descriptionPublicationkeyboard_double_arrow_right Article 27 Jan 2015 English Publisher:Springer Science and Business Media LLCJournal:Numerical Algorithms, volume 70, pages 571-589 (issn: 1017-1398, eissn: 1572-9265,

Authors: Ezquerro, José Antonio; Grau Sánchez, Miguel; Hernández Verón, Miguel Angel; Noguera Batlle, Miquel;

doi: 10.1007/s11075-015-9962-0

handle: 2117/80873

A family of iterative methods that uses divided differences of first and second orders

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Abstract

The family of fourth-order Steffensen-type methods proposed by Zheng et al. (Appl. Math. Comput. 217, 9592-9597 (2011)) is extended to solve systems of nonlinear equations. This extension uses multidimensional divided differences of first and second orders. For a certain computational efficiency index, two optimal methods are identified in the family. Semilocal convergence is shown for one of these optimal methods under mild conditions. Moreover, a numerical example is given to illustrate the theoretical results. Peer Reviewed

Related Organizations

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

Keywords

Anàlisi numèrica, Iterative methods, :Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics [Àrees temàtiques de la UPC], :65 Numerical analysis::65H Nonlinear algebraic or transcendental equations [Classificació AMS], Efficiency, Nonlinear equations, Numerical methods and algorithms, Divided difference, Classificació AMS::65 Numerical analysis::65H Nonlinear algebraic or transcendental equations, Order of convergence, CONVERGENCE, SOLVING SYSTEMS, SECANT METHOD, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics, NONLINEAR EQUATIONS

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