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Article: Preconditioned Lanczos Methods for the Minimum Eigenvalue of a Symmetric Positive Definite Toeplitz Matrix

TitlePreconditioned Lanczos Methods for the Minimum Eigenvalue of a Symmetric Positive Definite Toeplitz Matrix
Authors
KeywordsToeplitz matrix
Sine transform matrix
Fast sine transform
Preconditioning
Lanczos method
Issue Date2000
PublisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at http://epubs.siam.org/sam-bin/dbq/toclist/SISC
Citation
SIAM Journal on Scientific Computing, 2000, v. 21 n. 6, p. 1973-1986 How to Cite?
AbstractIn this paper, we apply the preconditioned Lanczos (PL) method to compute the minimum eigenvalue of a symmetric positive definite Toeplitz matrix. The sine transform-based preconditioner is used to speed up the convergence rate of the PL method. The resulting method involves only Toeplitz and sine transform matrix-vector multiplications and hence can be computed efficiently by fast transform algorithms. We show that if the symmetric Toeplitz matrix is generated by a positive $2 \pi$-periodic even continuous function, then the PL method will converge sufficiently fast. Numerical results including Toeplitz and non-Toeplitz matrices are reported to illustrate the effectiveness of the method.
Persistent Identifierhttp://hdl.handle.net/10722/42998
ISSN
2015 Impact Factor: 1.792
2015 SCImago Journal Rankings: 2.166
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorNg, KPen_HK
dc.date.accessioned2007-03-23T04:36:32Z-
dc.date.available2007-03-23T04:36:32Z-
dc.date.issued2000en_HK
dc.identifier.citationSIAM Journal on Scientific Computing, 2000, v. 21 n. 6, p. 1973-1986en_HK
dc.identifier.issn1064-8275en_HK
dc.identifier.urihttp://hdl.handle.net/10722/42998-
dc.description.abstractIn this paper, we apply the preconditioned Lanczos (PL) method to compute the minimum eigenvalue of a symmetric positive definite Toeplitz matrix. The sine transform-based preconditioner is used to speed up the convergence rate of the PL method. The resulting method involves only Toeplitz and sine transform matrix-vector multiplications and hence can be computed efficiently by fast transform algorithms. We show that if the symmetric Toeplitz matrix is generated by a positive $2 \pi$-periodic even continuous function, then the PL method will converge sufficiently fast. Numerical results including Toeplitz and non-Toeplitz matrices are reported to illustrate the effectiveness of the method.en_HK
dc.format.extent193210 bytes-
dc.format.extent26112 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypeapplication/msword-
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/SISCen_HK
dc.relation.ispartofSIAM Journal on Scientific Computing-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectToeplitz matrixen_HK
dc.subjectSine transform matrixen_HK
dc.subjectFast sine transformen_HK
dc.subjectPreconditioningen_HK
dc.subjectLanczos methoden_HK
dc.titlePreconditioned Lanczos Methods for the Minimum Eigenvalue of a Symmetric Positive Definite Toeplitz Matrixen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1064-8275&volume=21&issue=6&spage=1973&epage=1986&date=2000&atitle=Preconditioned+Lanczos+Methods+for+the+Minimum+Eigenvalue+of+a+Symmetric+Positive+Definite+Toeplitz+Matrixen_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1137/S1064827597330169en_HK
dc.identifier.scopuseid_2-s2.0-0034513884-
dc.identifier.hkuros63220-
dc.identifier.isiWOS:000087640400002-

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