Introducing memory to a family of multi-step multidimensional iterative methods with weight function

[EN] In this paper, we construct a derivative-free multi-step iterative scheme based on Steffensen's method. To avoid excessively increasing the number of functional evaluations and, at the same time, to increase the order of convergence, we freeze the divided differences used from the seco...

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Autores: Cordero Barbero, Alicia|||0000-0002-7462-9173, Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761, Triguero-Navarro, Paula|||0000-0002-7319-9992, Villalba, Eva G.
Tipo de recurso: artículo
Fecha de publicación:2023
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:10251/204608
Acceso en línea:https://riunet.upv.es/handle/10251/204608
Access Level:acceso abierto
Palabra clave:Iterative methods
Nonlinear systems
Memory schemes
Basin of attraction
Dynamical plane
MATEMATICA APLICADA
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spelling Introducing memory to a family of multi-step multidimensional iterative methods with weight functionCordero Barbero, Alicia|||0000-0002-7462-9173Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761Triguero-Navarro, Paula|||0000-0002-7319-9992Villalba, Eva G.Iterative methodsNonlinear systemsMemory schemesBasin of attractionDynamical planeMATEMATICA APLICADA[EN] In this paper, we construct a derivative-free multi-step iterative scheme based on Steffensen's method. To avoid excessively increasing the number of functional evaluations and, at the same time, to increase the order of convergence, we freeze the divided differences used from the second step and use a weight function on already evaluated operators. Therefore, we define a family of multi-step methods with convergence order 2m, where m is the number of steps, free of derivatives, with several parameters and with dynamic behaviour, in some cases, similar to Steffensen's method. In addition, we study how to increase the convergence order of the defined family by introducing memory in two different ways: using the usual divided differences and the Kurchatov divided differences. We perform some numerical experiments to see the behaviour of the proposed family and suggest different weight functions to visualize with dynamical planes in some cases the dynamical behaviour.This research was partially supported by Universitat Politècnica de València Contrato Predoctoral, Spain PAID-01-20-17 (UPV) .Elsevier GmbHEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarEscuela Técnica Superior de Ingeniería IndustrialUNIVERSIDAD POLITECNICA DE VALENCIARepositorio Institucional de la Universitat Politècnica de València Riunet20232023-06-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/204608reponame: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 (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2046082026-06-13T07:49:27Z
dc.title.none.fl_str_mv Introducing memory to a family of multi-step multidimensional iterative methods with weight function
title Introducing memory to a family of multi-step multidimensional iterative methods with weight function
spellingShingle Introducing memory to a family of multi-step multidimensional iterative methods with weight function
Cordero Barbero, Alicia|||0000-0002-7462-9173
Iterative methods
Nonlinear systems
Memory schemes
Basin of attraction
Dynamical plane
MATEMATICA APLICADA
title_short Introducing memory to a family of multi-step multidimensional iterative methods with weight function
title_full Introducing memory to a family of multi-step multidimensional iterative methods with weight function
title_fullStr Introducing memory to a family of multi-step multidimensional iterative methods with weight function
title_full_unstemmed Introducing memory to a family of multi-step multidimensional iterative methods with weight function
title_sort Introducing memory to a family of multi-step multidimensional iterative methods with weight function
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
Villalba, Eva G.
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
Villalba, Eva G.
author_role author
author2 Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
Triguero-Navarro, Paula|||0000-0002-7319-9992
Villalba, Eva G.
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
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 Iterative methods
Nonlinear systems
Memory schemes
Basin of attraction
Dynamical plane
MATEMATICA APLICADA
topic Iterative methods
Nonlinear systems
Memory schemes
Basin of attraction
Dynamical plane
MATEMATICA APLICADA
description [EN] In this paper, we construct a derivative-free multi-step iterative scheme based on Steffensen's method. To avoid excessively increasing the number of functional evaluations and, at the same time, to increase the order of convergence, we freeze the divided differences used from the second step and use a weight function on already evaluated operators. Therefore, we define a family of multi-step methods with convergence order 2m, where m is the number of steps, free of derivatives, with several parameters and with dynamic behaviour, in some cases, similar to Steffensen's method. In addition, we study how to increase the convergence order of the defined family by introducing memory in two different ways: using the usual divided differences and the Kurchatov divided differences. We perform some numerical experiments to see the behaviour of the proposed family and suggest different weight functions to visualize with dynamical planes in some cases the dynamical behaviour.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-06-01
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/10251/204608
url https://riunet.upv.es/handle/10251/204608
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 (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 Elsevier GmbH
publisher.none.fl_str_mv Elsevier GmbH
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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