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.

Practical band Toeplitz preconditioning and boundary layer effects

SERRA CAPIZZANO, STEFANO
2003-01-01

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.
2003
Conjugate gradient method; Matrix algebra; Multigrid; Preconditioning; Toeplitz matrix
SERRA CAPIZZANO, Stefano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/1490618
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