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

Fu Rong Lin

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

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@Article{JCM-19-629, author = {}, title = {Genuine-Optimal Circulant Preconditioners for Wiener-Hopf Equations}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {6}, pages = {629--638}, 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. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9015.html} }
TY - JOUR T1 - Genuine-Optimal Circulant Preconditioners for Wiener-Hopf Equations JO - Journal of Computational Mathematics VL - 6 SP - 629 EP - 638 PY - 2001 DA - 2001/12 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9015.html KW - Wiener-Hopf equations KW - Circulant preconditioner KW - Preconditioned conjugate gradient method AB - 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.
Fu Rong Lin. (1970). Genuine-Optimal Circulant Preconditioners for Wiener-Hopf Equations. Journal of Computational Mathematics. 19 (6). 629-638. doi:
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