearizations of Regular Matrix Polynomials, preprint.

Peter Lancaster, Model-Updating for Symmetric Quadratic Eigenvalue Problems, preprint.

### L. Lin

Nicholas J. Higham and Lijing Lin, On $p$th Roots of Stochastic Matrices, Linear Algebra and its Applications, 435, (2011).

Lijing Lin, Roots of Stochastic Matrices and Fractional Matrix Powers, (2011).

Nicholas J. Higham and Lijing Lin, A Schur--Pad\'e Algorithm for Fractional Powers of a Matrix, SIAM J. on Matrix Analysis and Applications, 32, (2011).

Nicholas J. Higham and Lijing Lin, An Improved Schur--Pade Algorithm for Fractional Powers of a Matrix and their Frechet Derivatives, SIAM. J. Matrix Anal. & Appl., 34, (2013).

Lijing Lin, Nicholas J. Higham and Jianxin Pan, Covariance Structure Regularization via Entropy Loss Function, Computational Statistics & Data Analysis, 72, (2014).

### M. Lotz

Felipe Cucker, Raphael Hauser and Martin Lotz, Adversarial Smoothed Analysis, Journal of Complexity, (2010).

Peter Burgisser, Felipe Cucker and Martin Lotz, Coverage processes on spheres and condition numbers for linear programming, Annals of Probability, 38, (2010).

Peter Burgisser, Felipe Cucker and Martin Lotz, The probability that a slightly perturbed numerical analysis problem is difficult, Mathematics of Computation, 77, (2008).

Dennis Amelunxen, Martin Lotz, Michael B. Mccoy and Joel A. Tropp, Living on the edge: A geometric theory of phase transitions in convex optimization, preprint, (2013).

Martin Lotz, On the volume of tubular neighborhoods of real algebraic varieties, preprint, (2012).

Dennis Amelunxen and Martin Lotz, Gordon's inequality and condition numbers in conic optimization, preprint, (2014).

### C. Lucas

Sven Hammarling and Craig Lucas, Updating the QR factorization and the least squares problem, preprint, (2008).

Craig Lucas, Algorithms for Cholesky and QR Factorizations, and the Semidefinite Generalized Eigenvalue Problem, (2004).

Sven Hammarling, Nicholas J. Higham and Craig Lucas, LAPACK-Style Codes for Pivoted Cholesky and QR Updating, preprint.

### D. S. Mackey

Ralph Byers, D. Steven Mackey, Volker Mehrmann and Hongguo Xu, Symplectic, BVD, and Palindromic Approaches to Discrete-Time Control Problems, preprint, (2008).

D. Steven Mackey, Niloufer Mackey, Christian Mehl and Volker Mehrmann, Numerical methods for palindromic eigenvalue problems: Computing the anti-triangular Schur form, Numerical Linear Algebra with Applications.

D. Steven Mackey, Niloufer Mackey and Francoise Tisseur, On the Definition of Two Natural Classes of Scalar Product, preprint, (2007).

H. Fassbender, D. S. Mackey, N. Mackey and C. Schroder, Structured Polynomial Eigenproblems Related to Time-Delay Systems , preprint, (2009).

Nicholas J. Higham, D. Steven Mackey and Françoise Tisseur, Definite Matrix Polynomials and their Linearization by Definite Pencils, SIAM Journal on Matrix Analysis and Applications, 31, (2009).

D. Steven Mackey, Niloufer Mackey, Christian Mehl and Volker Mehrmann, Jordan Structures of Alternating Matrix Polynomials, preprint, (2009).

Fernando De Teran, Frolian M. Dopico and D. Steven Mackey, Linearizations of Singular Matrix Polynomials and the Recovery of Minimal Indices, preprint, (2009).

Fernando De Teran, Froilan M. Dopico and D. Steven Mackey, Fiedler Companion Linearizations and the Recovery of Minimal Indices, preprint, (2009).

D. Steven Mackey, Niloufer Mackey, Christian Mehl and Volker Mehrmann, Smith Forms of Palindromic Matrix Polynomials, preprint, (2010).

Fernando De Teran, Froilan M. Dopico and D. Steven Mackey, Palindromic Companion Forms for Matrix Polynomials of Odd Degree, preprint, (2010).

