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An infinite family of one step iterators for solving non linear equation to increase the order of convergence and a new algoritm of global convergence

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An infinite family of one step iterators for solving non linear equation to increase the order of convergence and a new algoritm of global convergence

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dc.contributor.author Moreno Flores, Joaquín es_ES
dc.date.accessioned 2014-05-12T13:12:02Z
dc.date.issued 2013-11
dc.identifier.issn 0898-1221
dc.identifier.uri http://hdl.handle.net/10251/37419
dc.description.abstract In this paper we present an infinite family of one-step iterative formulas for solving nonlinear equations (Present Method One), from now on PMI, that can be expressed as xn+1=Fm(xn), with 1<= m<= infinite, integer, Fm being functions to be built later, in such a way that the velocity of convergence of such iterations increases more and more as m goes to infinity; in other words: given an arbitrary integer m0>=1, we will prove that the corresponding iteration formula of the family, xn+1= Fm0(xn), has an order of convergence m0+1. The increment of the velocity of convergence of the sequence of the iterator family xn+1=Fm+1(xn) with respect to the previous one xn+1=Fm(xn) is attained at the expense of one derivative evaluation more. Besides, we introduce a new algorithm (Present Method Two), from now on PMII, that plays the role of seeker for an initial value to guarantee the local convergence of the PMI. Both of them can be combined as an algorithm of global convergence, included the case of singular roots, that does not depend on the chosen initial value, and that allows to find all the roots in a feasible interval in a general and complete way. These are, in my opinion, the main results of this work. © 2013 Elsevier Ltd. All rights reserved. es_ES
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation.ispartof Computers and Mathematics with Applications es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Nonlinear equations es_ES
dc.subject Root-solver es_ES
dc.subject Iterative methods es_ES
dc.subject Convergence order es_ES
dc.subject Global convergence es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title An infinite family of one step iterators for solving non linear equation to increase the order of convergence and a new algoritm of global convergence es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.camwa.2013.08.003
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 Moreno Flores, J. (2013). An infinite family of one step iterators for solving non linear equation to increase the order of convergence and a new algoritm of global convergence. Computers and Mathematics with Applications. 66(8):1418-1436. doi:10.1016/j.camwa.2013.08.003 es_ES
dc.description.accrualMethod S es_ES
dc.description.upvformatpinicio 1418 es_ES
dc.description.upvformatpfin 1436 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 66 es_ES
dc.description.issue 8 es_ES
dc.relation.senia 259238


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