Tyrone Rees has led the Computational Mathematics Group at the STFC Rutherford Appleton Laboratory since 2019. He completed his DPhil with Andy Wathen at the University of Oxford on Preconditioning iterative methods for PDE constrained optimization. Prior to joining RAL he spent two years as a postdoctoral fellow at the University of British Columbia in Vancouver, Canada.

His research interests lie at the intersection of numerical linear algebra, the numerical solution of PDEs, and continuous optimization. He is particularly interested in the use of iterative methods to solve large, sparse systems of equations, and the acceleration of such methods using precondtioners. As well as theoretical issues surrounding these methods he is also interested using them to efficiently solve problems from applications, with a particular interest in the systems arising in the optimal control of PDEs.

  • Krylov subspace methods
  • Preconditioning
  • PDE constrained optimization
  • Nonlinear Least-squares
  1. Al Daas, H., Jolivet, P., Rees, T. Efficient Algebraic Two-Level Schwarz Preconditioner For Sparse Matrices arXiv:2201.02250, (submitted) 2022 link 
  2. Markvardsen, A., Rees, T., Wathen, M., Lister, A., Odagiu, P., Anuchitanukul, A., Farmer, T., Lim, A., Montesino, F., Snow, T., McCluskey, A. FitBenchmarking: an open source Python package comparing data fitting software Journal of Open Source Software, 6(62), 3127 (2021) link
  3. Al Daas, H., Rees, T., Scott, J. Two-level Nystrom-Schur preconditioner for sparse symmetric positive definite matrices SIAM J. Sci. Comput., Vol 46, pp. A3837-A3861, 2021 link
  4. Rees, T., Wathen, M. An element-based preconditioner for mixed finite element problems SIAM J. Sci. Comput., Vol 43, pp. S884-S907, 2021 link code
  5. Gould, N.I.M, Rees, T., Scott, J. A. A higher order method for solving nonlinear least-squares problems RAL Preprint RAL-P-2017-010, (Submitted) 2017 link code
  6. Gould, N.I.M, Rees, T., Scott, J. A. Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems Computational Optimization and Applications, 73(1), 1-35 link code
  7. Rees, T., The iterative solution of linear systems arising in the primal-dual interior point algorithm for linear programming RAL Preprint RAL-P-2016-007, (Submitted) 2016 link code
  8. Rees, T. and Scott, J., A comparative study of null-space factorizations for sparse symmetric saddle point systems Numerical Linear Algebra with Applications, Vol 25, Issue 1, 2018. link
  9. Greif, C., Rees, T. and Szyld, D. B., Multi-preconditioned GMRES, SeMA Journal, Vol. 74, 213-231, 2017 link code
  10. Pestana, J. and Rees, T., Null-space preconditioners for saddle point systems, SIAM. J. Matrix Anal. & Appl., 37(3), 1103-1128, 2016. link
  11. Barker, A. T., Rees, T. and Stoll, M., A fast solver for an H1 regularized optimal control problem, Communications in Computational Physics, 19(01), 143-167, 2016. link
  12. Gould, N.I.M., Orban, D. and Rees, T., Projected Krylov methods for saddle-point systems, SIAM. J. Matrix Anal. & Appl., 35(4), 1329–1343, 2014. link
  13. Greif, C., Rees, T. and Szyld, D. B., Additive Schwarz with Variable Weights, Domain Decomposition Methods in Science and Engineering XXI, 2014 link
  14. Rees, T. and Wathen, A.J., Preconditioning iterative methods for the optimal control of the Stokes equations, SIAM J. Sci. Comput., Vol. 33, pp. 2903-2926, 2011. link 
  15. Rees, T., Stoll, M. and Wathen, A.J., All-at-once preconditioning in PDE-constrained optimization. Kybernetika, Vol 45., pp. 341-360, 2010 link
  16. Rees, T. and Stoll, M., Block triangular preconditioners for PDE-constrained optimization. Numerical Linear Algebra with Applications, Vol. 17, pp. 977-996, 2010. link
  17. Rees, T., Dollar, H.S. and Wathen, A. J., Optimal solvers for PDE-Constrained Optimization, SIAM J. Sci. Comput., Vol. 32, pp. 271-298, 2010. link code
  18. Wathen, A. J. and Rees, T., Chebyshev semi-iteration in preconditioning for problems including the mass matrix, Electronic Transactions on Numerical Analysis, Volume 34 pp. 125-135, 2009 link

DPhil Thesis

  • Preconditioning Iterative Methods for PDE Constrained Optimization link

Principal author

Contributing author

See also my GitHub profile.