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Choosing the most stable members of Kou's family of iterative methods

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Choosing the most stable members of Kou's family of iterative methods

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dc.contributor.author Cordero Barbero, Alicia es_ES
dc.contributor.author Guasp, Lucia es_ES
dc.contributor.author Torregrosa Sánchez, Juan Ramón es_ES
dc.date.accessioned 2019-06-01T20:02:00Z
dc.date.available 2019-06-01T20:02:00Z
dc.date.issued 2018 es_ES
dc.identifier.issn 0377-0427 es_ES
dc.identifier.uri http://hdl.handle.net/10251/121422
dc.description.abstract [EN] In this manuscript, we analyze the dynamical anomalies of a parametric family of iterative schemes designed by Kou et al. It is known that its order of convergence is three for any arbitrary value of the parameter, but it has order four (and it is optimal in the sense of Kung-Traub's conjecture) when a specific value is selected. Among all the elements of this family, one can choose this fourth-order element or any of the infinite members of third order of convergence, if only the speed of convergence is considered. However, the stability of the methods plays an important role in their reliability when they are applied on different problems. This is the reason why we analyze in this paper the dynamical behavior on quadratic polynomials of the mentioned family. The study of fixed points and their stability, joint with the critical points and their associated parameter planes, show the richness of the class and allow us to find members of it with excellent numerical properties, as well as other ones with very unstable behavior. Some test functions are analyzed for confirming the theoretical results. (C) 2017 Elsevier B.V. All rights reserved. es_ES
dc.description.sponsorship This research was supported by Ministerio de Economia y Competitividad MTM2014-52016-C2-2-P and Generalitat Valenciana PROMETEO/2016/089. es_ES
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation GV/PROMETEO/2016/089 es_ES
dc.relation MINECO/MTM2014-52016-C2-2-P es_ES
dc.relation.ispartof Journal of Computational and Applied Mathematics es_ES
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Nonlinear equation es_ES
dc.subject Iterative method es_ES
dc.subject Dynamical behavior es_ES
dc.subject Fatou and Julia sets es_ES
dc.subject Basin of attraction es_ES
dc.subject Periodic orbits es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Choosing the most stable members of Kou's family of iterative methods es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.cam.2017.02.012 es_ES
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.; Guasp, L.; Torregrosa Sánchez, JR. (2018). Choosing the most stable members of Kou's family of iterative methods. Journal of Computational and Applied Mathematics. 330:759-769. https://doi.org/10.1016/j.cam.2017.02.012 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://doi.org/10.1016/j.cam.2017.02.012 es_ES
dc.description.upvformatpinicio 759 es_ES
dc.description.upvformatpfin 769 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 330 es_ES
dc.relation.pasarela S\357128 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Ministerio de Economía, Industria y Competitividad es_ES


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