Euler Polynomials for the Matrix Exponential Approximation

[EN] In this work, a new method to compute the matrix exponential function by using an approximation based on Euler polynomials is proposed. These polynomials are used in combination with the scaling and squaring technique, considering an absolute forward-type theoretical error. Its numerical and co...

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Detalles Bibliográficos
Autores: Alonso Abalos, José Miguel|||0000-0001-6812-7364, Ibáñez González, Jacinto Javier|||0000-0002-6912-4453, Defez Candel, Emilio|||0000-0002-3303-6371, Alonso-Jordá, Pedro|||0000-0002-6882-6592
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/204238
Acceso en línea:https://riunet.upv.es/handle/10251/204238
Access Level:acceso abierto
Palabra clave:Matrix functions
Matrix exponential
Euler polynomials
MATEMATICA APLICADA
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
12.- Garantizar las pautas de consumo y de producción sostenibles
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repository_id_str
spelling Euler Polynomials for the Matrix Exponential ApproximationAlonso Abalos, José Miguel|||0000-0001-6812-7364Ibáñez González, Jacinto Javier|||0000-0002-6912-4453Defez Candel, Emilio|||0000-0002-3303-6371Alonso-Jordá, Pedro|||0000-0002-6882-6592Matrix functionsMatrix exponentialEuler polynomialsMATEMATICA APLICADACIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL12.- Garantizar las pautas de consumo y de producción sostenibles[EN] In this work, a new method to compute the matrix exponential function by using an approximation based on Euler polynomials is proposed. These polynomials are used in combination with the scaling and squaring technique, considering an absolute forward-type theoretical error. Its numerical and computational properties have been evaluated and compared with the most current and competitive codes dedicated to the computation of the matrix exponential. Under a heterogeneous test battery and a set of exhaustive experiments, it has been demonstrated that the new method offers performance in terms of accuracy and stability which is as good as or even better than those of the considered methods, with an intermediate computational cost among all of them. All of the above makes this a very competitive alternative that should be considered in the growing list of available numerical methods and implementations dedicated to the approximation of the matrix exponential.Acknowledgements This work has been partially supported by Spanish Ministerio de Ciencia e Innovaci?n (Project PID2020-113656RB-C22) supported by MCIN/AEI/10.13039/501100011033 and by the Vicerrectorado de Investigaci?n de la Universitat Polit?cnica de Val?ncia (PAID-11-21).ElsevierDepartamento de Sistemas Informáticos y ComputaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarEscuela Técnica Superior de Ingeniería de Caminos, Canales y PuertosEscuela Técnica Superior de Ingeniería InformáticaInstituto de Instrumentación para Imagen MolecularAGENCIA ESTATAL DE INVESTIGACIONUNIVERSIDAD POLITECNICA DE VALENCIAUniversitat Politècnica de ValènciaRepositorio Institucional de la Universitat Politècnica de València Riunet20232023-06-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/204238reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengUniversitat Politècnica de València https://doi.org/10.13039/501100004233 Programa PAID de Apoyo a la I+D+i PAID-11-21 Novel High-Performance Methods for the Computation of Matrix Functions and Their Applications in EngineeringAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113656RB-C22 COMPUTACION Y COMUNICACIONES DE ALTAS PRESTACIONES CONSCIENTES DEL CONSUMO ENERGÉTICO. APLICACIONES AL APRENDIZAJE PROFUNDO COMPUTACIONAL - UPVopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2042382026-06-13T07:49:27Z
dc.title.none.fl_str_mv Euler Polynomials for the Matrix Exponential Approximation
title Euler Polynomials for the Matrix Exponential Approximation
spellingShingle Euler Polynomials for the Matrix Exponential Approximation
Alonso Abalos, José Miguel|||0000-0001-6812-7364
Matrix functions
Matrix exponential
Euler polynomials
MATEMATICA APLICADA
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
12.- Garantizar las pautas de consumo y de producción sostenibles
title_short Euler Polynomials for the Matrix Exponential Approximation
title_full Euler Polynomials for the Matrix Exponential Approximation
title_fullStr Euler Polynomials for the Matrix Exponential Approximation
title_full_unstemmed Euler Polynomials for the Matrix Exponential Approximation
title_sort Euler Polynomials for the Matrix Exponential Approximation
dc.creator.none.fl_str_mv Alonso Abalos, José Miguel|||0000-0001-6812-7364
Ibáñez González, Jacinto Javier|||0000-0002-6912-4453
Defez Candel, Emilio|||0000-0002-3303-6371
Alonso-Jordá, Pedro|||0000-0002-6882-6592
author Alonso Abalos, José Miguel|||0000-0001-6812-7364
author_facet Alonso Abalos, José Miguel|||0000-0001-6812-7364
Ibáñez González, Jacinto Javier|||0000-0002-6912-4453
Defez Candel, Emilio|||0000-0002-3303-6371
Alonso-Jordá, Pedro|||0000-0002-6882-6592
author_role author
author2 Ibáñez González, Jacinto Javier|||0000-0002-6912-4453
Defez Candel, Emilio|||0000-0002-3303-6371
Alonso-Jordá, Pedro|||0000-0002-6882-6592
author2_role author
author
author
dc.contributor.none.fl_str_mv Departamento de Sistemas Informáticos y Computación
Departamento de Matemática Aplicada
Instituto Universitario de Matemática Multidisciplinar
Escuela Técnica Superior de Ingeniería de Caminos, Canales y Puertos
Escuela Técnica Superior de Ingeniería Informática
Instituto de Instrumentación para Imagen Molecular
AGENCIA ESTATAL DE INVESTIGACION
UNIVERSIDAD POLITECNICA DE VALENCIA
Universitat Politècnica de València
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Matrix functions
Matrix exponential
Euler polynomials
MATEMATICA APLICADA
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
12.- Garantizar las pautas de consumo y de producción sostenibles
topic Matrix functions
Matrix exponential
Euler polynomials
MATEMATICA APLICADA
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
12.- Garantizar las pautas de consumo y de producción sostenibles
description [EN] In this work, a new method to compute the matrix exponential function by using an approximation based on Euler polynomials is proposed. These polynomials are used in combination with the scaling and squaring technique, considering an absolute forward-type theoretical error. Its numerical and computational properties have been evaluated and compared with the most current and competitive codes dedicated to the computation of the matrix exponential. Under a heterogeneous test battery and a set of exhaustive experiments, it has been demonstrated that the new method offers performance in terms of accuracy and stability which is as good as or even better than those of the considered methods, with an intermediate computational cost among all of them. All of the above makes this a very competitive alternative that should be considered in the growing list of available numerical methods and implementations dedicated to the approximation of the matrix exponential.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-06-01
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/10251/204238
url https://riunet.upv.es/handle/10251/204238
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Universitat Politècnica de València https://doi.org/10.13039/501100004233 Programa PAID de Apoyo a la I+D+i PAID-11-21 Novel High-Performance Methods for the Computation of Matrix Functions and Their Applications in Engineering
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113656RB-C22 COMPUTACION Y COMUNICACIONES DE ALTAS PRESTACIONES CONSCIENTES DEL CONSUMO ENERGÉTICO. APLICACIONES AL APRENDIZAJE PROFUNDO COMPUTACIONAL - UPV
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/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 - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
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: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
_version_ 1869403653805178880
score 15.300719

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