Volume 19, Issue 6
Genuine-Optimal Circulant Preconditioners for Wiener-Hopf Equations
DOI:

J. Comp. Math., 19 (2001), pp. 629-638

Published online: 2001-12

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• Abstract

In this paper, we construct the genuine-optimal circulant preconditioner for finitesection. 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.

• Keywords

Wiener-Hopf equations Circulant preconditioner Preconditioned conjugate gradient method