Efficient Scaling and Squaring Method for the Matrix Exponential

[EN] This work presents a new algorithm to compute the matrix exponential within a given tolerance. Combined with the scaling and squaring procedure, the algorithm incorporates Taylor, partitioned, and classical Pade'\ methods shown to be superior in performance to the approximants used in...

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Autores: Blanes Zamora, Sergio|||0000-0001-5819-8898, Kopylov, Nikita|||0000-0002-5557-0858, Seydaoglu, Muaz
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:dnet:riunet______::43fb9793eda7a815e83e5a8279ccdcd8
Acceso en línea:https://riunet.upv.es/handle/10251/234944
Access Level:acceso abierto
Palabra clave:Matrix exponential
Padé approximants
Taylor methods
Scaling and squaring
Fraction decomposition
Lie group
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spelling Efficient Scaling and Squaring Method for the Matrix ExponentialBlanes Zamora, Sergio|||0000-0001-5819-8898Kopylov, Nikita|||0000-0002-5557-0858Seydaoglu, MuazMatrix exponentialPadé approximantsTaylor methodsScaling and squaringFraction decompositionLie group[EN] This work presents a new algorithm to compute the matrix exponential within a given tolerance. Combined with the scaling and squaring procedure, the algorithm incorporates Taylor, partitioned, and classical Pade'\ methods shown to be superior in performance to the approximants used in state-of-the-art software. The algorithm computes matrix--matrix products and also matrix inverses, but it can be implemented to avoid the computation of inverses, making it convenient for some problems. If the matrix A belongs to a Lie algebra, then eA belongs to its associated Lie group, being a property which is preserved by diagonal Pade'\ approximants, and the algorithm has another option to use only these. Numerical experiments show the superior performance with respect to state-of-the-art implementations.This work has been funded by Ministerio de Ciencia e Innovacion (Spain) through project PID2022-136585NB-C21, MCIN/AEI/10.13039/501100011033/FEDER, UE, and also by Generalitat Valenciana (Spain) through project CIAICO/2021/180.Society for Industrial and Applied MathematicsDepartamento de Matemática AplicadaEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño IndustrialInstituto Universitario de Matemática MultidisciplinarGeneralitat ValencianaAgencia Estatal de InvestigaciónEuropean Regional Development FundRepositorio Institucional de la Universitat Politècnica de València Riunet20252025-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/234944reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023 PID2022-136585NB-C21 NUEVAS APLICACIONES DE METODOS DE INTEGRACION NUMERICA GEOMETRICA A PROBLEMAS EVOLUTIVOS, ECUACIONES DIFERENCIALES ESTOCASTICAS Y SIMULACIONES MONTECARLOGeneralitat Valenciana https://doi.org/10.13039/501100003359 CIAICO%2F2021%2F180open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:dnet:riunet______::43fb9793eda7a815e83e5a8279ccdcd82026-06-13T07:49:27Z
dc.title.none.fl_str_mv Efficient Scaling and Squaring Method for the Matrix Exponential
title Efficient Scaling and Squaring Method for the Matrix Exponential
spellingShingle Efficient Scaling and Squaring Method for the Matrix Exponential
Blanes Zamora, Sergio|||0000-0001-5819-8898
Matrix exponential
Padé approximants
Taylor methods
Scaling and squaring
Fraction decomposition
Lie group
title_short Efficient Scaling and Squaring Method for the Matrix Exponential
title_full Efficient Scaling and Squaring Method for the Matrix Exponential
title_fullStr Efficient Scaling and Squaring Method for the Matrix Exponential
title_full_unstemmed Efficient Scaling and Squaring Method for the Matrix Exponential
title_sort Efficient Scaling and Squaring Method for the Matrix Exponential
dc.creator.none.fl_str_mv Blanes Zamora, Sergio|||0000-0001-5819-8898
Kopylov, Nikita|||0000-0002-5557-0858
Seydaoglu, Muaz
author Blanes Zamora, Sergio|||0000-0001-5819-8898
author_facet Blanes Zamora, Sergio|||0000-0001-5819-8898
Kopylov, Nikita|||0000-0002-5557-0858
Seydaoglu, Muaz
author_role author
author2 Kopylov, Nikita|||0000-0002-5557-0858
Seydaoglu, Muaz
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
Instituto Universitario de Matemática Multidisciplinar
Generalitat Valenciana
Agencia Estatal de Investigación
European Regional Development Fund
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Matrix exponential
Padé approximants
Taylor methods
Scaling and squaring
Fraction decomposition
Lie group
topic Matrix exponential
Padé approximants
Taylor methods
Scaling and squaring
Fraction decomposition
Lie group
description [EN] This work presents a new algorithm to compute the matrix exponential within a given tolerance. Combined with the scaling and squaring procedure, the algorithm incorporates Taylor, partitioned, and classical Pade'\ methods shown to be superior in performance to the approximants used in state-of-the-art software. The algorithm computes matrix--matrix products and also matrix inverses, but it can be implemented to avoid the computation of inverses, making it convenient for some problems. If the matrix A belongs to a Lie algebra, then eA belongs to its associated Lie group, being a property which is preserved by diagonal Pade'\ approximants, and the algorithm has another option to use only these. Numerical experiments show the superior performance with respect to state-of-the-art implementations.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/234944
url https://riunet.upv.es/handle/10251/234944
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023 PID2022-136585NB-C21 NUEVAS APLICACIONES DE METODOS DE INTEGRACION NUMERICA GEOMETRICA A PROBLEMAS EVOLUTIVOS, ECUACIONES DIFERENCIALES ESTOCASTICAS Y SIMULACIONES MONTECARLO
Generalitat Valenciana https://doi.org/10.13039/501100003359 CIAICO%2F2021%2F180
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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