A Monte Carlo method for computing the action of a matrix exponential on a vector

Detalhes bibliográficos
Autor(a) principal: Acebron, J. A.
Data de Publicação: 2019
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10071/19104
Resumo: A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a given continuous-time Markov chain. The vector solution is computed probabilistically by averaging over a suitable multiplicative functional. This representation extends the existing linear algebra Monte Carlo-based methods, and was used in practice to develop an efficient algorithm capable of computing both, a single entry or the full vector solution. Finally, several relevant benchmarks were executed to assess the performance of the algorithm. A comparison with the results obtained with a Krylov-based method shows the remarkable performance of the algorithm for solving large-scale problems.
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spelling A Monte Carlo method for computing the action of a matrix exponential on a vectorMonte Carlo methodsCommunicabilityMatrix functionsNetwork analysisA Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a given continuous-time Markov chain. The vector solution is computed probabilistically by averaging over a suitable multiplicative functional. This representation extends the existing linear algebra Monte Carlo-based methods, and was used in practice to develop an efficient algorithm capable of computing both, a single entry or the full vector solution. Finally, several relevant benchmarks were executed to assess the performance of the algorithm. A comparison with the results obtained with a Krylov-based method shows the remarkable performance of the algorithm for solving large-scale problems.Elsevier2020-07-04T00:00:00Z2019-01-01T00:00:00Z20192019-12-11T16:44:07Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10071/19104eng0096-300310.1016/j.amc.2019.06.059Acebron, J. A.info: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:RCAAP2023-11-09T17:48:53Zoai:repositorio.iscte-iul.pt:10071/19104Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:23:55.019955Repositório 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 A Monte Carlo method for computing the action of a matrix exponential on a vector
title A Monte Carlo method for computing the action of a matrix exponential on a vector
spellingShingle A Monte Carlo method for computing the action of a matrix exponential on a vector
Acebron, J. A.
Monte Carlo methods
Communicability
Matrix functions
Network analysis
title_short A Monte Carlo method for computing the action of a matrix exponential on a vector
title_full A Monte Carlo method for computing the action of a matrix exponential on a vector
title_fullStr A Monte Carlo method for computing the action of a matrix exponential on a vector
title_full_unstemmed A Monte Carlo method for computing the action of a matrix exponential on a vector
title_sort A Monte Carlo method for computing the action of a matrix exponential on a vector
author Acebron, J. A.
author_facet Acebron, J. A.
author_role author
dc.contributor.author.fl_str_mv Acebron, J. A.
dc.subject.por.fl_str_mv Monte Carlo methods
Communicability
Matrix functions
Network analysis
topic Monte Carlo methods
Communicability
Matrix functions
Network analysis
description A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a given continuous-time Markov chain. The vector solution is computed probabilistically by averaging over a suitable multiplicative functional. This representation extends the existing linear algebra Monte Carlo-based methods, and was used in practice to develop an efficient algorithm capable of computing both, a single entry or the full vector solution. Finally, several relevant benchmarks were executed to assess the performance of the algorithm. A comparison with the results obtained with a Krylov-based method shows the remarkable performance of the algorithm for solving large-scale problems.
publishDate 2019
dc.date.none.fl_str_mv 2019-01-01T00:00:00Z
2019
2019-12-11T16:44:07Z
2020-07-04T00:00:00Z
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/10071/19104
url http://hdl.handle.net/10071/19104
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0096-3003
10.1016/j.amc.2019.06.059
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
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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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