CIRCULANT INTEGRAL-OPERATORS AS PRECONDITIONERS FOR WIENER-HOPF EQUATIONS
Publication in refereed journal

香港中文大學研究人員

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替代計量分析
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摘要In this paper, we study the solutions of finite-section Wiener-Hopf equations by the preconditioned conjugate gradient method. Our main aim is to give an easy and general scheme of constructing good circulant integral operators as preconditioners for such equations. The circulant integral operators are constructed from sequences of conjugate symmetric functions {C-tau}(tau). Let k(t) denote the kernel function of the Wiener-Hopf equation and (k) over cap(t) be its Fourier transform. We prove that for sufficiently large tau if {C-tau}(tau) is uniformly bounded on the real line R and the convolution product of the Fourier transform of C-tau with (k) over cap(t) converges to (k) over cap(t) uniformly on R, then the circulant preconditioned Wiener-Hopf operator will have a clustered spectrum. It follows that the conjugate gradient method, when applied to solving the preconditioned operator equation, converges superlinearly. Several circulant integral operators possessing the clustering and fast convergence properties are constructed explicitly. Numerical examples are also given to demonstrate the performance of different circulant integral operators as preconditioners for Wiener-Hopf operators.
著者CHAN RH, JIN XQ, NG MK
期刊名稱Integral Equations and Operator Theory
出版年份1995
月份1
日期1
卷號21
期次1
出版社BIRKHAUSER VERLAG AG
頁次12 - 23
國際標準期刊號0378-620X
語言英式英語
Web of Science 學科類別Mathematics; MATHEMATICS

上次更新時間 2020-29-11 於 00:11