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A class of efficient high-order iterative methods with memory for nonlinear equations and their dynamics

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A class of efficient high-order iterative methods with memory for nonlinear equations and their dynamics

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dc.contributor.author Howk, Cory L. es_ES
dc.contributor.author Hueso, J.L. es_ES
dc.contributor.author Martínez Molada, Eulalia es_ES
dc.contributor.author Teruel-Ferragud, Carles es_ES
dc.date.accessioned 2019-09-07T20:02:12Z
dc.date.available 2019-09-07T20:02:12Z
dc.date.issued 2018 es_ES
dc.identifier.issn 0170-4214 es_ES
dc.identifier.uri http://hdl.handle.net/10251/125220
dc.description.abstract [EN] In this paper we obtain some theoretical results about iterative methods with memory for nonlinear equations. The class of algorithms we consider focus on incorporating memory without increasing the computational cost of the algorithm. This class uses for the predictor step of each iteration a quantity that has already been calculated in the previous iteration, typically the quantity governing the slope from the previous corrector step. In this way we do not introduce any extra computation, and more importantly, we avoid new function evaluations, allowing us to obtain high-order iterative methods in a simple way. A specific class of methods of this type is introduced, and we prove the convergence order is 2(n) + 2(n-2) with n + 1 function evaluations. An exhaustive efficiency study is performed to show the competitiveness of these methods. Finally, we test some specific examples and explore the effect that this predictor may have on the convergence set by setting a dynamical study. es_ES
dc.description.sponsorship Ministerio de Economia y Competitividad de Espana, Grant/Award Number: MTM2014-52016-C2-2-P; Generalitat Valenciana Prometeo, Grant/Award Number: /2016/089 es_ES
dc.language Inglés es_ES
dc.publisher John Wiley & Sons es_ES
dc.relation 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 GV/PROMETEO/2016/089 es_ES
dc.relation.ispartof Mathematical Methods in the Applied Sciences es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Convergence rate es_ES
dc.subject Dynamics es_ES
dc.subject Efficiency es_ES
dc.subject Iterative methods with memory es_ES
dc.subject Kung-Traub conjecture es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title A class of efficient high-order iterative methods with memory for nonlinear equations and their dynamics es_ES
dc.type Artículo es_ES
dc.type Comunicación en congreso es_ES
dc.identifier.doi 10.1002/mma.4821 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 Howk, CL.; Hueso, J.; Martínez Molada, E.; Teruel-Ferragud, C. (2018). A class of efficient high-order iterative methods with memory for nonlinear equations and their dynamics. Mathematical Methods in the Applied Sciences. 41(17):7263-7282. https://doi.org/10.1002/mma.4821 es_ES
dc.description.accrualMethod S es_ES
dc.relation.conferencename 17th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE 2017) es_ES
dc.relation.conferencedate Julio 04-08,2017 es_ES
dc.relation.conferenceplace Rota, Spain es_ES
dc.relation.publisherversion http://doi.org/10.1002/mma.4821 es_ES
dc.description.upvformatpinicio 7263 es_ES
dc.description.upvformatpfin 7282 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 41 es_ES
dc.description.issue 17 es_ES
dc.relation.pasarela S\372892 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Ministerio de Economía y Empresa es_ES


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