Research

I am interested in numerical linear algebra and its applications to scientific computing. Much of my research has focused on understanding Krylov subspace methods for linear systems and developing effective preconditioners for these methods. I have also worked on applying results from tropical algebra to problems in numerical linear algebra.

Publications

Please note that preprints may differ from accepted journal articles.

Journal Articles

  1. Preconditioners for symmetrized Toeplitz and multilevel Toeplitz matrices
    SIAM J. Matrix Anal. Appl., 40:870-887, 2019.
    [Preprint] [Article] [Code]
  2. Max-Balancing Hungarian Scalings
    with James Hook, Françoise Tisseur and Jonathan Hogg
    SIAM J. Matrix Anal. Appl., 40:320-346, 2019.
    [Preprint] [Article]
  3. Spectral properties of flipped Toeplitz matrices and related preconditioning
    with Mariarosa Mazza
    BIT, 59:463-482, 2018.
    [Preprint] [Article]
  4. On the Existence and Uniqueness of the Eigenvalue Decomposition of a Parahermitian Matrix
    with Stephan Weiss and Ian Proudler
    IEEE Trans. Signal Process., 66:2659-2672, 2018.
    [Preprint] [Article] [Correction]
  5. Preconditioning and iterative solution of all-at-once systems for evolutionary partial differential equations
    with Eleanor McDonald and Andy Wathen
    SIAM J. Sci. Comput. 40:A1012-A1033, 2018.
    [Preprint] [Article]
  6. Fast multipole preconditioners for sparse matrices arising from elliptic equations
    with Huda Ibeid, Rio Yokota and David Keyes
    Comput. Vis. Sci., 18:213-229, 2018.
    [Preprint] [Article] [Code]
  7. Refined saddle-point preconditioners for discretized Stokes problems
    with John Pearson and David Silvester
    Numer. Math., 138:331-363, 2018.
    [Preprint] [Article] [Code]
  8. GMRES convergence bounds for eigenvalue problems
    with Melina Freitag and Patrick Kürschner
    Comput. Methods Appl. Math., 18:203-222, 2018.
    [Preprint] [Article]
  9. Null-space preconditioners for saddle point problems
    with Tyrone Rees
    SIAM J. Matrix Anal. Appl., 37:1088-1102, 2016.
    [Preprint] [Article]
  10. Efficient block preconditioning for a C1 finite element discretisation of the Dirichlet biharmonic problem
    with Richard Muddle, Matthias Heil, Françoise Tisseur and Milan Mihajlović
    SIAM J. Sci. Comput., 38:A325-A345, 2016.
    [Preprint] [Article]
  11. Block Preconditioners for Linear Systems Arising from Multiscale Collocation with Compactly Supported RBFs
    with Patricio Farrell
    Numer. Linear Algebra Appl., 22:731-747, 2015.
    [Preprint] [Article]
  12. A preconditioned MINRES method for nonsymmetric Toeplitz matrices
    with Andy Wathen
    SIAM J. Matrix Anal. Appl., 36:273-288, 2015.
    [Preprint] [Article]
  13. Natural preconditioning and iterative methods for saddle point systems
    with Andy Wathen
    SIAM Rev., 57:71-91, 2015.
    [Preprint] [Article]
  14. Some observations on weighted GMRES
    with Stefan Güttel
    Numer. Alg., 67:733-752, 2014.
    [Preprint] [Article]
  15. On the eigenvalues and eigenvectors of block triangular preconditioned block matrices
    SIAM J. Matrix Anal. Appl., 35:517-525, 2014.
    [Preprint] [Article]
  16. The antitriangular factorisation of saddle point matrices
    with Andy Wathen
    SIAM J. Matrix Anal. Appl., 35:339-353, 2014.
    [Preprint] [Article]
  17. GMRES convergence bounds that depend on the right-hand side vector
    with David Titley-Peloquin and Andy Wathen
    IMA J. Numer. Anal., 34:462-479, 2014.
    [Article]
  18. Combination preconditioning of saddle point systems for positive definiteness
    with Andy Wathen
    Numer. Linear Algebra Appl., 20:785-808, 2013.
    [Preprint] [Article]
  19. On choice of preconditioner for minimum residual methods for non-Hermitian matrices
    with Andy Wathen
    J. Comput. Appl. Math., 249:57-68, 2013.
    [Preprint] [Article]

Refereed Conference Proceedings

  1. Enforcing eigenvector smoothness for a compact DFT-based polynomial eigenvalue decomposition
    with Fraser Coutts, Keith Thompson, Ian K. Proudler and Stephan Weiss
    In 2018 IEEE 10th Sensor Array and Multichannel Signal Processing Workshop (SAM), pp. 159-163, 2018.
    [Preprint] [Article]
  2. Impact of space-time covariance estimation errors on a parahermitian matrix EVD
    with Connor Deloasa, Fraser Coutts and Stephan Weiss
    In 2018 IEEE 10th Sensor Array and Multichannel Signal Processing Workshop (SAM), pp. 164-168, 2018.
    [Preprint] [Article]
  3. Investigation of a polynomial matrix generalised EVD for multi-channel Wiener filtering
    with Jamie Corr, Stephan Weiss, Ian K. Proudler, Soydan Redif and Marc Moonen
    In 2016 50th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, pp. 1354-1358, 2016.
    [Preprint] [Article]
  4. Preconditioning for nonsymmetry and time-dependence
    with Eleanor McDonald, Sean Hon and Andy Wathen
    In Proceedings of the 23rd International Conference on Domain Decomposition Methods
    [Preprint] [Article]
  5. Right-Hand Side Dependent Bounds for GMRES Applied to Ill-Posed Problems
    In System Modeling and Optimization, IFIP Advances in Information and Communication Technology, Volume 443, pp. 230-236, 2014.
    [Preprint] [Article]

DPhil Thesis