m-step preconditioners for nonhermitian positive definite Toeplitz systems

Bibliographic Details
Main Author: Liu, Zhongyun
Publication Date: 2016
Other Authors: Yu, Jing, Zhang, Yan, Zhang, Yulin
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/1822/50409
Summary: It is known that if A is a Toeplitz matrix，then A enjoys a circulant and skew circulant splitting(de— noted by CSCS)，i．e．，A=C+ S with C a circulant matrix and S a skew circulant matrix． Based on the CSCS iteration，we give m-step preconditioners P for certain classes of Toeplitz matrices in this paper．We show that if both C and S are positive definite，then the spectrum of the preconditioned matrix(PA)^* PA are clustered around one for some moderate size ． Experimental results show that the proposed preconditioners perform slightly better than T．Chan’S preconditioners for some moderate size m．
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spelling m-step preconditioners for nonhermitian positive definite Toeplitz systemsCirculantSkew circulant splittingm-step polynomial preconditionersConjugate gradientmethodToeplitz matrixCiências Naturais::MatemáticasIt is known that if A is a Toeplitz matrix，then A enjoys a circulant and skew circulant splitting(de— noted by CSCS)，i．e．，A=C+ S with C a circulant matrix and S a skew circulant matrix． Based on the CSCS iteration，we give m-step preconditioners P for certain classes of Toeplitz matrices in this paper．We show that if both C and S are positive definite，then the spectrum of the preconditioned matrix(PA)^* PA are clustered around one for some moderate size ． Experimental results show that the proposed preconditioners perform slightly better than T．Chan’S preconditioners for some moderate size m．info:eu-repo/semantics/publishedVersionMathematics Society of HunanUniversidade do MinhoLiu, ZhongyunYu, JingZhang, YanZhang, Yulin20162016-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/50409eng1006-8074info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-11T04:52:11Zoai:repositorium.sdum.uminho.pt:1822/50409Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T15:01:04.116318Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv m-step preconditioners for nonhermitian positive definite Toeplitz systems
title m-step preconditioners for nonhermitian positive definite Toeplitz systems
spellingShingle m-step preconditioners for nonhermitian positive definite Toeplitz systems
Liu, Zhongyun
Circulant
Skew circulant splitting
m-step polynomial preconditioners
Conjugate gradientmethod
Toeplitz matrix
Ciências Naturais::Matemáticas
title_short m-step preconditioners for nonhermitian positive definite Toeplitz systems
title_full m-step preconditioners for nonhermitian positive definite Toeplitz systems
title_fullStr m-step preconditioners for nonhermitian positive definite Toeplitz systems
title_full_unstemmed m-step preconditioners for nonhermitian positive definite Toeplitz systems
title_sort m-step preconditioners for nonhermitian positive definite Toeplitz systems
author Liu, Zhongyun
author_facet Liu, Zhongyun
Yu, Jing
Zhang, Yan
Zhang, Yulin
author_role author
author2 Yu, Jing
Zhang, Yan
Zhang, Yulin
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Liu, Zhongyun
Yu, Jing
Zhang, Yan
Zhang, Yulin
dc.subject.por.fl_str_mv Circulant
Skew circulant splitting
m-step polynomial preconditioners
Conjugate gradientmethod
Toeplitz matrix
Ciências Naturais::Matemáticas
topic Circulant
Skew circulant splitting
m-step polynomial preconditioners
Conjugate gradientmethod
Toeplitz matrix
Ciências Naturais::Matemáticas
description It is known that if A is a Toeplitz matrix，then A enjoys a circulant and skew circulant splitting(de— noted by CSCS)，i．e．，A=C+ S with C a circulant matrix and S a skew circulant matrix． Based on the CSCS iteration，we give m-step preconditioners P for certain classes of Toeplitz matrices in this paper．We show that if both C and S are positive definite，then the spectrum of the preconditioned matrix(PA)^* PA are clustered around one for some moderate size ． Experimental results show that the proposed preconditioners perform slightly better than T．Chan’S preconditioners for some moderate size m．
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-01-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1822/50409
url http://hdl.handle.net/1822/50409
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1006-8074
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Mathematics Society of Hunan
publisher.none.fl_str_mv Mathematics Society of Hunan
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
_version_ 1833595043885088768

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