On an efficient k-step iterative method for nonlinear equations

[EN] This paper is devoted to the construction and analysis of an efficient k-step iterative method for nonlinear equations. The main advantage of this method is that it does not need to evaluate any high order Frechet derivative. Moreover, all the k-step have the same matrix, in particular only one...

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Detalles Bibliográficos
Autores: Amat, S., Bermúdez, C., Hernández-Verón, Miguel Angel, Martínez Molada, Eulalia|||0000-0003-2869-4334
Tipo de recurso: artículo
Fecha de publicación:2016
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:10251/99611
Acceso en línea:https://riunet.upv.es/handle/10251/99611
Access Level:acceso abierto
Palabra clave:Nonlinear equations
Iterative methods
Efficiency
Order of convergence
Dynamics
Semilocal convergence
MATEMATICA APLICADA
Descripción
Sumario:[EN] This paper is devoted to the construction and analysis of an efficient k-step iterative method for nonlinear equations. The main advantage of this method is that it does not need to evaluate any high order Frechet derivative. Moreover, all the k-step have the same matrix, in particular only one LU decomposition is required in each iteration. We study the convergence order, the efficiency and the dynamics in order to motivate the proposed family. We prove, using some recurrence relations, a semilocal convergence result in Banach spaces. Finally, a numerical application related to nonlinear conservative systems is presented. (C) 2016 Elsevier B.V. All rights reserved.