Fernando De Teran, Froilan Dopico and D. Steven Mackey, Fiedler companion linearizations for rectangular matrix polynomials, preprint, (2011).

D. Steven Mackey, The Continuing Influence of Fiedler's Work on Companion Matrices , preprint, (2011).

D. Steven Mackey, Niloufer Mackey, Christian Mehl and Volker Mehrmann, Skew-symmetric matrix polynomials and their Smith forms, preprint, (2012).

Fernando De Teran, Froilan M. Dopico and D. Steven Mackey, Spectral equivalence of matrix polynomials and the index sum theorem , preprint, (2013).

D. Steven Mackey, Minimal indices and minimal bases via filtrations, preprint, (2012).

D. Steven Mackey, Niloufer Mackey, Christian Mehl and Volker Mehrmann, Möbius Transformations of Matrix Polynomials, preprint, (2014).

D. Steven Mackey and Vasilije Perovic, Linearizations of Matrix Polynomials in Bernstein Basis, preprint, (2014).

D. Steven Mackey, Niloufer Mackey and Françoise Tisseur, Structured Mapping Problems for Matrices Associated with Scalar Products Part I: Lie and Jordan Algebras, preprint, (2007).

D. Steven Mackey, Structured Linearizations for Matrix Polynomials, (2006).

D. S. Mackey, Niloufer Mackey and Françoise Tissuer, G-reflectors: Analogues of householder transformations in scalar product spaces, Linear Algebra and its Applications, 385, (2004).

Nicholas J. Higham, D. Steven Mackey, Niloufer Mackey and Françoise Tisseur, Functions Preserving Matrix Groups and Iterations for the Matrix Square Root, SIAM Journal On Matrix Analysis and Applications, 26, (2005).

Nicholas J. Higham, D. Steven Mackey, Niloufer Mackey and Françoise Tisseur, Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups, SIAM Journal On Matrix Analysis and Applications, 25, (2004).

Nicholas J. Higham, D. Steven Mackey and Françoise Tisseur, The Conditioning of Linearizations of Matrix Polynomials, SIAM J. Matrix Anal. Appl., 28, (2006).

D. Steven Mackey, Niloufer Mackey, Christian Mehl and Volker Mehrmann, Vector Spaces of Linearizations for Matrix Polynomials, SIAM J. Matrix Anal. Appl., 28, (2006).

D. Steven Mackey, Niloufer Mackey, Christian Mehl and Volker Mehrmann, Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations, SIAM J. Matrix Anal. Appl., 28, (2006).

Nicholas J. Higham, D. Steven Mackey, Niloufer Mackey and Françoise Tisseur, Symmetric Linearizations for Matrix Polynomials, SIAM Journal on Matrix Analysis and Applications, 29, (2006).

D. Steven Mackey, Niloufer Mackey and Françoise Tisseur, G-Reflectors: Analogues of Householder Transformations in Scalar Product Spaces, Linear Algebra and its Applications, 385, (2004).

Nicole Frahm, Daniel E. Kaufmann, Karina Yusim, Mark Muldoon, Can Kesmir, Caitlyn H. Linde, Will Fischer, Todd M. Allen, Bin Li, Ben H. McMahon, Kellie L. Faircloth, Hannah S. Hewitt, Elizabeth W. Mackey, Toshiyuki Miura, Ashok Khatri, Steven Wolinsky, Andrew McMichael, Robert K. Funkhouser, Bruce D. Walker, Christian Brander and Bette T. Korber, Increased Sequence Diversity Coverage Improves Detection of HIV-Specific T Cell Responses, Journal of Immunology, 179, (2007).

D.S. Mackey, N. Mackey and F. Tisseur, Structured Factorizations in Scalar Product Spaces, SIAM Journal on Matrix Analysis and Applications, 27, (2006).

D. Steven Mackey, Niloufer Mackey and Françoise Tisseur, Structured tools for structured matrices, Electronic Journal of Linear Algebra, 10.

Nicholas J. Higham, D. Steven Mackey, Françoise Tisseur and Seamus D. Garvey, Scaling, Sensitivity and Stability in the Numerical Solution of Quadratic Eigenvalue Problems , International Journal for Numerical Methods in Engineering, 73, (2008).

