Advances in the Approximation of the Matrix Hyperbolic Tangent

[EN] In this paper, we introduce two approaches to compute the matrix hyperbolic tangent. While one of them is based on its own definition and uses the matrix exponential, the other one is focused on the expansion of its Taylor series. For this second approximation, we analyse two different alternat...

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Authors: Ibáñez González, Jacinto Javier|||0000-0002-6912-4453, Alonso Abalos, José Miguel|||0000-0001-6812-7364, Sastre, Jorge|||0000-0002-8612-6717, Defez Candel, Emilio|||0000-0002-3303-6371, Alonso-Jordá, Pedro|||0000-0002-6882-6592
Format: article
Publication Date:2021
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/186472
Online Access:https://riunet.upv.es/handle/10251/186472
Access Level:Open access
Keyword:Matrix functions
Matrix hyperbolic tangent
Matrix exponential
Taylor series
Matrix polynomial evaluation
MATEMATICA APLICADA
TEORIA DE LA SEÑAL Y COMUNICACIONES
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
id ES_cf8a08fd19dc84cb8625d93f2b3e45a8
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network_acronym_str ES
network_name_str España
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spelling Advances in the Approximation of the Matrix Hyperbolic TangentIbáñez González, Jacinto Javier|||0000-0002-6912-4453Alonso Abalos, José Miguel|||0000-0001-6812-7364Sastre, Jorge|||0000-0002-8612-6717Defez Candel, Emilio|||0000-0002-3303-6371Alonso-Jordá, Pedro|||0000-0002-6882-6592Matrix functionsMatrix hyperbolic tangentMatrix exponentialTaylor seriesMatrix polynomial evaluationMATEMATICA APLICADATEORIA DE LA SEÑAL Y COMUNICACIONESCIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL[EN] In this paper, we introduce two approaches to compute the matrix hyperbolic tangent. While one of them is based on its own definition and uses the matrix exponential, the other one is focused on the expansion of its Taylor series. For this second approximation, we analyse two different alternatives to evaluate the corresponding matrix polynomials. This resulted in three stable and accurate codes, which we implemented in MATLAB and numerically and computationally compared by means of a battery of tests composed of distinct state-of-the-art matrices. Our results show that the Taylor series-based methods were more accurate, although somewhat more computationally expensive, compared with the approach based on the exponential matrix. To avoid this drawback, we propose the use of a set of formulas that allows us to evaluate polynomials in a more efficient way compared with that of the traditional Paterson¿Stockmeyer method, thus, substantially reducing the number of matrix products (practically equal in number to the approach based on the matrix exponential), without penalising the accuracy of the resultThis research was funded by the Spanish Ministerio de Ciencia e Innovacion under grant number TIN2017-89314-P.MDPI AGEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Sistemas Informáticos y ComputaciónDepartamento de Matemática AplicadaDepartamento de ComunicacionesInstituto Universitario de Telecomunicación y Aplicaciones MultimediaInstituto 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 INVESTIGACIONRepositorio Institucional de la Universitat Politècnica de València Riunet20212021-06-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/186472reponame: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 2013-2016 TIN2017-89314-P LIBRERIAS DE ALTAS PRESTACIONES PARA EL CALCULO DE FUNCIONES DE MATRICES Y APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1864722026-06-13T07:49:27Z
dc.title.none.fl_str_mv Advances in the Approximation of the Matrix Hyperbolic Tangent
title Advances in the Approximation of the Matrix Hyperbolic Tangent
spellingShingle Advances in the Approximation of the Matrix Hyperbolic Tangent
Ibáñez González, Jacinto Javier|||0000-0002-6912-4453
Matrix functions
Matrix hyperbolic tangent
Matrix exponential
Taylor series
Matrix polynomial evaluation
MATEMATICA APLICADA
TEORIA DE LA SEÑAL Y COMUNICACIONES
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
title_short Advances in the Approximation of the Matrix Hyperbolic Tangent
title_full Advances in the Approximation of the Matrix Hyperbolic Tangent
title_fullStr Advances in the Approximation of the Matrix Hyperbolic Tangent
title_full_unstemmed Advances in the Approximation of the Matrix Hyperbolic Tangent
title_sort Advances in the Approximation of the Matrix Hyperbolic Tangent
dc.creator.none.fl_str_mv Ibáñez González, Jacinto Javier|||0000-0002-6912-4453
Alonso Abalos, José Miguel|||0000-0001-6812-7364
Sastre, Jorge|||0000-0002-8612-6717
Defez Candel, Emilio|||0000-0002-3303-6371
Alonso-Jordá, Pedro|||0000-0002-6882-6592
author Ibáñez González, Jacinto Javier|||0000-0002-6912-4453
author_facet Ibáñez González, Jacinto Javier|||0000-0002-6912-4453
Alonso Abalos, José Miguel|||0000-0001-6812-7364
Sastre, Jorge|||0000-0002-8612-6717
Defez Candel, Emilio|||0000-0002-3303-6371
Alonso-Jordá, Pedro|||0000-0002-6882-6592
author_role author
author2 Alonso Abalos, José Miguel|||0000-0001-6812-7364
Sastre, Jorge|||0000-0002-8612-6717
Defez Candel, Emilio|||0000-0002-3303-6371
Alonso-Jordá, Pedro|||0000-0002-6882-6592
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Escuela Técnica Superior de Ingeniería de Telecomunicación
Departamento de Sistemas Informáticos y Computación
Departamento de Matemática Aplicada
Departamento de Comunicaciones
Instituto Universitario de Telecomunicación y Aplicaciones Multimedia
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
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Matrix functions
Matrix hyperbolic tangent
Matrix exponential
Taylor series
Matrix polynomial evaluation
MATEMATICA APLICADA
TEORIA DE LA SEÑAL Y COMUNICACIONES
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
topic Matrix functions
Matrix hyperbolic tangent
Matrix exponential
Taylor series
Matrix polynomial evaluation
MATEMATICA APLICADA
TEORIA DE LA SEÑAL Y COMUNICACIONES
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
description [EN] In this paper, we introduce two approaches to compute the matrix hyperbolic tangent. While one of them is based on its own definition and uses the matrix exponential, the other one is focused on the expansion of its Taylor series. For this second approximation, we analyse two different alternatives to evaluate the corresponding matrix polynomials. This resulted in three stable and accurate codes, which we implemented in MATLAB and numerically and computationally compared by means of a battery of tests composed of distinct state-of-the-art matrices. Our results show that the Taylor series-based methods were more accurate, although somewhat more computationally expensive, compared with the approach based on the exponential matrix. To avoid this drawback, we propose the use of a set of formulas that allows us to evaluate polynomials in a more efficient way compared with that of the traditional Paterson¿Stockmeyer method, thus, substantially reducing the number of matrix products (practically equal in number to the approach based on the matrix exponential), without penalising the accuracy of the result
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-06-01
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/10251/186472
url https://riunet.upv.es/handle/10251/186472
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 2013-2016 TIN2017-89314-P LIBRERIAS DE ALTAS PRESTACIONES PARA EL CALCULO DE FUNCIONES DE MATRICES Y APLICACIONES
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
dc.publisher.none.fl_str_mv MDPI AG
publisher.none.fl_str_mv MDPI AG
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 15.301603

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