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Stability analysis of a family of optimal fourth-order methods for multiple roots

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Stability analysis of a family of optimal fourth-order methods for multiple roots

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dc.contributor.author Zafar, Fiza es_ES
dc.contributor.author Cordero Barbero, Alicia es_ES
dc.contributor.author Torregrosa Sánchez, Juan Ramón es_ES
dc.date.accessioned 2021-01-26T04:32:00Z
dc.date.available 2021-01-26T04:32:00Z
dc.date.issued 2019-07 es_ES
dc.identifier.issn 1017-1398 es_ES
dc.identifier.uri http://hdl.handle.net/10251/159838
dc.description.abstract [EN] Complex dynamics tools applied on the rational functions resulting from a parametric family of roots solvers for nonlinear equations provide very useful results that have been stated in the last years. These qualitative properties allow the user to select the most efficient members from the family of iterative schemes, in terms of stability and wideness of the sets of convergent initial guesses. These tools have been widely used in the case of iterative procedures for finding simple roots and only recently are being applied on the case of multiplicity m >1. In this paper, by using weight function procedure, we design a general class of iterative methods for calculating multiple roots that includes some known methods. In this class, conditions on the weight function are not very restrictive, so a large number of different subfamilies can be generated, all of them are optimal with fourth-order of convergence. Their dynamical analysis gives us enough information to select those with better properties and test them on different numerical experiments, showing their numerical properties. es_ES
dc.description.sponsorship This research was partially supported by Ministerio de Economia y Competitividad MTM2014-52016-C2-2-P, Generalitat Valenciana PROMETEO/2016/089 and Schlumberger Foundation-Faculty for Future Program. es_ES
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Numerical Algorithms es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Nonlinear equations es_ES
dc.subject Multiple zeros es_ES
dc.subject Optimal methods es_ES
dc.subject Weight functions es_ES
dc.subject Complex dynamics es_ES
dc.subject Parameter and dynamical planes es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Stability analysis of a family of optimal fourth-order methods for multiple roots es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s11075-018-0577-0 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2014-52016-C2-2-P/ES/DISEÑO DE METODOS ITERATIVOS EFICIENTES PARA RESOLVER PROBLEMAS NO LINEALES: CONVERGENCIA, COMPORTAMIENTO DINAMICO Y APLICACIONES. ECUACIONES MATRICIALES./ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO%2F2016%2F089/ES/Resolución de ecuaciones y sistemas no lineales mediante técnicas iterativas: análisis dinámico y aplicaciones/ 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 Zafar, F.; Cordero Barbero, A.; Torregrosa Sánchez, JR. (2019). Stability analysis of a family of optimal fourth-order methods for multiple roots. Numerical Algorithms. 81(3):947-981. https://doi.org/10.1007/s11075-018-0577-0 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s11075-018-0577-0 es_ES
dc.description.upvformatpinicio 947 es_ES
dc.description.upvformatpfin 981 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 81 es_ES
dc.description.issue 3 es_ES
dc.relation.pasarela S\393522 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Schlumberger Foundation es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
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