- -

An eighth-order family of optimal multiple root finders and its dynamics

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

An eighth-order family of optimal multiple root finders and its dynamics

Mostrar el registro sencillo del ítem

Ficheros en el ítem

Thumbnail
Nombre: autor.pdf
Tamaño: 4.664Mb
Formato: PDF
Descripción: Versión del Autor.
Abrir
[Cerrado]
Nombre: An eighth-order ...
Tamaño: 3.858Mb
Formato: PDF
Descripción: Versión editorial
Solicitar una copia al autor
dc.contributor.author Behl, Ramandeep es_ES
dc.contributor.author Cordero Barbero, Alicia es_ES
dc.contributor.author Motsa, Sandile S. es_ES
dc.contributor.author Torregrosa Sánchez, Juan Ramón es_ES
dc.date.accessioned 2019-06-07T20:02:07Z
dc.date.available 2019-06-07T20:02:07Z
dc.date.issued 2018 es_ES
dc.identifier.issn 1017-1398 es_ES
dc.identifier.uri http://hdl.handle.net/10251/121735
dc.description.abstract [EN] There is a very small number of higher-order iteration functions for multiple zeros whose order of convergence is greater than four. Some scholars have tried to propose optimal eighth-order methods for multiple zeros. But, unfortunately, they did not get success in this direction and attained only sixth-order convergence. So, as far as we know, there is not a single optimal eighth-order iteration function in the available literature that will work for multiple zeros. Motivated and inspired by this fact, we present an optimal eighth-order iteration function for multiple zeros. An extensive convergence study is discussed in order to demonstrate the optimal eighth-order convergence of the proposed scheme. In addition, we also demonstrate the applicability of our proposed scheme on real-life problems and illustrate that the proposed methods are more efficient among the available multiple root finding techniques. Finally, dynamical study of the proposed schemes also confirms the theoretical results. es_ES
dc.description.sponsorship This research was partially supported by the Ministerio de Economia y Competitividad MTM2014-52016-C2-2-P and Generalitat Valenciana PROMETEO/2016/089 and by FONDOCYT 2014-1C1-088 Dominican Republic. 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 Optimal iterative methods es_ES
dc.subject Multiple roots es_ES
dc.subject Efficiency index es_ES
dc.subject Kung-Traub conjecture es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title An eighth-order family of optimal multiple root finders and its dynamics es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s11075-017-0361-6 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.relation.projectID info:eu-repo/grantAgreement/FONDOCYT//2014-1C1-088/ 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 Behl, R.; Cordero Barbero, A.; Motsa, SS.; Torregrosa Sánchez, JR. (2018). An eighth-order family of optimal multiple root finders and its dynamics. Numerical Algorithms. 77(4):1249-1272. https://doi.org/10.1007/s11075-017-0361-6 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://doi.org/10.1007/s11075-017-0361-6 es_ES
dc.description.upvformatpinicio 1249 es_ES
dc.description.upvformatpfin 1272 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 77 es_ES
dc.description.issue 4 es_ES
dc.relation.pasarela S\357146 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
dc.contributor.funder Fondo Nacional de Innovación y Desarrollo Científico y Tecnológico, República Dominicana es_ES
dc.description.references Kung, H.T., Traub, J.F.: Optimal order of one-point and multipoint iteration. J. Assoc. Comput. Mach. 21, 643–651 (1974) es_ES
dc.description.references Ostrowski, A.M.: Solution of equations and systems of equations. Academic Press, New York (1960) es_ES
dc.description.references Traub, J.F.: Iterative Methods for the solution of equations. Prentice-Hall, Englewood Cliffs (1964) es_ES
dc.description.references Petković, M. S., Neta, B., Petković, L. D., Dzunić, J.: Multipoint methods for solving nonlinear equations. Academic Press (2013) es_ES
dc.description.references Behl, R., Cordero, A., Motsa, S.S., Torregrosa, J.R.: On developing fourth-order optimal families of methods for multiple roots and their dynamics. Appl. Math. Comput. 265(15), 520–532 (2015) es_ES
dc.description.references Behl, R., Cordero, A., Motsa, S.S., Torregrosa, J.R., Kanwar, V.: An optimal fourth-order family of methods for multiple roots and its dynamics. Numer. Algor. 71(4), 775–796 (2016) es_ES
dc.description.references Chicharro, F.I., Cordero, A., Torregrosa, J.R.: Drawing dynamical and parameters planes of iterative families and methods. Sci World J 2013(Article ID 780153), 11 (2013) es_ES
dc.description.references Li, S., Liao, X., Cheng, L.: A new fourth-order iterative method for finding multiple roots of nonlinear equations. Appl. Math. Comput. 215, 1288–1292 (2009) es_ES
dc.description.references Li, S., Cheng, L., Neta, B.: Some fourth-order nonlinear solvers with closed formulae for multiple roots. Comput. Math. Appl. 59, 126–135 (2010) es_ES
dc.description.references Neta, B., Chun, C., Scott, M.: On the development of iterative methods for multiple roots. Appl. Math. Comput. 224, 358–361 (2013) es_ES
dc.description.references Sharma, J.R., Sharma, R.: Modified Jarratt method for computing multiple roots. Appl. Math. Comput. 217, 878–881 (2010) es_ES
dc.description.references Zhou, X., Chen, X., Song, Y.: Constructing higher-order methods for obtaining the multiple roots of nonlinear equations. Comput. Appl. Math. 235, 4199–4206 (2011) es_ES
dc.description.references Zhou, X., Chen, X., Song, Y.: Families of third and fourth order methods for multiple roots of nonlinear equations. Appl. Math. Comput. 219, 6030–6038 (2013) es_ES
dc.description.references Neta, B.: Extension of Murakami’s high-order non-linear solver to multiple roots. Int. J. Comput. Math. 87(5), 1023–1031 (2010) es_ES
dc.description.references Geum, Y.H., Kim, Y.I., Neta, B.: A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics. Appl. Math. Comput. 270, 387–400 (2015) es_ES
dc.description.references Geum, Y.H., Kim, Y.I., Neta, B.: A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points. Appl. Math. Comput. 283, 120–140 (2016) es_ES
dc.description.references Artidiello, S., Cordero, A., Torregrosa, J.R., Vassileva, M.P.: Two weighted eight-order classes of iterative root-finding methods. Int. J. Comput. Math. 92(9), 1790–1805 (2015) es_ES
dc.description.references Shacham, M.: Numerical solution of constrained nonlinear algebraic equations. Int. J. Numer. Method Eng. 23, 1455–1481 (1986) es_ES
dc.description.references Cordero, A., Torregrosa, J.R.: Variants of Newton’s method using fifth-order quadrature formulas. Appl. Math. Comput. 190(1), 686–698 (2007) es_ES


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

Mostrar el registro sencillo del ítem