A general class of arbitrary order iterative methods for computing generalized inverses

[EN] A family of iterative schemes for approximating the inverse and generalized inverse of a complex matrix is designed, having arbitrary order of convergence p. For each p, a class of iterative schemes appears, for which we analyze those elements able to converge with very far initial estimations....

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Autores: Cordero Barbero, Alicia|||0000-0002-7462-9173, Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761, Soto-Quiros, Pablo
Tipo de recurso: artículo
Fecha de publicación:2021
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:10251/181026
Acceso en línea:https://riunet.upv.es/handle/10251/181026
Access Level:acceso abierto
Palabra clave:Matrix equations
Inverse matrix
Iterative method
Order of convergence
Dependence on initial estimations
MATEMATICA APLICADA
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spelling A general class of arbitrary order iterative methods for computing generalized inversesCordero Barbero, Alicia|||0000-0002-7462-9173Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761Soto-Quiros, PabloMatrix equationsInverse matrixIterative methodOrder of convergenceDependence on initial estimationsMATEMATICA APLICADA[EN] A family of iterative schemes for approximating the inverse and generalized inverse of a complex matrix is designed, having arbitrary order of convergence p. For each p, a class of iterative schemes appears, for which we analyze those elements able to converge with very far initial estimations. This class generalizes many known iterative methods which are obtained for particular values of the parameters. The order of convergence is stated in each case, depending on the first non-zero parameter. For different examples, the accessibility of some schemes, that is, the set of initial estimations leading to convergence, is analyzed in order to select those with wider sets. This wideness is related with the value of the first non-zero value of the parameters defining the method. Later on, some numerical examples (academic and also from signal processing) are provided to confirm the theoretical results and to show the feasibility and effectiveness of the new methods. (C) 2021 The Authors. Published by Elsevier Inc.This research was supported in part by PGC2018-095896-B-C22 (MCIU/AEI/FEDER, UE) and in part by VIE from Instituto Tecnologico de Costa Rica (Research #1440037)ElsevierEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarAGENCIA ESTATAL DE INVESTIGACIONInstituto Tecnológico de Costa RicaRepositorio Institucional de la Universitat Politècnica de València Riunet20212021-11-15journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/181026reponame: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 2017-2020 PGC2018-095896-B-C22 DISEÑO, ANALISIS Y ESTABILIDAD DE PROCESOS ITERATIVOS APLICADOS A LAS ECUACIONES INTEGRALES Y MATRICIALES Y A LA COMUNICACION AEROESPACIALITCR ITCR 1440037open 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:10251/1810262026-06-13T07:49:27Z
dc.title.none.fl_str_mv A general class of arbitrary order iterative methods for computing generalized inverses
title A general class of arbitrary order iterative methods for computing generalized inverses
spellingShingle A general class of arbitrary order iterative methods for computing generalized inverses
Cordero Barbero, Alicia|||0000-0002-7462-9173
Matrix equations
Inverse matrix
Iterative method
Order of convergence
Dependence on initial estimations
MATEMATICA APLICADA
title_short A general class of arbitrary order iterative methods for computing generalized inverses
title_full A general class of arbitrary order iterative methods for computing generalized inverses
title_fullStr A general class of arbitrary order iterative methods for computing generalized inverses
title_full_unstemmed A general class of arbitrary order iterative methods for computing generalized inverses
title_sort A general class of arbitrary order iterative methods for computing generalized inverses
dc.creator.none.fl_str_mv Cordero Barbero, Alicia|||0000-0002-7462-9173
Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
Soto-Quiros, Pablo
author Cordero Barbero, Alicia|||0000-0002-7462-9173
author_facet Cordero Barbero, Alicia|||0000-0002-7462-9173
Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
Soto-Quiros, Pablo
author_role author
author2 Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
Soto-Quiros, Pablo
author2_role author
author
dc.contributor.none.fl_str_mv Escuela Técnica Superior de Ingeniería de Telecomunicación
Departamento de Matemática Aplicada
Instituto Universitario de Matemática Multidisciplinar
AGENCIA ESTATAL DE INVESTIGACION
Instituto Tecnológico de Costa Rica
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Matrix equations
Inverse matrix
Iterative method
Order of convergence
Dependence on initial estimations
MATEMATICA APLICADA
topic Matrix equations
Inverse matrix
Iterative method
Order of convergence
Dependence on initial estimations
MATEMATICA APLICADA
description [EN] A family of iterative schemes for approximating the inverse and generalized inverse of a complex matrix is designed, having arbitrary order of convergence p. For each p, a class of iterative schemes appears, for which we analyze those elements able to converge with very far initial estimations. This class generalizes many known iterative methods which are obtained for particular values of the parameters. The order of convergence is stated in each case, depending on the first non-zero parameter. For different examples, the accessibility of some schemes, that is, the set of initial estimations leading to convergence, is analyzed in order to select those with wider sets. This wideness is related with the value of the first non-zero value of the parameters defining the method. Later on, some numerical examples (academic and also from signal processing) are provided to confirm the theoretical results and to show the feasibility and effectiveness of the new methods. (C) 2021 The Authors. Published by Elsevier Inc.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-11-15
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/10251/181026
url https://riunet.upv.es/handle/10251/181026
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 2017-2020 PGC2018-095896-B-C22 DISEÑO, ANALISIS Y ESTABILIDAD DE PROCESOS ITERATIVOS APLICADOS A LAS ECUACIONES INTEGRALES Y MATRICIALES Y A LA COMUNICACION AEROESPACIAL
ITCR ITCR 1440037
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
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score 15.300719

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