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.