Multidimensional stability analysis of a family of bi-parametric iterative methods

[EN] In this paper, we present a multidimensional real dynamical study of the Ostrowsky-Chun family of iterative methods to solve systems of nonlinear equations. This family was defined initially for solving scalar equations but, in general, scalar methods can be transferred to make them suitable to...

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Autores: Cordero Barbero, Alicia|||0000-0002-7462-9173, Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761, García-Maimo, Javier, Vassileva, Maria P.
Tipo de recurso: artículo
Fecha de publicación:2017
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:10251/106299
Acceso en línea:https://riunet.upv.es/handle/10251/106299
Access Level:acceso abierto
Palabra clave:Nonlinear system of equations
Iterative method
Basin of attraction
Dynamical plane
Stability
Fisher&apos
s equation
MATEMATICA APLICADA
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spelling Multidimensional stability analysis of a family of bi-parametric iterative methodsCordero Barbero, Alicia|||0000-0002-7462-9173Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761García-Maimo, JavierVassileva, Maria P.Nonlinear system of equationsIterative methodBasin of attractionDynamical planeStabilityFisher&aposs equationMATEMATICA APLICADA[EN] In this paper, we present a multidimensional real dynamical study of the Ostrowsky-Chun family of iterative methods to solve systems of nonlinear equations. This family was defined initially for solving scalar equations but, in general, scalar methods can be transferred to make them suitable to solve nonlinear systems. The complex dynamical behavior of the rational operator associated to a scalar method applied to low-degree polynomials has shown to be an efficient tool for analyzing the stability and reliability of the methods. However, a good scalar dynamical behavior does not guarantee a good one in multidimensional case. We found different real intervals where both parameters can be defined assuring a completely stable performance and also other regions where it is dangerous to select any of the parameters, as undesirable behavior as attracting elements that are not solution of the problem to be solved appear. This performance is checked on a problem of chemical wave propagation, Fisher's equation, where the difference in numerical results provided by those elements of the class with good stability properties and those showed to be unstable, is clear.This research was partially supported by Ministerio de Economia y Competitividad MTM2014-52016-C02-2-P and FONDOCYT 2014-1C1-088 Republica Dominicana.Springer-VerlagEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarMinisterio de Economía y CompetitividadFondo Nacional de Innovación y Desarrollo Científico y Tecnológico, República DominicanaRepositorio 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/10251/106299reponame: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 MTM2014-52016-C2-2-P DISEÑO DE METODOS ITERATIVOS EFICIENTES PARA RESOLVER PROBLEMAS NO LINEALES: CONVERGENCIA, COMPORTAMIENTO DINAMICO Y APLICACIONES. ECUACIONES MATRICIALES.Fondo Nacional de Innovación y Desarrollo Científico y Tecnológico, República Dominicana FONDOCYT 2014-1C1-088open 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:10251/1062992026-06-13T07:49:27Z
dc.title.none.fl_str_mv Multidimensional stability analysis of a family of bi-parametric iterative methods
title Multidimensional stability analysis of a family of bi-parametric iterative methods
spellingShingle Multidimensional stability analysis of a family of bi-parametric iterative methods
Cordero Barbero, Alicia|||0000-0002-7462-9173
Nonlinear system of equations
Iterative method
Basin of attraction
Dynamical plane
Stability
Fisher&apos
s equation
MATEMATICA APLICADA
title_short Multidimensional stability analysis of a family of bi-parametric iterative methods
title_full Multidimensional stability analysis of a family of bi-parametric iterative methods
title_fullStr Multidimensional stability analysis of a family of bi-parametric iterative methods
title_full_unstemmed Multidimensional stability analysis of a family of bi-parametric iterative methods
title_sort Multidimensional stability analysis of a family of bi-parametric iterative methods
dc.creator.none.fl_str_mv Cordero Barbero, Alicia|||0000-0002-7462-9173
Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
García-Maimo, Javier
Vassileva, Maria 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
García-Maimo, Javier
Vassileva, Maria P.
author_role author
author2 Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
García-Maimo, Javier
Vassileva, Maria P.
author2_role author
author
author
dc.contributor.none.fl_str_mv Escuela Técnica Superior de Ingeniería de Telecomunicación
Departamento de Matemática Aplicada
Instituto Universitario de Matemática Multidisciplinar
Ministerio de Economía y Competitividad
Fondo Nacional de Innovación y Desarrollo Científico y Tecnológico, República Dominicana
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Nonlinear system of equations
Iterative method
Basin of attraction
Dynamical plane
Stability
Fisher&apos
s equation
MATEMATICA APLICADA
topic Nonlinear system of equations
Iterative method
Basin of attraction
Dynamical plane
Stability
Fisher&apos
s equation
MATEMATICA APLICADA
description [EN] In this paper, we present a multidimensional real dynamical study of the Ostrowsky-Chun family of iterative methods to solve systems of nonlinear equations. This family was defined initially for solving scalar equations but, in general, scalar methods can be transferred to make them suitable to solve nonlinear systems. The complex dynamical behavior of the rational operator associated to a scalar method applied to low-degree polynomials has shown to be an efficient tool for analyzing the stability and reliability of the methods. However, a good scalar dynamical behavior does not guarantee a good one in multidimensional case. We found different real intervals where both parameters can be defined assuring a completely stable performance and also other regions where it is dangerous to select any of the parameters, as undesirable behavior as attracting elements that are not solution of the problem to be solved appear. This performance is checked on a problem of chemical wave propagation, Fisher's equation, where the difference in numerical results provided by those elements of the class with good stability properties and those showed to be unstable, is clear.
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/10251/106299
url https://riunet.upv.es/handle/10251/106299
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 MTM2014-52016-C2-2-P DISEÑO DE METODOS ITERATIVOS EFICIENTES PARA RESOLVER PROBLEMAS NO LINEALES: CONVERGENCIA, COMPORTAMIENTO DINAMICO Y APLICACIONES. ECUACIONES MATRICIALES.
Fondo Nacional de Innovación y Desarrollo Científico y Tecnológico, República Dominicana FONDOCYT 2014-1C1-088
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 Springer-Verlag
publisher.none.fl_str_mv Springer-Verlag
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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