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A class of Steffensen type methods with optimal order of convergente

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A class of Steffensen type methods with optimal order of convergente

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dc.contributor.author Cordero Barbero, Alicia es_ES
dc.contributor.author Torregrosa Sánchez, Juan Ramón es_ES
dc.date.accessioned 2015-07-01T08:44:15Z
dc.date.available 2015-07-01T08:44:15Z
dc.date.issued 2011-06-01
dc.identifier.issn 0096-3003
dc.identifier.issn 1873-5649
dc.identifier.uri http://hdl.handle.net/10251/52542
dc.description.abstract In this paper, a family of Steffensen type methods of fourth-order convergence for solving nonlinear smooth equations is suggested. In the proposed methods, a linear combination of divided differences is used to get a better approximation to the derivative of the given function. Each derivative-free member of the family requires only three evaluations of the given function per iteration. Therefore, this class of methods has efficiency index equal to 1.587. Kung and Traub conjectured that the order of convergence of any multipoint method without memory cannot exceed the bound 2d-1, where d is the number of functional evaluations per step. The new class of methods agrees with this conjecture for the case d=3. Numerical examples are made to show the performance of the presented methods, on smooth and nonsmooth equations, and to compare with other ones. © 2011 Elsevier Inc. All rights reserved. es_ES
dc.description.sponsorship This research was supported by Ministerio de Ciencia y Tecnologia MTM2010-18539. en_EN
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation Ministerio de Ciencia y Tecnologia [MTM2010-18539] es_ES
dc.relation.ispartof Applied Mathematics and Computation es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Convergence order es_ES
dc.subject Derivative free method es_ES
dc.subject Efficiency index es_ES
dc.subject Iterative methods es_ES
dc.subject Nonlinear equations es_ES
dc.subject Steffensen's method es_ES
dc.subject Class of methods es_ES
dc.subject Derivative-free es_ES
dc.subject Divided difference es_ES
dc.subject Fourth-order es_ES
dc.subject Functional evaluation es_ES
dc.subject Linear combinations es_ES
dc.subject Multi-point methods es_ES
dc.subject Nonsmooth equation es_ES
dc.subject Numerical example es_ES
dc.subject Optimal order of convergence es_ES
dc.subject Order of convergence es_ES
dc.subject Type methods es_ES
dc.subject Function evaluation es_ES
dc.subject Numerical methods es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title A class of Steffensen type methods with optimal order of convergente es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.amc.2011.02.067
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Cordero Barbero, A.; Torregrosa Sánchez, JR. (2011). A class of Steffensen type methods with optimal order of convergente. Applied Mathematics and Computation. 217(19):7653-7659. doi:10.1016/j.amc.2011.02.067 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1016/j.amc.2011.02.067 es_ES
dc.description.upvformatpinicio 7653 es_ES
dc.description.upvformatpfin 7659 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 217 es_ES
dc.description.issue 19 es_ES
dc.relation.senia 215648


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