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On improved three-step schemes with high efficiency index and their dynamics

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On improved three-step schemes with high efficiency index and their dynamics

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dc.contributor.author Babajee, Diyashvir K. R. es_ES
dc.contributor.author Cordero Barbero, Alicia es_ES
dc.contributor.author Soleymani, Fazlollah es_ES
dc.contributor.author Torregrosa Sánchez, Juan Ramón es_ES
dc.date.accessioned 2015-10-19T11:05:01Z
dc.date.available 2015-10-19T11:05:01Z
dc.date.issued 2014-01
dc.identifier.issn 1017-1398
dc.identifier.uri http://hdl.handle.net/10251/56199
dc.description.abstract This paper presents an improvement of the sixth-order method of Chun and Neta as a class of three-step iterations with optimal efficiency index, in the sense of Kung-Traub conjecture. Each member of the presented class reaches the highest possible order using four functional evaluations. Error analysis will be studied and numerical examples are also made to support the theoretical results. We then present results which describe the dynamics of the presented optimal methods for complex polynomials. The basins of attraction of the existing optimal methods and our methods are presented and compared to illustrate their performances. es_ES
dc.description.sponsorship This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02 and FONDOCYT Republica Dominicana. en_EN
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 Basin of attraction es_ES
dc.subject Kung-Traub conjecture es_ES
dc.subject Fractal es_ES
dc.subject Multi-point iterations es_ES
dc.subject Julia set es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title On improved three-step schemes with high efficiency index and their dynamics es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s11075-013-9699-6
dc.relation.projectID info:eu-repo/grantAgreement/MICINN//MTM2011-28636-C02-02/ES/DISEÑO Y ANALISIS DE METODOS EFICIENTES DE RESOLUCION DE ECUACIONES Y SISTEMAS NO LINEALES/ 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 Babajee, DKR.; Cordero Barbero, A.; Soleymani, F.; Torregrosa Sánchez, JR. (2014). On improved three-step schemes with high efficiency index and their dynamics. Numerical Algorithms. 65(1):153-169. https://doi.org/10.1007/s11075-013-9699-6 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1007/s11075-013-9699-6 es_ES
dc.description.upvformatpinicio 153 es_ES
dc.description.upvformatpfin 169 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 65 es_ES
dc.description.issue 1 es_ES
dc.relation.senia 269008 es_ES
dc.identifier.eissn 1572-9265
dc.contributor.funder Ministerio de Ciencia e Innovación es_ES
dc.contributor.funder Fondo Nacional de Innovación y Desarrollo Científico y Tecnológico, República Dominicana es_ES
dc.description.references Pang, J.S., Chan, D.: Iterative methods for variational and complementary problems. Math. Program. 24(1), 284–313 (1982) es_ES
dc.description.references Sun, D.: A class of iterative methods for solving nonlinear projection equations. J. Optim. Theory Appl. 91(1), 123–140 (1996) es_ES
dc.description.references Chun, C., Neta, B.: A new sixth-order scheme for nonlinear equations. Appl. Math. Lett. 25, 185–189 (2012) es_ES
dc.description.references Kung, H.T., Traub, J.F.: Optimal order of one-point and multipoint iteration. J. ACM 21, 643–651 (1974) es_ES
dc.description.references Neta, B.: A new family of high-order methods for solving equations. Int. J. Comput. Math. 14, 191–195 (1983) es_ES
dc.description.references Neta, B.: On Popovski’s method for nonlinear equations. Appl. Math. Comput. 201, 710–715 (2008) es_ES
dc.description.references Chun, C., Neta, B.: Some modifications of Newton’s method by the method of undeterminate coefficients. Comput. Math. Appl. 56, 2528–2538 (2008) es_ES
dc.description.references Chun, C., Lee, M.Y., Neta, B., Dzunic, J.: On optimal fourth-order iterative methods free from second derivative and their dynamics. Appl. Math. Comput. 218, 6427–6438 (2012) es_ES
dc.description.references Cordero, A., Torregrosa, J.R., Vassileva, M.P.: Three-step iterative methods with optimal eighth-order convergence. J. Comput. Appl. Math. 235, 3189–3194 (2011) es_ES
dc.description.references Cordero, A., Torregrosa, J.R., Vassileva, M.P.: A family of modified Ostrowski’s methods with optimal eighth order of convergence. Appl. Math. Lett. 24, 2082–2086 (2011) es_ES
dc.description.references Heydari, M., Hosseini, S.M., Loghmani, G.B.: On two new families of iterative methods for solving nonlinear equations with optimal order. Appl. Anal. Dis. Math. 5, 93–109 (2011) es_ES
dc.description.references Neta, B., Petkovic, M.S.: Construction of optimal order nonlinear solvers using inverse interpolation. Appl. Math. Comput. 217, 2448–2445 (2010) es_ES
dc.description.references Sharifi, M., Babajee, D.K.R., Soleymani, F.: Finding the solution of nonlinear equations by a class of optimal methods. Comput. Math. Appl. 63, 764–774 (2012) es_ES
dc.description.references Soleymani, F., Karimi Vanani, S., Khan, M., Sharifi, M.: Some modifications of King’s family with optimal eighth order of convergence. Math. Comput. Model. 55, 1373–1380 (2012) es_ES
dc.description.references Soleymani, F., Karimi Vanani, S., Jamali Paghaleh, M.: A class of three-step derivative-free root solvers with optimal convergence order. J. Appl. Math. 2012, Article ID 568740, 15 pp. (2012). doi: 10.1155/2012/568740 es_ES
dc.description.references Soleymani, F., Sharifi, M., Mousavi, B.S.: An improvement of Ostrowski’s and King’s techniques with optimal convergence order eight. J. Optim. Theory Appl. 153, 225–236 (2012) es_ES
dc.description.references Stewart, B.D.: Attractor basins of various root-finding methods. M.S. Thesis, Naval Postgraduate School, Department of Applied Mathematics, Monterey, CA (2001) es_ES
dc.description.references Amat, S., Busquier, S., Plaza, S.: Review of some iterative root-finding methods from a dynamical point of view. Scientia 10, 3–35 (2004) es_ES
dc.description.references Amat, S., Busquier, S., Plaza, S.: Dynamics of the King and Jarratt iterations. Aequ. Math. 69, 212–223 (2005) es_ES
dc.description.references Amat, S., Busquier, S., Plaza, S.: Chaotic dynamics of a third-order Newton type method. J. Math. Anal. Appl. 366, 24–32 (2010) es_ES
dc.description.references Neta, B., Chun, C., Scott, M.: A note on the modified super-Halley method. Appl. Math. Comput. 218, 9575–9577 (2012) es_ES
dc.description.references Scott, M., Neta, B., Chun, C.: Basin attractors for various methods. Appl. Math. Comput. 218, 2584–2599 (2011) es_ES
dc.description.references Ardelean, G.: A comparison between iterative methods by using the basins of attraction. Appl. Math. Comput. 218, 88–95 (2011) es_ES
dc.description.references Traub, J.F.: Iterative Methods for the Solution of Equations. Prentice Hall, New York (1964) es_ES
dc.description.references Babajee, D.K.R.: Analysis of higher order variants of Newton’s method and their applications to differential and integral equations and in ocean acidification. Ph.D. Thesis, University of Mauritius (2010) es_ES


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