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

Fu-Rong Lin

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 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.  

  • Keywords

Wiener-Hopf equations, Circulant preconditioner, Preconditioned conjugate gradient method, Quadrature rules, Hilbert-Schmidt norm.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

frlin@stu.edu.cn (Fu-Rong Lin)

  • BibTex
  • RIS
  • TXT
@Article{JCM-19-629, author = {Lin , Fu-Rong}, 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 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.  

}, 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 AU - Lin , Fu-Rong 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, Circulant preconditioner, Preconditioned conjugate gradient method, Quadrature rules, Hilbert-Schmidt norm. AB -

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.  

Lin , Fu-Rong. (2001). Genuine-Optimal Circulant Preconditioners for Wiener-Hopf Equations. Journal of Computational Mathematics. 19 (6). 629-638. doi:
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