Genuine-Optimal Circulant Preconditioners for Wiener-Hopf Equations

Genuine-Optimal Circulant Preconditioners for Wiener-Hopf Equations

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.

Author Details

Fu-Rong Lin