GENUINE-OPTIMAL CIRCULANT PRECONDITIONERS FOR WIENER-HOPF EQUATIONS

• 来源期刊: 计算数学
• 学科: 数学
• 关键词: Wiener-Hopf equations Circulant preconditioner Preconditioned conjugate gradient method Quadrature rules Hilbert-Schmidt norm.
• 年，卷（期）: 2001,（6）
• 页码范围: 629-638
• 页数: 10页
• 分类号: O1
• 语种: 英文

摘要

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.