### Y. Nakatsukasa

Yuji Nakatsukasa, Eigenvalue perturbation bounds for Hermitian block tridiagonal matrices, preprint, (2011).

Yuji Nakatsukasa, Kensuke Aishima and Ichitaro Yamazaki, dqds with aggressive early deflation, preprint, (2011).

Yuji Nakatsukasa, On the condition numbers of a multiple eigenvalue of a generalized eigenvalue problem, preprint, (2011).

Yuji Nakatsukasa, Naoki Saito and Ernest Woei, Mysteries around the graph Laplacian eigenvalue 4, preprint, (2011).

Yuji Nakatsukasa, The tan theta theorem with relaxed conditions, preprint, (2011).

Yuji Nakatsukasa, Gerschgorin's theorem for generalized eigenvalue problems in the Euclidean metric, Mathematics of Computation, 80, (2011).

Ren-Cang Li, Yuji Nakatsukasa, Ninoslav Truhar and Wei-guo Wang, Perturbation of multiple eigenvalues of Hermitian matrices, preprint, (2012).

Yuji Nakatsukasa and Nicholas J. Higham, Backward stability of iterations for computing the polar decomposition, SIAM Journal on Matrix Analysis and Applications, 33, (2012).

Alex Townsend, Vanni Noferini and Yuji Nakatsukasa, Vector spaces of linearizations for matrix polynomials: a bivariate polynomial approach, preprint, (2012).

Yuji Nakatsukasa and Nicholas J. Higham, Stable and Efficient Spectral Divide and Conquer Algorithms for the Symmetric Eigenvalue Decomposition and the SVD, SIAM J. Sci. Comput., 35, (2013).

Fernando De Teran, Ross Lippert, Yuji Nakatsukasa and Vanni Noferini, Flanders' theorem for many matrices under commutativity assumptions, preprint, (2013).

### V. Noferini

Alex Townsend, Vanni Noferini and Yuji Nakatsukasa, Vector spaces of linearizations for matrix polynomials: a bivariate polynomial approach, preprint, (2012).

Fernando De Teran, Ross Lippert, Yuji Nakatsukasa and Vanni Noferini, Flanders' theorem for many matrices under commutativity assumptions, preprint, (2013).

Vanni Noferini, When is a Hamiltonian matrix the commutator of two skew-Hamiltonian matrices?, preprint, (2014).

Vanni Noferini, Meisam Sharify and Francoise Tisseur, Tropical roots as approximations to eigenvalues of matrix polynomials, preprint, (2014).

Vanni Noferini and Federico Poloni, Duality of matrix pencils and linearizations, preprint, (2013).

### C. A. H. Paul

Papayiannis Andreas, Johnson Paul, Yumashev Dmitry and Duck Peter, Continuous-Time Revenue Managment in Carparks - Part two: Refining the PDE, (2013).

C. T. H. Baker, C. A. H. Paul and H. Tian, Differential algebraic equations with after-effect, Journal of Computational and Applied Mathematics, 140, (2002).

C. T. H. Baker, G. A. Bocharov, C. A. H. Paul and F. A. Rihan, Computational modelling with functional differential equations: identification, selection and sensitivity, Applied Numerical Mathematics, 53, (2005).

C. T. H. Baker, G. A. Bocharov, J. M. Ford, P. M. Lumb, S. J. Norton, C. A. H. Paul, T. Junt, P. Krebs and B. Ludewig, Computational approahes to parameter estimation and model selection in immunology, Journal of Computational and Applied Mathematics, 184, (2005).

C. T. H. Baker and C. A. H. Paul, Discontinuous solutions of neutral delay differential equations, Applied Numerical Mathematics, 56, (2006).

### J. Pestana

Stefan Güttel and Jen Pestana, Some observations on weighted GMRES, preprint, (2013).

Patricio Farrell and Jennifer Pestana, Block preconditioners for linear systems arising from multilevel RBF collocation, preprint, (2014).

Jennifer Pestana and Andrew Wathen, A preconditioned MINRES method for nonsymmetric Toeplitz matrices, preprint, (2014).

