Efficient and accurate algorithms for computing matrix trigonometric functions

[EN] Trigonometric matrix functions play a fundamental role in second order differential equations. This work presents an algorithm based on Taylor series for computing the matrix cosine. It uses a backward error analysis with improved bounds. Numerical experiments show that MATLAB implementations o...

ver descrição completa

Detalhes bibliográficos
Autores: Alonso-Jordá, Pedro|||0000-0002-6882-6592, Ibáñez González, Jacinto Javier|||0000-0002-6912-4453, Sastre, Jorge|||0000-0002-8612-6717, Peinado Pinilla, Jesús|||0000-0002-9048-5106, Defez Candel, Emilio|||0000-0002-3303-6371
Tipo de documento: artigo
Data de publicação:2017
País:España
Recursos:Universitat Politècnica de València (UPV)
Repositório:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglês
OAI Identifier:oai:riunet.upv.es:10251/82821
Acesso em linha:https://riunet.upv.es/handle/10251/82821
Access Level:Acceso aberto
Palavra-chave:Matrix cosine
Matrix sine
Scaling and squaring method
Taylor series
Backward error
Parallel implementation
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
MATEMATICA APLICADA
LENGUAJES Y SISTEMAS INFORMATICOS
TEORIA DE LA SEÑAL Y COMUNICACIONES
id ES_9ba7e08eb04689aae8e782d3fb97e58f
oai_identifier_str oai:riunet.upv.es:10251/82821
network_acronym_str ES
network_name_str España
repository_id_str
spelling Efficient and accurate algorithms for computing matrix trigonometric functionsAlonso-Jordá, Pedro|||0000-0002-6882-6592Ibáñez González, Jacinto Javier|||0000-0002-6912-4453Sastre, Jorge|||0000-0002-8612-6717Peinado Pinilla, Jesús|||0000-0002-9048-5106Defez Candel, Emilio|||0000-0002-3303-6371Matrix cosineMatrix sineScaling and squaring methodTaylor seriesBackward errorParallel implementationCIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIALMATEMATICA APLICADALENGUAJES Y SISTEMAS INFORMATICOSTEORIA DE LA SEÑAL Y COMUNICACIONES[EN] Trigonometric matrix functions play a fundamental role in second order differential equations. This work presents an algorithm based on Taylor series for computing the matrix cosine. It uses a backward error analysis with improved bounds. Numerical experiments show that MATLAB implementations of this algorithm has higher accuracy than other MATLAB implementations of the state of the art in the majority of tests. Furthermore, we have implemented the designed algorithm in language C for general purpose processors, and in CUDA for one and two NVIDIA GPUs. We obtained a very good performance from these implementations thanks to the high computational power of these hardware accelerators and our effort driven to avoid as much communications as possible. All the implemented programs are accessible through the MATLAB environment. (C) 2016 Elsevier B.V. All rights reserved.This work has been supported by Spanish Ministerio de Economía y Competitividad and European Regional Development Fund (ERDF) grant TIN2014-59294-PElsevierEscuela 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 MolecularMinisterio de Economía y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20172017-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/82821reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 TIN2014-59294-P FUNCIONES DE MATRICES: CALCULO Y APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/828212026-06-13T07:49:27Z
dc.title.none.fl_str_mv Efficient and accurate algorithms for computing matrix trigonometric functions
title Efficient and accurate algorithms for computing matrix trigonometric functions
spellingShingle Efficient and accurate algorithms for computing matrix trigonometric functions
Alonso-Jordá, Pedro|||0000-0002-6882-6592
Matrix cosine
Matrix sine
Scaling and squaring method
Taylor series
Backward error
Parallel implementation
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
MATEMATICA APLICADA
LENGUAJES Y SISTEMAS INFORMATICOS
TEORIA DE LA SEÑAL Y COMUNICACIONES
title_short Efficient and accurate algorithms for computing matrix trigonometric functions
title_full Efficient and accurate algorithms for computing matrix trigonometric functions
title_fullStr Efficient and accurate algorithms for computing matrix trigonometric functions
title_full_unstemmed Efficient and accurate algorithms for computing matrix trigonometric functions
title_sort Efficient and accurate algorithms for computing matrix trigonometric functions
dc.creator.none.fl_str_mv Alonso-Jordá, Pedro|||0000-0002-6882-6592
Ibáñez González, Jacinto Javier|||0000-0002-6912-4453
Sastre, Jorge|||0000-0002-8612-6717
Peinado Pinilla, Jesús|||0000-0002-9048-5106
Defez Candel, Emilio|||0000-0002-3303-6371
author Alonso-Jordá, Pedro|||0000-0002-6882-6592
author_facet Alonso-Jordá, Pedro|||0000-0002-6882-6592
Ibáñez González, Jacinto Javier|||0000-0002-6912-4453
Sastre, Jorge|||0000-0002-8612-6717
Peinado Pinilla, Jesús|||0000-0002-9048-5106
Defez Candel, Emilio|||0000-0002-3303-6371
author_role author
author2 Ibáñez González, Jacinto Javier|||0000-0002-6912-4453
Sastre, Jorge|||0000-0002-8612-6717
Peinado Pinilla, Jesús|||0000-0002-9048-5106
Defez Candel, Emilio|||0000-0002-3303-6371
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
Ministerio de Economía y Competitividad
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Matrix cosine
Matrix sine
Scaling and squaring method
Taylor series
Backward error
Parallel implementation
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
MATEMATICA APLICADA
LENGUAJES Y SISTEMAS INFORMATICOS
TEORIA DE LA SEÑAL Y COMUNICACIONES
topic Matrix cosine
Matrix sine
Scaling and squaring method
Taylor series
Backward error
Parallel implementation
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
MATEMATICA APLICADA
LENGUAJES Y SISTEMAS INFORMATICOS
TEORIA DE LA SEÑAL Y COMUNICACIONES
description [EN] Trigonometric matrix functions play a fundamental role in second order differential equations. This work presents an algorithm based on Taylor series for computing the matrix cosine. It uses a backward error analysis with improved bounds. Numerical experiments show that MATLAB implementations of this algorithm has higher accuracy than other MATLAB implementations of the state of the art in the majority of tests. Furthermore, we have implemented the designed algorithm in language C for general purpose processors, and in CUDA for one and two NVIDIA GPUs. We obtained a very good performance from these implementations thanks to the high computational power of these hardware accelerators and our effort driven to avoid as much communications as possible. All the implemented programs are accessible through the MATLAB environment. (C) 2016 Elsevier B.V. All rights reserved.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-01-01
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/10251/82821
url https://riunet.upv.es/handle/10251/82821
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 TIN2014-59294-P FUNCIONES DE MATRICES: CALCULO Y APLICACIONES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
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
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
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_ 1869414572958416896
score 15,300719

Registros relacionados