Jacobian-Free Vectorial Iterative Scheme to Find Simple Several Solutions Simultaneously

[EN] This manuscript is devoted to a derivative-free parametric iterative step to obtain roots simultaneously for both nonlinear systems and equations. We prove that when it is added to an arbitrary scheme, it doubles the convergence order of the original procedure and defines a new algorithm that o...

Descripción completa

Detalles Bibliográficos
Autores: Cordero Barbero, Alicia|||0000-0002-7462-9173, Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761, Triguero-Navarro, Paula|||0000-0002-7319-9992
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:riunet.upv.es:10251/220055
Acceso en línea:https://riunet.upv.es/handle/10251/220055
Access Level:acceso abierto
Palabra clave:Derivative-free
Iterative procedures
Jacobian-free
Nonlinear equations and systems
Simultaneously
id ES_c0aa5a2f25ffbc182aa1a3a840f40e64
oai_identifier_str oai:riunet.upv.es:10251/220055
network_acronym_str ES
network_name_str España
repository_id_str
spelling Jacobian-Free Vectorial Iterative Scheme to Find Simple Several Solutions SimultaneouslyCordero Barbero, Alicia|||0000-0002-7462-9173Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761Triguero-Navarro, Paula|||0000-0002-7319-9992Derivative-freeIterative proceduresJacobian-freeNonlinear equations and systemsSimultaneously[EN] This manuscript is devoted to a derivative-free parametric iterative step to obtain roots simultaneously for both nonlinear systems and equations. We prove that when it is added to an arbitrary scheme, it doubles the convergence order of the original procedure and defines a new algorithm that obtains several solutions simultaneously. Different numerical experiments are carried out to check the behavior of the iterative methods by changing the value of the parameter and the initial guesses. Also, it performs a numerical example where the dynamical planes are carried out to see and compare the basins of attraction.This research was partially supported by Centro Universitario EDEM - Escuela de Empresarios, Valencia, Spain and by Universitat Politécnica de Valéncia Contrato Predoctoral PAID-01-20-17 (UPV).John Wiley & SonsDepartamento de Matemática AplicadaEscuela Técnica Superior de Ingeniería de TelecomunicaciónInstituto Universitario de Matemática MultidisciplinarEscuela Técnica Superior de Ingeniería IndustrialUNIVERSIDAD POLITECNICA DE VALENCIARepositorio 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/pdfhttps://riunet.upv.es/handle/10251/220055reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengUniversitat Politècnica de València https://doi.org/10.13039/501100004233 PAID-01-20-17 Procesos iterativos multidimensionales de altas prestaciones para resolver ecuaciones vectoriales y matriciales no linealesopen 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:10251/2200552026-06-13T07:49:27Z
dc.title.none.fl_str_mv Jacobian-Free Vectorial Iterative Scheme to Find Simple Several Solutions Simultaneously
title Jacobian-Free Vectorial Iterative Scheme to Find Simple Several Solutions Simultaneously
spellingShingle Jacobian-Free Vectorial Iterative Scheme to Find Simple Several Solutions Simultaneously
Cordero Barbero, Alicia|||0000-0002-7462-9173
Derivative-free
Iterative procedures
Jacobian-free
Nonlinear equations and systems
Simultaneously
title_short Jacobian-Free Vectorial Iterative Scheme to Find Simple Several Solutions Simultaneously
title_full Jacobian-Free Vectorial Iterative Scheme to Find Simple Several Solutions Simultaneously
title_fullStr Jacobian-Free Vectorial Iterative Scheme to Find Simple Several Solutions Simultaneously
title_full_unstemmed Jacobian-Free Vectorial Iterative Scheme to Find Simple Several Solutions Simultaneously
title_sort Jacobian-Free Vectorial Iterative Scheme to Find Simple Several Solutions Simultaneously
dc.creator.none.fl_str_mv Cordero Barbero, Alicia|||0000-0002-7462-9173
Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
Triguero-Navarro, Paula|||0000-0002-7319-9992
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
Triguero-Navarro, Paula|||0000-0002-7319-9992
author_role author
author2 Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
Triguero-Navarro, Paula|||0000-0002-7319-9992
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Ingeniería de Telecomunicación
Instituto Universitario de Matemática Multidisciplinar
Escuela Técnica Superior de Ingeniería Industrial
UNIVERSIDAD POLITECNICA DE VALENCIA
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Derivative-free
Iterative procedures
Jacobian-free
Nonlinear equations and systems
Simultaneously
topic Derivative-free
Iterative procedures
Jacobian-free
Nonlinear equations and systems
Simultaneously
description [EN] This manuscript is devoted to a derivative-free parametric iterative step to obtain roots simultaneously for both nonlinear systems and equations. We prove that when it is added to an arbitrary scheme, it doubles the convergence order of the original procedure and defines a new algorithm that obtains several solutions simultaneously. Different numerical experiments are carried out to check the behavior of the iterative methods by changing the value of the parameter and the initial guesses. Also, it performs a numerical example where the dynamical planes are carried out to see and compare the basins of attraction.
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/10251/220055
url https://riunet.upv.es/handle/10251/220055
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 PAID-01-20-17 Procesos iterativos multidimensionales de altas prestaciones para resolver ecuaciones vectoriales y matriciales no lineales
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 John Wiley & Sons
publisher.none.fl_str_mv John Wiley & Sons
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_ 1869418496627048448
score 15,811543

Similares en LA Referencia