### C. Powell

Darran Furnival, Howard Elman and Catherine Powell, H(div) Preconditioning for a Mixed Finite Element Formulation of the Stochastic Diffusion Problem, preprint, (2008).

Nicholas J. Higham and G. W. Stewart, Numerical Linear Algebra in Statistical Computing, (1987).

O.G. Ernst, C.E Powell, D.J. Silvester and E. Ullmann, Efficient Solvers for a Linear Stochastic Galerkin Mixed Formulation of Diffusion Problems with Random Data, SIAM Journal of Scientific Computing, 31, (2009).

Catherine E. Powell and Elisabeth Ullmann, Preconditioning stochastic Galerkin saddle point systems, preprint, (2009).

Andrew D. Gordon and Catherine E. Powell, Solving Stochastic Collocation Systems with Algebraic Multigrid, preprint, (2010).

Alexei Bespalov, Catherine E. Powell and David Silvester, A priori error analysis of stochastic Galerkin mixed approximations of elliptic PDEs with random data, SIAM Journal on Numerical Analysis, 50, (2012).

David Silvester, Alexei Bespalov and Catherine E. Powell, A framework for the development of implicit solvers for incompressible flow problems, preprint, (2011).

Catherine E. Powell and David J. Silvester, Preconditioning steady-state Navier-Stokes equations with random data, SIAM Journal on Scientific Computing (submitted).

Alex Bespalov, Catherine E. Powell and David Silvester, Energy norm a posteriori error estimation for parametric operator equations, SIAM Journal on Scientific Computing, 36, (2014).

Catherine E. Powell and Andrew D. Gordon, A Preconditioner for Fictitious Domain Formulations of Elliptic PDEs on Uncertain Parameterized Domains , preprint, (2013).

Catherine E. Powell, Optimal Preconditioning for Mixed Finite Element Formulation of Second-Order Elliptic Problems, (2003).

Catherine Powell and David Silvester, Optimal Preconditioning for Raviart-Thomas Mixed Formulation of Second-Order Elliptic Problems , SIAM Journal on Matrix Analysis and Applications, 25, (2003).

Catherine Powell, Parameter-free H(div) preconditioning for mixed finite element formulation of diffusion problems, IMA Journal of Numerical Analysis, 25, (2005).

Catherine Powell and David Silvester, Black-Box Preconditioning for Self-Adjoint Elliptic PDEs , Lecture Notes in Computational Science and Engineering (Springer), 35.

M. Soleimani, C.E. Powell and N. Polydorides, Improving the forward solver for the complete electrode model in EIT using algebraic multigrid, IEEE Transactions on Medical Imaging, 24, (2005).

Catherine E Powell, Robust Preconditioning for Second-Order Elliptic PDEs with Random Field Coefficients, preprint.

David J. Silvester and Catherine E. Powell, PIFISS Potential (Incompressible) Flow & Iterative Solution Software guide, preprint.

### T. Shardlow

Hagen Gilsing and Tony Shardlow, SDELab: stochastic differential equations with MATLAB, preprint.

Gabriel Lord and Tony Shardlow, Post processing for stochastic parabolic partial differential equations, preprint.

Anna Mills, Stephen Marsland and Tony Shardlow, Computing the Geodesic Interpolating Spline, preprint.

Evelyn Buckwar, Rachel Kuske, Salah-Eldin Mohammed and Tony Shardlow, The Weak Euler Scheme for Stochastic Differential Delay Equations, preprint.

P.E. Kloeden, G.J. Lord, A. Neuenkirch and T. Shardlow, The exponential integrator scheme for stochastic partial differential equations: Pathwise error bounds, preprint, (2010).

P.E. Kloeden and T. Shardlow, THE MILSTEIN SCHEME FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITHOUT ANTICIPATIVE CALCULUS, preprint, (2010).

Tony Shardlow, Splitting for dissipative particle dynamics, SIAM Journal on Scientific Computing, 24, (2003).

Tony Shardlow, Weak convergence of a numerical method for a stochastic heat equations, BIT Numerical Mathematics, 43, (2003).

Tony Shardlow and Yubin Yan, Geometric ergodicity for dissipative particle dynamics, Stochastics and Dynamics, 6, (2006).

Tony Shardlow, Nucleation of waves in excitable media by noise, Multiscale Modeling and Simulation, 3, (2004).

