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Practical Band Toeplitz Preconditioning and Boundary Layer Effects

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Abstract

In the last decade many efficient iterative solvers for n×n Hermitian positive definite Toeplitz systems have been devised. Many of them are based on band Toeplitz preconditioners: they are optimal but require the knowledge of the zeros of the underlying generating function. In some cases this information is available and in some cases is not. In [27] an economic numerical procedure for finding these zeros within a given precision has been devised. Here we provide conditions on the approximation error of these zeros in order to maintain the optimality that is a convergence rate independent of the dimension n of the considered linear systems.

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  1. Dipartimento di Chimica, Fisica e Matematica, Università dell'Insubria, Sede di Como, Via Valleggio 11, 22100, Como, Italy

    S. Serra-Capizzano

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Serra-Capizzano, S. Practical Band Toeplitz Preconditioning and Boundary Layer Effects. Numerical Algorithms 34, 427–440 (2003). https://doi.org/10.1023/B:NUMA.0000005355.94096.bc

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