Preconditioners for flipped Toeplitz matrices

Dr Jennifer Pestana (Department of Mathematics and Statistics, University of Strathclyde)

Frank Adams Room 1,

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 step sizes. 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.

When the Toeplitz matrix is nonsymmetric, preconditioning is largely heuristic, but it was recently shown that these nonsymmetric problems can be solved using methods and analysis for symmetric problems after a simple permutation, or flip. In this talk we discuss the implications of this flipping for the spectrum of Toeplitz matrices, and present new preconditioners that are guaranteed to be effective.

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