- -

A convex combination approach for mean-based variants of Newton's method

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

A convex combination approach for mean-based variants of Newton's method

Mostrar el registro sencillo del ítem

Ficheros en el ítem

Thumbnail
Nombre: Cordero;Francesch ...
Tamaño: 2.099Mb
Formato: PDF
Descripción: Versión editorial
Abrir
dc.contributor.author Cordero Barbero, Alicia es_ES
dc.contributor.author Franceschi, Jonathan es_ES
dc.contributor.author Torregrosa Sánchez, Juan Ramón es_ES
dc.contributor.author Zagati, Anna C. es_ES
dc.date.accessioned 2020-05-22T03:02:28Z
dc.date.available 2020-05-22T03:02:28Z
dc.date.issued 2019-09-02 es_ES
dc.identifier.uri http://hdl.handle.net/10251/144084
dc.description.abstract [EN] Several authors have designed variants of Newton¿s method for solving nonlinear equations by using different means. This technique involves a symmetry in the corresponding fixed-point operator. In this paper, some known results about mean-based variants of Newton¿s method (MBN) are re-analyzed from the point of view of convex combinations. A new test is developed to study the order of convergence of general MBN. Furthermore, a generalization of the Lehmer mean is proposed and discussed. Numerical tests are provided to support the theoretical results obtained and to compare the different methods employed. Some dynamical planes of the analyzed methods on several equations are presented, revealing the great difference between the MBN when it comes to determining the set of starting points that ensure convergence and observing their symmetry in the complex plane. es_ES
dc.description.sponsorship This research was partially funded by Spanish Ministerio de Ciencia, Innovacion y Universidades PGC2018-095896-B-C22 and by Generalitat Valenciana PROMETEO/2016/089 (Spain). es_ES
dc.language Inglés es_ES
dc.publisher MDPI AG es_ES
dc.relation.ispartof Symmetry (Basel) es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Nonlinear equations es_ES
dc.subject Iterative methods es_ES
dc.subject General means es_ES
dc.subject Basin of attraction es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title A convex combination approach for mean-based variants of Newton's method es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3390/sym11091106 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.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095896-B-C22/ES/DISEÑO, ANALISIS Y ESTABILIDAD DE PROCESOS ITERATIVOS APLICADOS A LAS ECUACIONES INTEGRALES Y MATRICIALES Y A LA COMUNICACION AEROESPACIAL/ 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.; Franceschi, J.; Torregrosa Sánchez, JR.; Zagati, AC. (2019). A convex combination approach for mean-based variants of Newton's method. Symmetry (Basel). 11(9):1-16. https://doi.org/10.3390/sym11091106 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.3390/sym11091106 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 16 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 11 es_ES
dc.description.issue 9 es_ES
dc.identifier.eissn 2073-8994 es_ES
dc.relation.pasarela S\393514 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
dc.description.references Weerakoon, S., & Fernando, T. G. I. (2000). A variant of Newton’s method with accelerated third-order convergence. Applied Mathematics Letters, 13(8), 87-93. doi:10.1016/s0893-9659(00)00100-2 es_ES
dc.description.references Özban, A. . (2004). Some new variants of Newton’s method. Applied Mathematics Letters, 17(6), 677-682. doi:10.1016/s0893-9659(04)90104-8 es_ES
dc.description.references Zhou, X. (2007). A class of Newton’s methods with third-order convergence. Applied Mathematics Letters, 20(9), 1026-1030. doi:10.1016/j.aml.2006.09.010 es_ES
dc.description.references Singh, M. K., & Singh, A. K. (2017). A New-Mean Type Variant of Newton´s Method for Simple and Multiple Roots. International Journal of Mathematics Trends and Technology, 49(3), 174-177. doi:10.14445/22315373/ijmtt-v49p524 es_ES
dc.description.references Verma, K. L. (2016). On the centroidal mean Newton’s method for simple and multiple roots of nonlinear equations. International Journal of Computing Science and Mathematics, 7(2), 126. doi:10.1504/ijcsm.2016.076403 es_ES
dc.description.references Cordero, A., & Torregrosa, J. R. (2007). Variants of Newton’s Method using fifth-order quadrature formulas. Applied Mathematics and Computation, 190(1), 686-698. doi:10.1016/j.amc.2007.01.062 es_ES
dc.description.references Chicharro, F. I., Cordero, A., & Torregrosa, J. R. (2013). Drawing Dynamical and Parameters Planes of Iterative Families and Methods. The Scientific World Journal, 2013, 1-11. doi:10.1155/2013/780153 es_ES


Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem