Year: 2001
Author: Fu-Rong Lin
Journal of Computational Mathematics, Vol. 19 (2001), Iss. 6 : pp. 629–638
Abstract
In this paper, we construct the genuine-optimal circulant preconditioner for finite-section Wiener-Hopf equations. The genuine-optimal circulant preconditioner is defined as the minimizer of Hilbert-Schmidt norm over certain integral operators. We prove that the difference between the genuine-optimal circulant preconditioner and the original integral operator is the sum of a small norm operator and a finite rank operator. Thus, the preconditioned conjugate gradient (PCG) method, when applied to solve the preconditioned equations, converges superlinearly. Finally, we give an efficient algorithm for the solution of Wiener-Hopf equation discretized by high order quadrature rules.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2001-JCM-9015
Journal of Computational Mathematics, Vol. 19 (2001), Iss. 6 : pp. 629–638
Published online: 2001-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Wiener-Hopf equations Circulant preconditioner Preconditioned conjugate gradient method Quadrature rules Hilbert-Schmidt norm.