Circulant integral operators as preconditioners for Wiener-Hopf equations | |
Chan，Raymond H.1; Jin，Xiao Qing2; Ng，Michael K.1 | |
1995 | |
Source Publication | Integral Equations and Operator Theory |
ISSN | 0378-620X |
Volume | 21Issue:1Pages:12-23 |
Abstract | 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}. Let k(t) denote the kernel function of the Wiener-Hopf equation and {Mathematical expression} be its Fourier transform. We prove that for sufficiently large τ if {C} is uniformly bounded on the real line R and the convolution product of the Fourier transform of C with {Mathematical expression} 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. © 1995 Birkhäuser Verlag. |
Keyword | AMS(MOS) Subject Classifications: 45E10, 45L10, 65R20, 65J10 |
DOI | 10.1007/BF01262989 |
URL | View the original |
Language | 英语 |
Scopus ID | 2-s2.0-0039838010 |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | University of Macau |
Affiliation | 1.Department of Mathematics,The Chinese University of Hong Kong,Shatin,Hong Kong 2.Faculty of Science and Technology,University of Macau,Macao |
Recommended Citation GB/T 7714 | Chan，Raymond H.,Jin，Xiao Qing,Ng，Michael K.. Circulant integral operators as preconditioners for Wiener-Hopf equations[J]. Integral Equations and Operator Theory,1995,21(1):12-23. |
APA | Chan，Raymond H.,Jin，Xiao Qing,&Ng，Michael K..(1995).Circulant integral operators as preconditioners for Wiener-Hopf equations.Integral Equations and Operator Theory,21(1),12-23. |
MLA | Chan，Raymond H.,et al."Circulant integral operators as preconditioners for Wiener-Hopf equations".Integral Equations and Operator Theory 21.1(1995):12-23. |
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