Stationary splitting iterative methods for the matrix equation AX B = C

Detalhes bibliográficos
Autor(a) principal: Liu, Zhongyun
Data de Publicação: 2020
Outros Autores: Li, Zhen, Ferreira, Carla, Zhang, Yulin
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/68183
Resumo: Stationary splitting iterative methods for solving AXB = Care considered in this paper. The main tool to derive our new method is the induced splitting of a given nonsingular matrix A = M −N by a matrix H such that (I −H) invertible. Convergence properties of the proposed method are discussed and numerical experiments are presented to illustrate its computational efficiency and the effectiveness of some preconditioned variants. In particular, for certain surface fitting applications, our method is much more efficient than the progressive iterative approximation (PIA), a conventional iterative method often used in computer-aided geometric design (CAGD).
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spelling Stationary splitting iterative methods for the matrix equation AX B = CHermitian positive definiteH-matricesStationary splitting iterationInduced splittingCurves fittingCiências Naturais::MatemáticasScience & TechnologyStationary splitting iterative methods for solving AXB = Care considered in this paper. The main tool to derive our new method is the induced splitting of a given nonsingular matrix A = M −N by a matrix H such that (I −H) invertible. Convergence properties of the proposed method are discussed and numerical experiments are presented to illustrate its computational efficiency and the effectiveness of some preconditioned variants. In particular, for certain surface fitting applications, our method is much more efficient than the progressive iterative approximation (PIA), a conventional iterative method often used in computer-aided geometric design (CAGD).The authors would like to thank the supports of the National Natural Science Foundation of China under Grant No. 11371075, the Hunan Key Laboratory of mathematical modeling and analysis in engineering, and the Portuguese Funds through FCT–Fundação para a Ciência e a Tecnologia, within the Project UID/MAT/00013/2013.ElsevierUniversidade do MinhoLiu, ZhongyunLi, ZhenFerreira, CarlaZhang, Yulin20202020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/68183eng0096-300310.1016/j.amc.2020.125195https://www.sciencedirect.com/science/article/abs/pii/S0096300320301648info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:15:55Zoai:repositorium.sdum.uminho.pt:1822/68183Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:08:27.511163Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Stationary splitting iterative methods for the matrix equation AX B = C
title Stationary splitting iterative methods for the matrix equation AX B = C
spellingShingle Stationary splitting iterative methods for the matrix equation AX B = C
Liu, Zhongyun
Hermitian positive definite
H-matrices
Stationary splitting iteration
Induced splitting
Curves fitting
Ciências Naturais::Matemáticas
Science & Technology
title_short Stationary splitting iterative methods for the matrix equation AX B = C
title_full Stationary splitting iterative methods for the matrix equation AX B = C
title_fullStr Stationary splitting iterative methods for the matrix equation AX B = C
title_full_unstemmed Stationary splitting iterative methods for the matrix equation AX B = C
title_sort Stationary splitting iterative methods for the matrix equation AX B = C
author Liu, Zhongyun
author_facet Liu, Zhongyun
Li, Zhen
Ferreira, Carla
Zhang, Yulin
author_role author
author2 Li, Zhen
Ferreira, Carla
Zhang, Yulin
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Liu, Zhongyun
Li, Zhen
Ferreira, Carla
Zhang, Yulin
dc.subject.por.fl_str_mv Hermitian positive definite
H-matrices
Stationary splitting iteration
Induced splitting
Curves fitting
Ciências Naturais::Matemáticas
Science & Technology
topic Hermitian positive definite
H-matrices
Stationary splitting iteration
Induced splitting
Curves fitting
Ciências Naturais::Matemáticas
Science & Technology
description Stationary splitting iterative methods for solving AXB = Care considered in this paper. The main tool to derive our new method is the induced splitting of a given nonsingular matrix A = M −N by a matrix H such that (I −H) invertible. Convergence properties of the proposed method are discussed and numerical experiments are presented to illustrate its computational efficiency and the effectiveness of some preconditioned variants. In particular, for certain surface fitting applications, our method is much more efficient than the progressive iterative approximation (PIA), a conventional iterative method often used in computer-aided geometric design (CAGD).
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01T00:00:00Z
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/1822/68183
url http://hdl.handle.net/1822/68183
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0096-3003
10.1016/j.amc.2020.125195
https://www.sciencedirect.com/science/article/abs/pii/S0096300320301648
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 Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
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