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Article: Factorized banded inverse preconditioners for matrices with Toeplitz structure

TitleFactorized banded inverse preconditioners for matrices with Toeplitz structure
Authors
KeywordsInverse preconditioners
Nonlinear image restoration
Toeplitz-related matrices
Issue Date2005
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, 2005, v. 26 n. 6, p. 1852-1870 How to Cite?
AbstractIn this paper, we study factorized banded inverse preconditioned for matrices with Toeplitz structure. We show that if a Toeplitz matrix T has certain off-diagonal decay property, then the factorized banded inverse preconditioner approximates T-1 accurately, and the spectra of these preconditioned matrices are clustered around 1. In nonlinear image restoration applications, Toeplitz-related systems of the form I+T* DT are required to solve, where D is a positive nonconstant diagonal matrix. We construct inverse preconditioners for such matrices. Numerical results show that the performance of our proposed preconditioners are superior to that of circulant preconditioners. A two-dimensional nonlinear image restoration example is also presented to demonstrate the effectiveness of the proposed preconditioner. © 2005 Society for Industrial and Applied Mathematics.
Persistent Identifierhttp://hdl.handle.net/10722/44908
ISSN
2015 Impact Factor: 1.792
2015 SCImago Journal Rankings: 2.166
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorLin, FRen_HK
dc.contributor.authorNg, MKen_HK
dc.contributor.authorChing, WKen_HK
dc.date.accessioned2007-10-30T06:13:10Z-
dc.date.available2007-10-30T06:13:10Z-
dc.date.issued2005en_HK
dc.identifier.citationSIAM Journal On Scientific Computing, 2005, v. 26 n. 6, p. 1852-1870en_HK
dc.identifier.issn1064-8275en_HK
dc.identifier.urihttp://hdl.handle.net/10722/44908-
dc.description.abstractIn this paper, we study factorized banded inverse preconditioned for matrices with Toeplitz structure. We show that if a Toeplitz matrix T has certain off-diagonal decay property, then the factorized banded inverse preconditioner approximates T-1 accurately, and the spectra of these preconditioned matrices are clustered around 1. In nonlinear image restoration applications, Toeplitz-related systems of the form I+T* DT are required to solve, where D is a positive nonconstant diagonal matrix. We construct inverse preconditioners for such matrices. Numerical results show that the performance of our proposed preconditioners are superior to that of circulant preconditioners. A two-dimensional nonlinear image restoration example is also presented to demonstrate the effectiveness of the proposed preconditioner. © 2005 Society for Industrial and Applied Mathematics.en_HK
dc.format.extent818226 bytes-
dc.format.extent1815 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/SISCen_HK
dc.relation.ispartofSIAM Journal on Scientific Computingen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectInverse preconditionersen_HK
dc.subjectNonlinear image restorationen_HK
dc.subjectToeplitz-related matricesen_HK
dc.titleFactorized banded inverse preconditioners for matrices with Toeplitz structureen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1064-8275&volume=26&issue=6&spage=1852&epage=1870&date=2005&atitle=Factorized+banded+inverse+preconditioners+for+matrices+with+toeplitz+structureen_HK
dc.identifier.emailChing, WK:wching@hku.hken_HK
dc.identifier.authorityChing, WK=rp00679en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1137/030601272en_HK
dc.identifier.scopuseid_2-s2.0-27844585669en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-27844585669&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume26en_HK
dc.identifier.issue6en_HK
dc.identifier.spage1852en_HK
dc.identifier.epage1870en_HK
dc.identifier.isiWOS:000231357700003-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridLin, FR=7402777425en_HK
dc.identifier.scopusauthoridNg, MK=7202076432en_HK
dc.identifier.scopusauthoridChing, WK=13310265500en_HK

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