### M. Sharify

Marianne Akian, Stéphane Gaubert and Meisam Sharify, Log-majorization of the moduli of the eigenvalues of a matrix polynomial by tropical roots, preprint, (2013).

Vanni Noferini, Meisam Sharify and Francoise Tisseur, Tropical roots as approximations to eigenvalues of matrix polynomials, preprint, (2014).

### D. J. Silvester

Howard Elman, Victoria Howle, John Shadid, David Silvester and Ray Tuminaro, Least squares preconditioners for stabilized discretizations of the Navier-Stokes equations, SIAM Journal on Scientific Computing, 30, (2007).

Philip Gresho, David Griffiths and David Silvester, Adaptive time-stepping for incompressible flow. Part I: scalar advection-diffusion, SIAM Journal on Scientific Computing, 30, (2008).

O.G. Ernst, C.E Powell, D.J. Silvester and E. Ullmann, Efficient Solvers for a Linear Stochastic Galerkin Mixed Formulation of Diffusion Problems with Random Data, SIAM Journal of Scientific Computing, 31, (2009).

Glyn Rees, David Silvester and Milan Mihajlovic, A truncated ILU smoother for multigrid preconditioning of convection dominated flow problems, preprint, (2011).

Qifeng Liao and David Silvester, A simple yet effective a posteriori estimator for classical mixed approximation of Stokes equations, Applied Numerical Mathematics, (2010).

David J. Silvester and Valeria Simoncini, An Optimal Iterative Solver for Symmetric Indefinite Systems stemming from Mixed Approximation, ACM Transactions on Mathematical Software, 37, (2011).

David A. Kay, Philip M. Gresho, David F. Griffiths and David J. Silvester, Adaptive time-stepping for incompressible flow Part II: Navier-Stokes Equations, SIAM Journal on Scientific Computing, 32, (2010).

Howard Elman, Milan Mihajlovic and David Silvester, Fast iterative solvers for buoyancy driven flow problems, Journal of Computational Physics, 230, (2011).

Qifeng Liao and David Silvester, Fast Implicit Solvers using Stabilized Mixed Approximation, preprint, (2011).

David Griffiths and David Silvester, Unstable modes of the Q1-P0 element, preprint, (2011).

Alexei Bespalov, Catherine E. Powell and David Silvester, A priori error analysis of stochastic Galerkin mixed approximations of elliptic PDEs with random data, SIAM Journal on Numerical Analysis, 50, (2012).

David Silvester, Alexei Bespalov and Catherine E. Powell, A framework for the development of implicit solvers for incompressible flow problems, preprint, (2011).

Christopher A. Smethurst, David J. Silvester and Milan D. Mihajlovic, Unstructured finite element method for the solution of the Boussinesq problem in 3D, preprint, (2012).

Catherine E. Powell and David J. Silvester, Preconditioning steady-state Navier-Stokes equations with random data, SIAM Journal on Scientific Computing (submitted).

Alex Bespalov, Catherine E. Powell and David Silvester, Energy norm a posteriori error estimation for parametric operator equations, SIAM Journal on Scientific Computing, 36, (2014).

David Silvester and Qifeng Liao, Robust Stabilized Stokes Approximation Methods for Highly Stretched Grids, IMA Journal of Numerical Analysis, 33, (2013).

Sebastien Duminil, Hassane Sadok and David Silvester, Fast solvers for discretized Navier-Stokes problems using vector extrapolation, Numerical Algorithms, 66, (2014).

Howard C. Elman, Alison Ramage and David J. Silvester, IFISS: A computational laboratory for investigating incompressible flow problems, SIAM Review, 56, (2014).

Catherine Powell and David Silvester, Optimal Preconditioning for Raviart-Thomas Mixed Formulation of Second-Order Elliptic Problems , SIAM Journal on Matrix Analysis and Applications, 25, (2003).

Catherine Powell and David Silvester, Black-Box Preconditioning for Self-Adjoint Elliptic PDEs , Lecture Notes in Computational Science and Engineering (Springer), 35.

Howard C. Elman, David J. Silvester and Andrew J. Wathen, Performance and analysis of saddle point preconditioner for the discrete steady-state Navier-Stokes equations, Numerische Mathematik, 90, (2002).

