- -

Semilocal Convergence Analysis of an Iteration of Order Five Using Recurrence Relations in Banach Spaces

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

Semilocal Convergence Analysis of an Iteration of Order Five Using Recurrence Relations in Banach Spaces

Mostrar el registro sencillo del ítem

Ficheros en el ítem

Thumbnail
Nombre: Omega_52.pdf
Tamaño: 337.4Kb
Formato: PDF
Descripción: Versión del Autor.
Abrir
[Cerrado]
Nombre: semilocal order 5.pdf
Tamaño: 539.2Kb
Formato: PDF
Descripción: Versión editorial
Solicitar una copia al autor
dc.contributor.author Singh, Sukhjit es_ES
dc.contributor.author Gupta, D.K. es_ES
dc.contributor.author Martínez Molada, Eulalia es_ES
dc.contributor.author Hueso Pagoaga, José Luís es_ES
dc.date.accessioned 2018-03-23T13:12:00Z
dc.date.available 2018-03-23T13:12:00Z
dc.date.issued 2016 es_ES
dc.identifier.issn 1660-5446 es_ES
dc.identifier.uri http://hdl.handle.net/10251/99653
dc.description.abstract [EN] Semilocal convergence for an iteration of order five for solving nonlinear equations in Banach spaces is established under second-order Fr,chet derivative satisfying the Lipschitz condition. It is done by deriving a number of recurrence relations. A theorem for the existence-uniqueness along with the estimation of error bounds of the solution is established. Its R-order is shown to be equal to five. Both efficiency and computational efficiency indices are given. A variety of examples are worked out to show its applicability. In comparison to existing methods having similar R-orders, improved results in terms of computational efficiency index and error bounds are found using our methodology. es_ES
dc.description.sponsorship The authors thank the referees for their valuable comments which have improved the presentation of the paper. The authors thankfully acknowledge the financial assistance provided by Council of Scientific and Industrial Research (CSIR), New Delhi, India. es_ES
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Mediterranean Journal of Mathematics es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Nonlinear equations es_ES
dc.subject Lipschitz condition es_ES
dc.subject Semilocal convergence es_ES
dc.subject Hammerstein integral equation es_ES
dc.subject Fredholm integral equation es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Semilocal Convergence Analysis of an Iteration of Order Five Using Recurrence Relations in Banach Spaces es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s00009-016-0741-5 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 Singh, S.; Gupta, D.; Martínez Molada, E.; Hueso Pagoaga, JL. (2016). Semilocal Convergence Analysis of an Iteration of Order Five Using Recurrence Relations in Banach Spaces. Mediterranean Journal of Mathematics. 13(6):4219-4235. doi:10.1007/s00009-016-0741-5 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://doi.org/10.1007/s00009-016-0741-5 es_ES
dc.description.upvformatpinicio 4219 es_ES
dc.description.upvformatpfin 4235 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 13 es_ES
dc.description.issue 6 es_ES
dc.relation.pasarela S\327221 es_ES
dc.contributor.funder Council of Scientific and Industrial Research, India
dc.description.references Cordero A., Hueso J.L., Martinez E., Torregrosa J.R.: Increasing the convergence order of an iterative method for nonlinear systems. Appl. Math. Lett. 25, 2369–2374 (2012) es_ES
dc.description.references Chen, L., Gu, C., Ma Y.: Semilocal convergence for a fifth order Newton’s method using Recurrence relations in Banach spaces. J. Appl. Math. 2011, 1–15 (2011) es_ES
dc.description.references Wang X., Kou J., Gu C.: Semilocal convergence of a sixth order Jarrat method in Banach spaces. Numer. Algorithms 57, 441–456 (2011) es_ES
dc.description.references Zheng L., Gu C.: Semilocal convergence of a sixth order method in Banach spaces. Numer. Algorithms 61, 413–427 (2012) es_ES
dc.description.references Zheng L., Gu C.: Recurrence relations for semilocal convergence of a fifth order method in Banach spaces. Numer. Algorithms 59, 623–638 (2012) es_ES
dc.description.references Proinov P.D., Ivanov S.I.: On the convergence of Halley’s method for multiple polynomial zeros. Mediterr. J. Math. 12, 555–572 (2015) es_ES
dc.description.references Ezquerro, J.A., Hernández-Verón M.A.: On the domain of starting points of Newton’s method under center lipschitz conditions. Mediterr. J. Math. (2015). doi: 10.1007/s00009-015-0596-1 es_ES
dc.description.references Cordero A., Hernández-Verón M.A., Romero N., Torregrosa J.R.: Semilocal convergence by using recurrence relations for a fifth-order method in Banach spaces. J. Comput. Appl. Math. 273, 205–213 (2015) es_ES
dc.description.references Parida P.K., Gupta D.K.: Recurrence relations for a Newton-like method in Banach spaces. J. Comput. Appl. Math. 206, 873–887 (2007) es_ES
dc.description.references Hueso J.L., Martínez E.: Semilocal convergence of a family of iterative methods in Banach spaces. Numer. Algorithms 67, 365–384 (2014) es_ES
dc.description.references Argyros, I.K., Hilout S.: Numerical methods in nonlinear analysis. World Scientific Publ. Comp., New Jersey (2013) es_ES
dc.description.references Argyros, I.K., Hilout, S., Tabatabai, M.A.: Mathematical modelling with applications in biosciences and engineering. Nova Publishers, New York (2011) es_ES
dc.description.references Argyros I.K., Khattri S.K.: Local convergence for a family of third order methods in Banach spaces. J. Math. 46, 53–62 (2004) es_ES
dc.description.references Argyros I.K., Hilout A.S.: On the local convergence of fast two-step Newton-like methods for solving nonlinear equations. J. Comput. Appl. Math. 245, 1–9 (2013) es_ES
dc.description.references Kantorovich, L.V., Akilov G.P.: Functional analysis. Pergamon Press, Oxford (1982) es_ES
dc.description.references Argyros I.K., George S., Magreñán A.A.: Local convergence for multi-point-parametric Chebyshev-Halley-type methods of higher convergence order. J. Comput. Appl. Math. 282, 215–224 (2015) es_ES
dc.description.references Argyros I.K., Magreñán A.A.: A study on the local convergence and the dynamics of Chebyshev-Halley-type methods free from second derivative. Numer. Algorithms 71, 1–23 (2015) es_ES
dc.description.references Amat S., Hernández M.A., Romero N.: A modified Chebyshev’s iterative method with at least sixth order of convergence. Appl. Math. Comput. 206, 164–174 (2008) es_ES
dc.description.references Chun, C., St $${\breve{a}}$$ a ˘ nic $${\breve{a}}$$ a ˘ , P., Neta, B.: Third-order family of methods in Banach spaces. Comput. Math. Appl. 61, 1665–1675 (2011) es_ES
dc.description.references Ostrowski, A.M.: Solution of equations in Euclidean and Banach spaces, 3rd edn. Academic Press, New-York (1977) es_ES
dc.description.references Jaiswal J.P.: Semilocal convergence of an eighth-order method in Banach spaces and its computational efficiency. Numer. Algorithms 71, 933–951 (2015) es_ES
dc.description.references Traub, J.F.: Iterative methods for the solution of equations. Prentice-Hall, Englewood Cliffs (1964) es_ES


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

Mostrar el registro sencillo del ítem