Stability analysis of fourth-order iterative method for finding multiple roots of nonlinear equations

[EN] The use of complex dynamics tools in order to deepen the knowledge of qualitative behaviour of iterative methods for solving non-linear equations is a growing area of research in the last few years with fruitful results. Most of the studies dealt with the analysis of iterative schemes for solvi...

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Autores: Cordero Barbero, Alicia|||0000-0002-7462-9173, Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761, Jaiswal, J.P.
Formato: artículo
Fecha de publicación:2019
País:España
Recursos:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/153685
Acesso em linha:https://riunet.upv.es/handle/10251/153685
Access Level:acceso abierto
Palavra-chave:Nonlinear equations
Iterative methods
Multiple roots
Stability
Strange fixed points
Free critical points
MATEMATICA APLICADA
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spelling Stability analysis of fourth-order iterative method for finding multiple roots of nonlinear equationsCordero Barbero, Alicia|||0000-0002-7462-9173Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761Jaiswal, J.P.Nonlinear equationsIterative methodsMultiple rootsStabilityStrange fixed pointsFree critical pointsMATEMATICA APLICADA[EN] The use of complex dynamics tools in order to deepen the knowledge of qualitative behaviour of iterative methods for solving non-linear equations is a growing area of research in the last few years with fruitful results. Most of the studies dealt with the analysis of iterative schemes for solving non-linear equations with simple roots; however, the case involving multiple roots remains almost unexplored. The main objective of this paper was to discuss the dynamical analysis of the rational map associated with an existing class of iterative procedures for multiple roots. This study was performed for cases of double and triple multiplicities, giving as a conjecture that the wideness of the convergence regions of the multiple roots increases when the multiplicity is higher and also that this family of parametric methods includes some specially fast and stable elements with global convergence.This research was partially supported by Ministerio de Ciencia, Innovación y Universidades PGC2018-095896-B-C22 and Generalitat Valenciana PROMETEO/2016/089UP4 Institute of Sciences, S.L.Escuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarGeneralitat ValencianaAgencia Estatal de InvestigaciónRepositorio Institucional de la Universitat Politècnica de València Riunet20192019-04-19journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/153685reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengGeneralitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2016%2F089 Resolución de ecuaciones y sistemas no lineales mediante técnicas iterativas: análisis dinámico y aplicacionesAgencia 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 AEROESPACIALopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1536852026-06-13T07:49:27Z
dc.title.none.fl_str_mv Stability analysis of fourth-order iterative method for finding multiple roots of nonlinear equations
title Stability analysis of fourth-order iterative method for finding multiple roots of nonlinear equations
spellingShingle Stability analysis of fourth-order iterative method for finding multiple roots of nonlinear equations
Cordero Barbero, Alicia|||0000-0002-7462-9173
Nonlinear equations
Iterative methods
Multiple roots
Stability
Strange fixed points
Free critical points
MATEMATICA APLICADA
title_short Stability analysis of fourth-order iterative method for finding multiple roots of nonlinear equations
title_full Stability analysis of fourth-order iterative method for finding multiple roots of nonlinear equations
title_fullStr Stability analysis of fourth-order iterative method for finding multiple roots of nonlinear equations
title_full_unstemmed Stability analysis of fourth-order iterative method for finding multiple roots of nonlinear equations
title_sort Stability analysis of fourth-order iterative method for finding multiple roots of nonlinear equations
dc.creator.none.fl_str_mv Cordero Barbero, Alicia|||0000-0002-7462-9173
Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
Jaiswal, J.P.
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
Jaiswal, J.P.
author_role author
author2 Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
Jaiswal, J.P.
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
Generalitat Valenciana
Agencia Estatal de Investigación
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Nonlinear equations
Iterative methods
Multiple roots
Stability
Strange fixed points
Free critical points
MATEMATICA APLICADA
topic Nonlinear equations
Iterative methods
Multiple roots
Stability
Strange fixed points
Free critical points
MATEMATICA APLICADA
description [EN] The use of complex dynamics tools in order to deepen the knowledge of qualitative behaviour of iterative methods for solving non-linear equations is a growing area of research in the last few years with fruitful results. Most of the studies dealt with the analysis of iterative schemes for solving non-linear equations with simple roots; however, the case involving multiple roots remains almost unexplored. The main objective of this paper was to discuss the dynamical analysis of the rational map associated with an existing class of iterative procedures for multiple roots. This study was performed for cases of double and triple multiplicities, giving as a conjecture that the wideness of the convergence regions of the multiple roots increases when the multiplicity is higher and also that this family of parametric methods includes some specially fast and stable elements with global convergence.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-04-19
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/10251/153685
url https://riunet.upv.es/handle/10251/153685
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Generalitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2016%2F089 Resolución de ecuaciones y sistemas no lineales mediante técnicas iterativas: análisis dinámico y aplicaciones
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
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 UP4 Institute of Sciences, S.L.
publisher.none.fl_str_mv UP4 Institute of Sciences, S.L.
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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