On circulant and skew-circulant splitting algorithms for (continuous) Sylvester equations

Detalhes bibliográficos
Autor(a) principal: Liu, Zhongyun
Data de Publicação: 2022
Outros Autores: Zhang, Fang, Ferreira, Carla, Zhang, Yulin
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/1822/76429
Resumo: We present a circulant and skew-circulant splitting (CSCS) iterative method for solving large sparse continuous Sylvester equations AX+XB=C, where the coefficient matrices A and B are Toeplitz matrices. A theoretical study shows that if the circulant and skew-circulant splitting factors of A and B are positive semi-definite (not necessarily Hermitian), and at least one factor is positive definite, then the CSCS method converges to the unique solution of the Sylvester equation. In addition, our analysis gives an upper bound for the convergence factor of the CSCS iteration which depends only on the eigenvalues of the circulant and skew-circulant splitting matrices. A computational comparison with alternative methods reveals the efficiency and reliability of the proposed method.
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spelling On circulant and skew-circulant splitting algorithms for (continuous) Sylvester equationsContinuous Sylvester equationsCSCS iterationToeplitz matricesConvergenceCiências Naturais::MatemáticasScience & TechnologyWe present a circulant and skew-circulant splitting (CSCS) iterative method for solving large sparse continuous Sylvester equations AX+XB=C, where the coefficient matrices A and B are Toeplitz matrices. A theoretical study shows that if the circulant and skew-circulant splitting factors of A and B are positive semi-definite (not necessarily Hermitian), and at least one factor is positive definite, then the CSCS method converges to the unique solution of the Sylvester equation. In addition, our analysis gives an upper bound for the convergence factor of the CSCS iteration which depends only on the eigenvalues of the circulant and skew-circulant splitting matrices. A computational comparison with alternative methods reveals the efficiency and reliability of the proposed method.NSFC -National Natural Science Foundation of China(11371075)ElsevierUniversidade do MinhoLiu, ZhongyunZhang, FangFerreira, CarlaZhang, Yulin20222025-01-01T00:00:00Z2022-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/76429eng0898-122110.1016/j.camwa.2022.01.027https://www.sciencedirect.com/science/article/pii/S0898122122000347info:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:13:17ZPortal AgregadorONG
dc.title.none.fl_str_mv On circulant and skew-circulant splitting algorithms for (continuous) Sylvester equations
title On circulant and skew-circulant splitting algorithms for (continuous) Sylvester equations
spellingShingle On circulant and skew-circulant splitting algorithms for (continuous) Sylvester equations
Liu, Zhongyun
Continuous Sylvester equations
CSCS iteration
Toeplitz matrices
Convergence
Ciências Naturais::Matemáticas
Science & Technology
title_short On circulant and skew-circulant splitting algorithms for (continuous) Sylvester equations
title_full On circulant and skew-circulant splitting algorithms for (continuous) Sylvester equations
title_fullStr On circulant and skew-circulant splitting algorithms for (continuous) Sylvester equations
title_full_unstemmed On circulant and skew-circulant splitting algorithms for (continuous) Sylvester equations
title_sort On circulant and skew-circulant splitting algorithms for (continuous) Sylvester equations
author Liu, Zhongyun
author_facet Liu, Zhongyun
Zhang, Fang
Ferreira, Carla
Zhang, Yulin
author_role author
author2 Zhang, Fang
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
Zhang, Fang
Ferreira, Carla
Zhang, Yulin
dc.subject.por.fl_str_mv Continuous Sylvester equations
CSCS iteration
Toeplitz matrices
Convergence
Ciências Naturais::Matemáticas
Science & Technology
topic Continuous Sylvester equations
CSCS iteration
Toeplitz matrices
Convergence
Ciências Naturais::Matemáticas
Science & Technology
description We present a circulant and skew-circulant splitting (CSCS) iterative method for solving large sparse continuous Sylvester equations AX+XB=C, where the coefficient matrices A and B are Toeplitz matrices. A theoretical study shows that if the circulant and skew-circulant splitting factors of A and B are positive semi-definite (not necessarily Hermitian), and at least one factor is positive definite, then the CSCS method converges to the unique solution of the Sylvester equation. In addition, our analysis gives an upper bound for the convergence factor of the CSCS iteration which depends only on the eigenvalues of the circulant and skew-circulant splitting matrices. A computational comparison with alternative methods reveals the efficiency and reliability of the proposed method.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-01-01T00:00:00Z
2025-01-01T00:00:00Z
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 https://hdl.handle.net/1822/76429
url https://hdl.handle.net/1822/76429
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0898-1221
10.1016/j.camwa.2022.01.027
https://www.sciencedirect.com/science/article/pii/S0898122122000347
dc.rights.driver.fl_str_mv info:eu-repo/semantics/embargoedAccess
eu_rights_str_mv embargoedAccess
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)
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