descriptionPublicationkeyboard_double_arrow_right Article , Preprint 28 May 2016Embargo end date: 01 Jan 2015 English Publisher:Springer Science and Business Media LLCJournal:Mediterranean Journal of Mathematics, volume 13, pages 4,109-4,128 (issn: 1660-5446, eissn: 1660-5454,

Authors: Amat Plata, Sergio; Grau Sánchez, Miguel; Hernández Verón, Miguel Angel; Rubio, María Jesús;

doi: 10.1007/s00009-016-0735-3 , 10.48550/arxiv.1506.05253

arXiv: http://arxiv.org/abs/1506.05253

handle: 2117/104682 , 10317/10795

On a Moser–Steffensen Type Method for Nonlinear Systems of Equations

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Abstract

This paper is devoted to the construction and analysis of a Moser-Steffensen iterative scheme. The method has quadratic convergence without evaluating any derivative nor inverse operator. We present a complete study of the order of convergence for systems of equations, hypotheses ensuring the local convergence and finally we focus our attention to its numerical behavior. The conclusion is that the method improves the applicability of both Newton and Steffensen methods having the same order of convergence.

Related Organizations

Polytechnic University of Cartagena
Spain
Universitat Polite`cnica de Catalunya
Spain
Universitat Politècnica de Catalunya
Spain
University of La Rioja
Spain
University of Cartagena
Colombia

Keywords

Differential equations, Steffensen’s method, Classificació AMS::47 Operator theory::47H Nonlinear operators and their properties, Equacions diferencials no lineals, :65 Numerical analysis::65H Nonlinear algebraic or transcendental equations [Classificació AMS], 1206 Análisis Numérico, Operadors no lineals, Nonlinear, 65J15, 47H17, :47 Operator theory::47H Nonlinear operators and their properties [Classificació AMS], :Matemàtiques i estadística::Anàlisi numèrica [Àrees temàtiques de la UPC], Moser’s strategy, Differential equations, Nonlinear, FOS: Mathematics, Mathematics - Numerical Analysis, Local convergence, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica, Nonlinear operators, Recurrence relations, Matemática Aplicada, Numerical Analysis (math.NA), Classificació AMS::65 Numerical analysis::65H Nonlinear algebraic or transcendental equations, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica, :Matemàtiques i estadística::Anàlisi matemàtica [Àrees temàtiques de la UPC], Numerical analysis

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