Areas of interest
- Sparse linear algebra
- Numerical analysis
- Large-scale scientific computation
- Mathematical software
Research centres and groups
My research focuses on the solution of large sparse systems of linear equations and large-scale linear and non linear optimization problems. An important orientation is the development of underlying theory and algorithms that are then realised as state-of-the-art mathematical software. For the last 30 years, I have been a major contributor to the internationally renowned HSL mathematical software library; I had overall responsibility for HSL from 2007 to 2018.
My key scientific contributions, which involve studying the underlying mathematics, new analysis and theoretical developments, leading to new library software, include:
* Sparse matrix ordering algorithms (bandwidth and profile minimisation and algorithms for challenging symmetric indefinite matrices that limit the need for numerical pivoting while maintaining sparsity);
* Algorithms to improve the efficiency and applicability of sparse direct solvers (including novel out-of-core techniques, the introduction of multiple front algorithms for coarse-grained parallelism, the use of single precision within a double precision solver, and sparse scaling algorithms);
* Robust limited memory incomplete factorization preconditioners for sparse linear systems;
* Novel techniques for solving large-scale sparse and mixed sparse-dense least squares problems.
* 2016- Professor of Applied Mathematics and Director at Reading of the Centre for Doctoral Training in the Mathematics of Planet Earth, The University of Reading. (0.6 FTE.)
* 2011- Science and Technology Research Council Individual Merit Research Fellow, Rutherford Appleton Laboratory. (0.3 FTE since 2016).
* 2007-2018 Numerical Analysis Group Leader, STFC Rutherford Appleton Laboratory.
* 1990-2007 Researcher, Numerical Analysis Group, STFC Rutherford Appleton Laboratory.
* 1987-1990 Higher Scientific Officer, Numerical Analysis Group, Harwell Laboratory, Oxfordshire.
* 1986-1987 Higher Scientific Officer, Theoretical Physics Department, National Radiological Protection Board, Oxfordshire.
* 1984-1986 Junior Research Fellow, St John's College, University of Oxford.
* 1981-1984 PhD student, University of Oxford.
* 1978-1981 Undergraduate, University of Oxford.
* BA Hons (I) Mathematics, University of Oxford, 1981
* DPhil Mathematics, University of Oxford, 1984
* Science and Technology Facilities Research Council Individual Merit Research Fellow
* Fellow of the Society for Industrial and Applied Mathematics (SIAM)
* Fellow of the Institute of Mathematics and its Applications
* President of SIAM UKIE (2021–2023).