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Article: Preconditioners for Wiener--Hopf Equations with High-Order Quadrature Rules

TitlePreconditioners for Wiener--Hopf Equations with High-Order Quadrature Rules
Authors
KeywordsWiener--Hopf equations
projection method
preconditioned conjugate gradient method
Fourier transform
quadrature rules
Issue Date1997
PublisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at http://epubs.siam.org/sam-bin/dbq/toclist/SINUM
Citation
SIAM Journal on Numerical Analysis, 1997, v. 34 n. 4, p. 1418-1431 How to Cite?
AbstractWe consider solving the Wiener--Hopf equations with high-order quadrature rules by preconditioned conjugate gradient (PCG) methods. We propose using convolution operators as preconditioners for these equations. We will show that with the proper choice of kernel functions for the preconditioners, the resulting preconditioned equations will have clustered spectra and therefore can be solved by the PCG method with superlinear convergence rate. Moreover, the discretization of these equations by high-order quadrature rules leads to matrix systems that involve only Toeplitz or diagonal matrix--vector multiplications and hence can be computed efficiently by FFTs. Numerical results are given to illustrate the fast convergence of the method and the improvement on accuracy by using higher-order quadrature rule. We also compare the performance of our preconditioners with the circulant integral operators.
Persistent Identifierhttp://hdl.handle.net/10722/44913
ISSN
2015 Impact Factor: 1.899
2015 SCImago Journal Rankings: 2.972
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorLin, FRen_HK
dc.contributor.authorNg, KPen_HK
dc.contributor.authorChan, RHen_HK
dc.date.accessioned2007-10-30T06:13:16Z-
dc.date.available2007-10-30T06:13:16Z-
dc.date.issued1997en_HK
dc.identifier.citationSIAM Journal on Numerical Analysis, 1997, v. 34 n. 4, p. 1418-1431en_HK
dc.identifier.issn0036-1429en_HK
dc.identifier.urihttp://hdl.handle.net/10722/44913-
dc.description.abstractWe consider solving the Wiener--Hopf equations with high-order quadrature rules by preconditioned conjugate gradient (PCG) methods. We propose using convolution operators as preconditioners for these equations. We will show that with the proper choice of kernel functions for the preconditioners, the resulting preconditioned equations will have clustered spectra and therefore can be solved by the PCG method with superlinear convergence rate. Moreover, the discretization of these equations by high-order quadrature rules leads to matrix systems that involve only Toeplitz or diagonal matrix--vector multiplications and hence can be computed efficiently by FFTs. Numerical results are given to illustrate the fast convergence of the method and the improvement on accuracy by using higher-order quadrature rule. We also compare the performance of our preconditioners with the circulant integral operators.en_HK
dc.format.extent274039 bytes-
dc.format.extent4654 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypetext/plain-
dc.languageengen_HK
dc.publisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at http://epubs.siam.org/sam-bin/dbq/toclist/SINUMen_HK
dc.relation.ispartofSIAM Journal on Numerical Analysis-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectWiener--Hopf equationsen_HK
dc.subjectprojection methoden_HK
dc.subjectpreconditioned conjugate gradient methoden_HK
dc.subjectFourier transformen_HK
dc.subjectquadrature rulesen_HK
dc.titlePreconditioners for Wiener--Hopf Equations with High-Order Quadrature Rulesen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0036-1429&volume=34&issue=4&spage=1418&epage=1431&date=1997&atitle=Preconditioners+for+Wiener--Hopf+Equations+with+High-Order+Quadrature+Rulesen_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1137/S0036142994270983en_HK
dc.identifier.hkuros34898-
dc.identifier.isiWOS:A1997XN43000006-

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