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 - <p style="text-align: justify;">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. &nbsp;</p>