Genuine-optimal circulant preconditioners for Wiener-Hopf equations
type: Item
instance of: scholarly article
zbMATH Open document ID: 0994.65147
author: Fu-Rong Lin
publication date: 2002-09-29T00:00:00Z
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 1702893
zbMATH Keywords: Wiener-Hopf equations
zbMATH Keywords: circulant preconditioner
zbMATH Keywords: preconditioned conjugate gradient method
zbMATH Keywords: quadrature rules
zbMATH Keywords: Hilbert-Schmidt norm
zbMATH Keywords: spacetime convergence
MaRDI profile type: Publication
title: Genuine-optimal circulant preconditioners for Wiener-Hopf equations
published in: Journal of Computational Mathematics
review text: The author constructs a genuine-optimal circulant preconditioner for finite-section Wiener-Hopf equations. This preconditioner is defined as the minimizer of the Hilbert-Schmidt norm for certain integral operators. It is proved that the difference between this preconditioner and the original integral operator is the sum of a small norm operator and a finite rank operator. From this follows that the preconditioned conjugate gradient method converges superlinearly if it is applied for solving the preconditioned equations. An efficient algorithm for the solution of Wiener-Hopf equation which is discretized by high order quadrature rules is given.
reviewed by: Josef Kofroň
description: scientific article; zbMATH DE number 1702893