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Study of the dynamics of third-order iterative methods on quadratic polynomials

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Study of the dynamics of third-order iterative methods on quadratic polynomials

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dc.contributor.author Cordero Barbero, Alicia es_ES
dc.contributor.author Torregrosa Sánchez, Juan Ramón es_ES
dc.contributor.author Vindel Cañas, Pura es_ES
dc.date.accessioned 2015-09-29T12:20:31Z
dc.date.available 2015-09-29T12:20:31Z
dc.date.issued 2012
dc.identifier.issn 0020-7160
dc.identifier.uri http://hdl.handle.net/10251/55273
dc.description.abstract In this paper, we analyse the dynamical behaviour of the operators associated with multi-point interpolation iterative methods and frozen derivative methods, for solving nonlinear equations, applied on second-degree complex polynomials. We obtain that, in both cases, the Julia set is connected and separates the basins of attraction of the roots of the polynomial. Moreover, the Julia set of the operator associated with multi-point interpolation methods is the same as the Newton operator, although it is more complicated for the frozen derivative operator. We explain these differences by obtaining the conjugacy function of each method and by showing that the operators associated with Newton's method and multi-point interpolation methods are both conjugate to powers of z. es_ES
dc.description.sponsorship The authors thank Professors X. Jarque and A. Garijo for their help. The authors also thank the referees for their valuable comments and suggestions that have improved the content of this paper. This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02 and by Vicerrectorado de Invetigacion, Universitat Politecnica de Valencia, PAID-06-2010-2285 en_EN
dc.language Inglés es_ES
dc.publisher Taylor & Francis Ltd es_ES
dc.relation.ispartof International Journal of Computer Mathematics es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Nonlinear equations es_ES
dc.subject Iterative methods es_ES
dc.subject Complex dynamics es_ES
dc.subject Conjugacy map es_ES
dc.subject Basin of attraction es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Study of the dynamics of third-order iterative methods on quadratic polynomials es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1080/00207160.2012.687446
dc.relation.projectID info:eu-repo/grantAgreement/MICINN//MTM2011-28636-C02-02/ES/DISEÑO Y ANALISIS DE METODOS EFICIENTES DE RESOLUCION DE ECUACIONES Y SISTEMAS NO LINEALES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/UPV//PAID-06-2010-2285/ 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.; Torregrosa Sánchez, JR.; Vindel Cañas, P. (2012). Study of the dynamics of third-order iterative methods on quadratic polynomials. International Journal of Computer Mathematics. 89(13):1826-1836. https://doi.org/10.1080/00207160.2012.687446 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1080/00207160.2012.687446 es_ES
dc.description.upvformatpinicio 1826 es_ES
dc.description.upvformatpfin 1836 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 89 es_ES
dc.description.issue 13 es_ES
dc.relation.senia 237512 es_ES
dc.identifier.eissn 1029-0265
dc.contributor.funder Ministerio de Ciencia e Innovación es_ES
dc.contributor.funder Universitat Politècnica de València es_ES
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