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Semilocal convergence of a Secant-type method under weak Lipschitz conditions in Banach spaces

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Semilocal convergence of a Secant-type method under weak Lipschitz conditions in Banach spaces

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dc.contributor.author Kumar, A. es_ES
dc.contributor.author Gupta, D.K. es_ES
dc.contributor.author Martínez Molada, Eulalia es_ES
dc.contributor.author Singh, Sukhjit es_ES
dc.date.accessioned 2019-06-01T20:02:06Z
dc.date.available 2019-06-01T20:02:06Z
dc.date.issued 2018 es_ES
dc.identifier.issn 0377-0427 es_ES
dc.identifier.uri http://hdl.handle.net/10251/121424
dc.description.abstract [EN] The semilocal convergence of double step Secant method to approximate a locally unique solution of a nonlinear equation is described in Banach space setting. Majorizing sequences are used under the assumption that the first-order divided differences of the involved operator satisfy the weaker Lipschitz and the center-Lipschitz continuity conditions. A theorem is established for the existence-uniqueness region along with the estimation of error bounds for the solution. Our work improves the results derived in Ren and Argyros (2015) in more stringent Lipschitz and center Lipschitz conditions and gives finer majorizing sequences. Also, an example is worked out where the conditions of Ren and Argyros (2015) fail but our's work. Numerical examples including nonlinear elliptic differential equations and integral equations are worked out. It is found that our conditions enlarge the convergence domain of the solution. Finally, taking a nonlinear system of in equations, the Efficiency Index (EI) and the Computational Efficiency Index (CEI) of double step Secant method are computed and its comparison with respect to other similar existing iterative methods are summarized in the tabular forms. (C) 2017 Elsevier B.V. All rights reserved. es_ES
dc.description.sponsorship This work was supported in part by the project of Generalitat Valenciana, Prometeo/2016/089, and the project MTM2014-52016-C2-2-P of the Spanish Ministry of Science and Innovation. es_ES
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation GV/PROMETEO/2016/089 es_ES
dc.relation MINECO/MTM2014-52016-C2-2-P es_ES
dc.relation.ispartof Journal of Computational and Applied Mathematics es_ES
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Semilocal convergence es_ES
dc.subject Double step Secant method es_ES
dc.subject Divided differences es_ES
dc.subject Majorizing sequences es_ES
dc.subject Error bounds es_ES
dc.subject Efficiency index es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Semilocal convergence of a Secant-type method under weak Lipschitz conditions in Banach spaces es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.cam.2017.02.042 es_ES
dc.rights.accessRights Embargado es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Kumar, A.; Gupta, D.; Martínez Molada, E.; Singh, S. (2018). Semilocal convergence of a Secant-type method under weak Lipschitz conditions in Banach spaces. Journal of Computational and Applied Mathematics. 330:732-741. https://doi.org/10.1016/j.cam.2017.02.042 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://doi.org/10.1016/j.cam.2017.02.042 es_ES
dc.description.upvformatpinicio 732 es_ES
dc.description.upvformatpfin 741 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 330 es_ES
dc.relation.pasarela 368267 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Ministerio de Economía y Empresa es_ES


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