David Kay and David J. Silvester, The reliability of local error estimators for convection diffusion equations, IMA Journal of Numerical Analysis, 21, (2001).

Sean Norburn and David J. Silvester, Fourier analysis of stabilised Q1-Q1 mixed finite element approximation, SIAM Journal on Numerical Analysis, 39, (2001).

David Silvester, Howard Elman, David Kay and Andrew Wathen, Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow, Journal of Computational and Applied Mathematics, 128, (2001).

David Silvester and Milan D. Mihajlovic, A Black-Box Multigrid Preconditioner for the Biharmonic Equation, BIT Numerical Mathematics, 44, (2004).

David J. Silvester and Catherine E. Powell, PIFISS Potential (Incompressible) Flow & Iterative Solution Software guide, preprint.

Howard C. Elman, Alison Ramage and David J. Silvester, Algorithm 866: IFISS, a Matlab toolbox for modelling incompressible flow, ACM Transactions on Mathematical Software (TOMS), 33, (2007).

Howard C. Elman, David J. Silvester and Andrew J. Wathen, Finite Elements and Fast Iterative Solvers: With Applications in Incompressible Fluid Dynamics, (2005).

### R. W. Thatcher

J.W. Dold, R.W. Thatcher and A.A. Shah, High order effects in one-step reaction-sheet jump conditions for premixed flames, Combustion Theory and Modelling, 7, (2003).

J.W. Dold, R.O. Weber, R.W. Thatcher and A.A. Shah, Flame ball with thermally sensitive intermediate kinetics, Combustion Theory and Modelling, 7, (2003).

R. W. Thatcher, A. A. Omon-Arancibia and J.W. Dold, Oscillatory flame edge propagation, isolated flame tubes and stability in a non-premixed counterflow, Combustion Theory and Modelling, 6, (2002).

P. Bolton and R.W. Thatcher, On mass conservation in least squares methods, Journal on Computational Physics, 203, (2005).

R. W. Thatcher and A. A. Omon-Arancibia, Multiple speeds of flame edge propagation for Lewis numbers above one, Combustion Theory and Modelling, 9, (2005).

R. W. Thatcher and E. Al. Sarairah, Steady and unsteady flame propagation in a premixed counterflow, Combustion Theory and Modelling, 11, (2007).

### R. M. Thomas

G. O. Jones and M. E. M. Thomas, The density of algebraic points on certain Pfaffian surfaces, The Quarterly Journal of Mathematics.

A J Wilkie, G O Jones and M E M Thomas, Integer-valued definable functions, preprint, (2012).

G. O. Jones, D. J. Miller and M. E. M. Thomas, Mildness and the density of rational points on certain transcendental curves, Notre Dame Journal of Formal Logic, 52, (2011).

Michael R. Thomas, A NON-CLASSICAL APPROACH TO MAXIMUM ENTROPY IN UNCERTAIN REASONING, (2004).

T. Basebi and Ruth M. Thomas, A study of moving mesh applied to a thin flame propagating in a detonator delay element, Computers and Mathematics with Applications, 45, (2003).

### F. Tisseur

Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder and Françoise Tisseur, NLEVP: A Collection of Nonlinear Eigenvalue Problems, preprint, (2008).

Philip I. Davies, Nicholas J. Higham and Françoise Tisseur, Analysis of the Cholesky Method with Iterative Refinement for Solving the Symmetric Definite Generalized Eigenproblem, SIAM Journal on Matrix Analysis and Applications, 23, (2001).

Chun-Hua Guo, Nicholas J. Higham and Françoise Tisseur, Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems, SIAM Journal On Matrix Analysis and Applications., 30, (2009).

D. Steven Mackey, Niloufer Mackey and Francoise Tisseur, On the Definition of Two Natural Classes of Scalar Product, preprint, (2007).

Francoise Tisseur, Seamus D. Garvey and Christopher Munro, Deflating Quadratic Matrix Polynomials with Structure Preserving Transformations, preprint, (2009).

Nicholas J. Higham, D. Steven Mackey and Françoise Tisseur, Definite Matrix Polynomials and their Linearization by Definite Pencils, SIAM Journal on Matrix Analysis and Applications, 31, (2009).

