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

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Title:	A family of iterative methods that uses divided differences of first and second orders
Author:	Ezquerro, José Antonio; Grau Sánchez, Miguel; Hernández Verón, Miguel Angel; Noguera Batlle, Miquel
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques
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.
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics -Numerical methods and algorithms -Nonlinear equations -Iterative methods -Divided difference -Order of convergence -Efficiency -NONLINEAR EQUATIONS -SOLVING SYSTEMS -SECANT METHOD -CONVERGENCE -Anàlisi numèrica -Classificació AMS::65 Numerical analysis::65H Nonlinear algebraic or transcendental equations
Rights:	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Submitted version Article
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