Preconditioned iterative methods for nonsymmetric Toeplitz and block Toeplitz matrices

Join Dr Jennifer Pestana from the University of Strathclyde for this seminar.

  • Thu 23 Nov 17

    14:00 - 15:00

  • Colchester Campus

    Room 5.300B

  • Event speaker

    Dr Jennifer Pestana

  • Event type

    Lectures, talks and seminars
    Department of Mathematical Sciences Seminar Series

  • Event organiser

    Mathematical Sciences, Department of

  • Contact details

    Dr Andrew Harrison

Linear systems with nonsingular Toeplitz or block Toeplitz matrices arise in many applications, notably when discretizing partial differential, fractional differential or integral equations using constant time steps. These linear systems are amenable to solution by iterative methods, e.g., Krylov subspace methods, but to keep the number of iterations low preconditioning is typically required.

The goal of preconditioning is form an equivalent linear system to the original that is somehow easier to solve. When the (block) Toeplitz matrix is symmetric, descriptive convergence theory guides the choice of preconditioner, but in the nonsymmetric case preconditioning is largely heuristic. In this talk we show how to symmetrize (block) Toeplitz matrices, so that the descriptive convergence theory for symmetric problems can be applied in order to design preconditioners that are guaranteed to be effective. Our numerical experiments validate the efficiency and robustness of the proposed approach.