Chun-Hua Guo, Nicholas J. Higham and Françoise Tisseur, An Improved Arc Algorithm for Detecting Definite Hermitian Pairs, SIAM Journal On Matrix Analysis and Applications., 31, (2009).

Laurence Grammont, Nicholas J. Higham and Françoise Tisseur, A Framework for Analyzing Nonlinear Eigenproblems and Parametrized Linear Systems, Linear Algebra and its Applications, 435, (2011).

Peter Lancaster and Françoise Tisseur, Hermitian Quadratic Matrix Polynomials: Solvents and Inverse Problems, preprint, (2010).

Maha Al-Ammari and Francoise Tisseur, Hermitian Matrix Polynomials with Real Eigenvalues of Definite Type. Part I: Classification, preprint, (2010).

Younes Chahlaoui, Françoise Tisseur and Paul Van Dooren, A new approach for MOR of second order Dynamical Systems, (2009).

Nicholas J. Higham, Christian Mehl and Françoise Tisseur, The Canonical Generalized Polar Decomposition, SIAM Journal On Matrix Analysis and Applications, 31, (2010).

Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder and Françoise Tisseur, NLEVP: A Collection of Nonlinear Eigenvalue Problems, preprint, (2010).

Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder and Françoise Tisseur, NLEVP: A Collection of Nonlinear Eigenvalue Problems. Users' Guide, preprint, (2010).

Françoise Tisseur and Stef Graillat, Structured Condition Numbers and Backward Errors in Scalar Product Spaces, preprint.

Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder and Françoise Tisseur, NLEVP: A Collection of Nonlinear Eigenvalue Problems, preprint, (2011).

Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder and Françoise Tisseur, NLEVP: A Collection of Nonlinear Eigenvalue Problems. Users' Guide, preprint, (2011).

Maha Al-Ammari and Francoise Tisseur, Standard Triples of Structured Matrix Polynomials, preprint, (2011).

Ion Zaballa and Francoise Tisseur, Finite and Infinite Elementary Divisors of Matrix Polynomials: A Global Approach, preprint, (2012).

Leo Taslaman, Francoise Tisseur and Ion Zaballa, Triangularizing matrix polynomials, preprint, (2012).

Ramaseshan Kannan, Stephen Hendry, Nicholas J. Higham and Francoise Tisseur, Detecting the Causes of Ill-Conditioning in Structural Finite Element Models, preprint, (2013).

Françoise Tisseur and Ion Zaballa, Triangularizing Quadratic Matrix Polynomials, SIAM J. MATRIX ANAL. APPL., 34, (2013).

Sven Hammarling, Christopher J. Munro and Francoise Tisseur, An Algorithm for the Complete Solution of Quadratic Eigenvalue Problems, preprint, (2011).

James Hook and Françoise Tisseur, Tropical Eigenvalues, preprint, (2014).

Vanni Noferini, Meisam Sharify and Francoise Tisseur, Tropical roots as approximations to eigenvalues of matrix polynomials, preprint, (2014).

Lars Karlsson and Francoise Tisseur, Algorithms for Hessenberg-Triangular Reduction of Fiedler Linearization of Matrix Polynomials, preprint, (2014).

D. Steven Mackey, Niloufer Mackey and Françoise Tisseur, Structured Mapping Problems for Matrices Associated with Scalar Products Part I: Lie and Jordan Algebras, preprint, (2007).

Françoise Tisseur and Nicholas J. Higham, Structured pseudospectra for polynomial eigenvalue problems, with applications, SIAM Journal On Matrix Analysis And Applications, 23, (2001).

Nicholas J. Higham and Françoise Tisseur, A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra, SIAM Journal On Matrix Analysis And Applications, 21, (2000).

Nicholas J. Higham and Françoise Tisseur, More on pseudospectra for polynomial eigenvalue problems and applications in control theory, Elsevier, Linear Algebra and its Applications, 351-352, (2002).

Nicholas J. Higham, Françoise Tisseur and Paul M. Van Dooren, Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems, Elsevier, Linear Algebra and its Applications, 351-352, (2002).

Françoise Tisseur and Karl Meerbergen, The quadratic eigenvalue problem, SIAM Review, 43, (2001).

