Optimal trigonometric preconditioners for nonsymmetric Toeplitz systems
type: Item
instance of: scholarly article
title: Optimal trigonometric preconditioners for nonsymmetric Toeplitz systems
zbMATH Open document ID: 0934.65053
DOI: 10.1016/S0024-3795(98)10042-3
author: Daniel Potts
author: Gabriele Steidl
published in: Linear Algebra and its Applications
publication date: 2000-04-03T00:00:00Z
review text: This paper is concerned with the solution sequences of systems of linear equations where the coefficient matrices are nonsingular nonsymmetric Toeplitz matrices arising from a generating function of the Wiener class. A technique for the construction of optimal trigonometric preconditioners of the corresponding normal equation is described. It is shown that the spectrum of the preconditioned matrix is clustered at 1 so that the preconditioned conjugate gradient method applied to the normal equation converges superlinearly. Numerical tests confirm the theoretical results.
reviewed by: Thomas Sonar
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 1370034
zbMATH Keywords: superlinear convergence
zbMATH Keywords: numerical examples
zbMATH Keywords: nonsymmetric Toeplitz matrices
zbMATH Keywords: Wiener class
zbMATH Keywords: optimal trigonometric preconditioners
zbMATH Keywords: normal equation
zbMATH Keywords: preconditioned conjugate gradient method
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1370034