Iterative methods with memory for solving systems of nonlinear equations using a second order approximation

[EN] Iterative methods for solving nonlinear equations are said to have memory when the calculation of the next iterate requires the use of more than one previous iteration. Methods with memory usually have a very stable behavior in the sense of the wideness of the set of convergent initial estimati...

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Autores: Cordero Barbero, Alicia|||0000-0002-7462-9173, Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761, Maimó, Javier G., Vassileva, María P.
Tipo de recurso: artículo
Fecha de publicación:2019
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:10251/159353
Acceso en línea:https://riunet.upv.es/handle/10251/159353
Access Level:acceso abierto
Palabra clave:Iterative methods
Secant method
Methods with memory
Multidimensional Newton polynomial interpolation
Basin of attraction
MATEMATICA APLICADA
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spelling Iterative methods with memory for solving systems of nonlinear equations using a second order approximationCordero Barbero, Alicia|||0000-0002-7462-9173Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761Maimó, Javier G.Vassileva, María P.Iterative methodsSecant methodMethods with memoryMultidimensional Newton polynomial interpolationBasin of attractionMATEMATICA APLICADA[EN] Iterative methods for solving nonlinear equations are said to have memory when the calculation of the next iterate requires the use of more than one previous iteration. Methods with memory usually have a very stable behavior in the sense of the wideness of the set of convergent initial estimations. With the right choice of parameters, iterative methods without memory can increase their order of convergence significantly, becoming schemes with memory. In this work, starting from a simple method without memory, we increase its order of convergence without adding new functional evaluations by approximating the accelerating parameter with Newton interpolation polynomials of degree one and two. Using this technique in the multidimensional case, we extend the proposed method to systems of nonlinear equations. Numerical tests are presented to verify the theoretical results and a study of the dynamics of the method is applied to different problems to show its stability.This research was supported by PGC2018-095896-B-C22 (MCIU/AEI/FEDER, UE), Generalitat Valenciana PROMETEO/2016/089, and FONDOCYT 2016-2017-212 Republica Dominicana.MDPI AGEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarGeneralitat ValencianaAgencia Estatal de InvestigaciónEuropean Regional Development FundFondo Nacional de Innovación y Desarrollo Científico y Tecnológico, República DominicanaRepositorio Institucional de la Universitat Politècnica de València Riunet20192019-11-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/159353reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengFondo Nacional de Innovación y Desarrollo Científico y Tecnológico, República Dominicana FONDOCYT 2016-2017-212Generalitat 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:10251/1593532026-06-13T07:49:27Z
dc.title.none.fl_str_mv Iterative methods with memory for solving systems of nonlinear equations using a second order approximation
title Iterative methods with memory for solving systems of nonlinear equations using a second order approximation
spellingShingle Iterative methods with memory for solving systems of nonlinear equations using a second order approximation
Cordero Barbero, Alicia|||0000-0002-7462-9173
Iterative methods
Secant method
Methods with memory
Multidimensional Newton polynomial interpolation
Basin of attraction
MATEMATICA APLICADA
title_short Iterative methods with memory for solving systems of nonlinear equations using a second order approximation
title_full Iterative methods with memory for solving systems of nonlinear equations using a second order approximation
title_fullStr Iterative methods with memory for solving systems of nonlinear equations using a second order approximation
title_full_unstemmed Iterative methods with memory for solving systems of nonlinear equations using a second order approximation
title_sort Iterative methods with memory for solving systems of nonlinear equations using a second order approximation
dc.creator.none.fl_str_mv Cordero Barbero, Alicia|||0000-0002-7462-9173
Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
Maimó, Javier G.
Vassileva, María 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
Maimó, Javier G.
Vassileva, María P.
author_role author
author2 Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
Maimó, Javier G.
Vassileva, María 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
Generalitat Valenciana
Agencia Estatal de Investigación
European Regional Development Fund
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 Iterative methods
Secant method
Methods with memory
Multidimensional Newton polynomial interpolation
Basin of attraction
MATEMATICA APLICADA
topic Iterative methods
Secant method
Methods with memory
Multidimensional Newton polynomial interpolation
Basin of attraction
MATEMATICA APLICADA
description [EN] Iterative methods for solving nonlinear equations are said to have memory when the calculation of the next iterate requires the use of more than one previous iteration. Methods with memory usually have a very stable behavior in the sense of the wideness of the set of convergent initial estimations. With the right choice of parameters, iterative methods without memory can increase their order of convergence significantly, becoming schemes with memory. In this work, starting from a simple method without memory, we increase its order of convergence without adding new functional evaluations by approximating the accelerating parameter with Newton interpolation polynomials of degree one and two. Using this technique in the multidimensional case, we extend the proposed method to systems of nonlinear equations. Numerical tests are presented to verify the theoretical results and a study of the dynamics of the method is applied to different problems to show its stability.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-11-01
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/10251/159353
url https://riunet.upv.es/handle/10251/159353
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Fondo Nacional de Innovación y Desarrollo Científico y Tecnológico, República Dominicana FONDOCYT 2016-2017-212
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 MDPI AG
publisher.none.fl_str_mv MDPI AG
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 15,301629

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