Françoise Tisseur, Tridiagonal-diagonal reduction of symmetric indefinite pairs , SIAM Journal On Matrix Analysis And Applications, 26, (2004).

Nicholas J. Higham, D. Steven Mackey, Niloufer Mackey and Françoise Tisseur, Functions Preserving Matrix Groups and Iterations for the Matrix Square Root, SIAM Journal On Matrix Analysis and Applications, 26, (2005).

Nicholas J. Higham, D. Steven Mackey, Niloufer Mackey and Françoise Tisseur, Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups, SIAM Journal On Matrix Analysis and Applications, 25, (2004).

Nicholas J. Higham, D. Steven Mackey and Françoise Tisseur, The Conditioning of Linearizations of Matrix Polynomials, SIAM J. Matrix Anal. Appl., 28, (2006).

Michael Karow, Daniel Kressner and Françoise Tisseur, Structured Eigenvalue Condition Numbers, SIAM J. Matrix Anal. Appl., 28, (2006).

Nicholas J. Higham, D. Steven Mackey, Niloufer Mackey and Françoise Tisseur, Symmetric Linearizations for Matrix Polynomials, SIAM Journal on Matrix Analysis and Applications, 29, (2006).

D. Steven Mackey, Niloufer Mackey and Françoise Tisseur, G-Reflectors: Analogues of Householder Transformations in Scalar Product Spaces, Linear Algebra and its Applications, 385, (2004).

Françoise Tisseur, Parallel Implementation of the Yau and Lu Method for Eigenvalue Computation, International Journal of Supercomputer Applications and High Performance Computing, 11, (1997).

D.S. Mackey, N. Mackey and F. Tisseur, Structured Factorizations in Scalar Product Spaces, SIAM Journal on Matrix Analysis and Applications, 27, (2006).

Dario A. Bini, Luca Gemignani and Françoise Tisseur, The Ehrlich--Aberth Method for the Nonsymmetric Tridiagonal Eigenvalue Problem, SIAM Journal on Matrix Analysis and Applications, 27, (2005).

Françoise Tisseur, A Chart of Backward Errors for Singly and Doubly Structured Eigenvalue Problems, SIAM Journal on Matrix Analysis and Applications, 24, (2003).

Françoise Tisseur Tisseur, Newton's Method in Floating Point Arithmetic and Iterative Refinement of Generalized Eigenvalue Problems, SIAM Journal on Matrix Analysis and Applications, 22.

Françoise Tisseur, Stability of Structured Hamiltonian Eigensolvers, SIAM Journal on Matrix Analysis and Applications, 23.

F Tisseur and J Dongarra, A Parallel Divide and Conquer Algorithm for the Symmetric Eigenvalue Problem on Distributed Memory Architectures, SIAM Journal on Scientific Computing, 20.

D. Steven Mackey, Niloufer Mackey and Françoise Tisseur, Structured tools for structured matrices, Electronic Journal of Linear Algebra, 10.

Françoise Tisseur and Jean-Pierre Dedieu, Perturbation theory for homogeneous polynomial eigenvalue problems, Linear Algebra and its Applications, 385.

Stéphane Domas and Françoise Tisseur, Parallel implementation of a symmetric eigensolver based on the Yau and Lu method.

Seamus D. Garvey, Françoise Tisseur, Michael I. Friswell, John E. T. Penny and Uwe Prells, Simultaneous tridiagonalization of two symmetric matrices, International Journal for Numerical Methods in Engineering, 57.

Jean-Pierre Dedieu, Myong-Hi Kim, Michael Shub and Françoise Tisseur, Implicit Gamma Theorems (I): Pseudoroots and Pseudospectra, Foundation of Computational Mathematics, 3.

Nicholas J. Higham, Ren-Cang Li and Françoise Tisseur, Backward Error of Polynomial Eigenproblems Solved by Linearization, SIAM Journal on Matrix Analysis and Applications, 29, (2007).

Nicholas J. Higham, D. Steven Mackey, Françoise Tisseur and Seamus D. Garvey, Scaling, Sensitivity and Stability in the Numerical Solution of Quadratic Eigenvalue Problems , International Journal for Numerical Methods in Engineering, 73, (2008).