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Article: Block diagonal and schur complement preconditioners for block-toeplitz systems with small size blocks

TitleBlock diagonal and schur complement preconditioners for block-toeplitz systems with small size blocks
Authors
KeywordsBlock diagonal
Block-toeplitz matrix
Preconditioners
Recursion
Schur complement
Issue Date2007
PublisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX
Citation
Siam Journal On Matrix Analysis And Applications, 2007, v. 29 n. 4, p. 1101-1119 How to Cite?
AbstractIn this paper we consider the solution of Hermitian positive definite block-Toeplitz systems with small size blocks. We propose and study block diagonal and Schur complement preconditioners for such block-Toeplitz matrices. We show that for some block-Toeplitz matrices, the spectra of the preconditioned matrices are uniformly bounded except for a fixed number of outliers where this fixed number depends only on the size of the block. Hence, conjugate gradient type methods, when applied to solving these preconditioned block-Toeplitz systems with small size blocks, converge very fast. Recursive computation of such block diagonal and Schur complement preconditioners is considered by using the nice matrix representation of the inverse of a block-Toeplitz matrix. Applications to block-Toeplitz systems arising from least squares filtering problems and queueing networks are presented. Numerical examples are given to demonstrate the effectiveness of the proposed method. © 2007 Society for Industrial and Applied Mathematics.
Persistent Identifierhttp://hdl.handle.net/10722/75407
ISSN
2015 Impact Factor: 1.883
2015 SCImago Journal Rankings: 2.052
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChing, WKen_HK
dc.contributor.authorNg, MKen_HK
dc.contributor.authorWen, YWen_HK
dc.date.accessioned2010-09-06T07:10:49Z-
dc.date.available2010-09-06T07:10:49Z-
dc.date.issued2007en_HK
dc.identifier.citationSiam Journal On Matrix Analysis And Applications, 2007, v. 29 n. 4, p. 1101-1119en_HK
dc.identifier.issn0895-4798en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75407-
dc.description.abstractIn this paper we consider the solution of Hermitian positive definite block-Toeplitz systems with small size blocks. We propose and study block diagonal and Schur complement preconditioners for such block-Toeplitz matrices. We show that for some block-Toeplitz matrices, the spectra of the preconditioned matrices are uniformly bounded except for a fixed number of outliers where this fixed number depends only on the size of the block. Hence, conjugate gradient type methods, when applied to solving these preconditioned block-Toeplitz systems with small size blocks, converge very fast. Recursive computation of such block diagonal and Schur complement preconditioners is considered by using the nice matrix representation of the inverse of a block-Toeplitz matrix. Applications to block-Toeplitz systems arising from least squares filtering problems and queueing networks are presented. Numerical examples are given to demonstrate the effectiveness of the proposed method. © 2007 Society for Industrial and Applied Mathematics.en_HK
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/SIMAXen_HK
dc.relation.ispartofSIAM Journal on Matrix Analysis and Applicationsen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectBlock diagonalen_HK
dc.subjectBlock-toeplitz matrixen_HK
dc.subjectPreconditionersen_HK
dc.subjectRecursionen_HK
dc.subjectSchur complementen_HK
dc.titleBlock diagonal and schur complement preconditioners for block-toeplitz systems with small size blocksen_HK
dc.typeArticleen_HK
dc.identifier.emailChing, WK:wching@hku.hken_HK
dc.identifier.authorityChing, WK=rp00679en_HK
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1137/S0895479803428230en_HK
dc.identifier.scopuseid_2-s2.0-54849429866en_HK
dc.identifier.hkuros141945en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-54849429866&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume29en_HK
dc.identifier.issue4en_HK
dc.identifier.spage1101en_HK
dc.identifier.epage1119en_HK
dc.identifier.eissn1095-7162-
dc.identifier.isiWOS:000253016700004-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridChing, WK=13310265500en_HK
dc.identifier.scopusauthoridNg, MK=34571761900en_HK
dc.identifier.scopusauthoridWen, YW=7401777008en_HK

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