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

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dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor.author	Ezquerro, José Antonio
dc.contributor.author	Grau Sánchez, Miguel
dc.contributor.author	Hernández Verón, Miguel Angel
dc.contributor.author	Noguera Batlle, Miquel
dc.date	2015-11-01
dc.identifier.citation	Ezquerro, J.A., Grau, M., Hernández-Verón, M.A., Noguera, M. A family of iterative methods that uses divided differences of first and second orders. "Numerical algorithms", 01 Novembre 2015, vol. 70, núm. 3, p. 571-589.
dc.identifier.citation	1017-1398
dc.identifier.citation	10.1007/s11075-015-9962-0
dc.identifier.uri	http://hdl.handle.net/2117/80873
dc.language.iso	eng
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
dc.subject	Numerical methods and algorithms
dc.subject	Nonlinear equations
dc.subject	Iterative methods
dc.subject	Divided difference
dc.subject	Order of convergence
dc.subject	Efficiency
dc.subject	NONLINEAR EQUATIONS
dc.subject	SOLVING SYSTEMS
dc.subject	SECANT METHOD
dc.subject	CONVERGENCE
dc.subject	Anàlisi numèrica
dc.subject	Classificació AMS::65 Numerical analysis::65H Nonlinear algebraic or transcendental equations
dc.title	A family of iterative methods that uses divided differences of first and second orders
dc.type	info:eu-repo/semantics/submittedVersion
dc.type	info:eu-repo/semantics/article
dc.description.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.
dc.description.abstract	Peer Reviewed

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