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Widening basins of attraction of optimal iterative methods

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Widening basins of attraction of optimal iterative methods

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dc.contributor.author Bakhtiari, Parisa es_ES
dc.contributor.author Cordero Barbero, Alicia es_ES
dc.contributor.author Lotfi, Taher es_ES
dc.contributor.author Mahdiani, Katayoun es_ES
dc.contributor.author Torregrosa Sánchez, Juan Ramón es_ES
dc.date.accessioned 2018-05-19T04:19:30Z
dc.date.available 2018-05-19T04:19:30Z
dc.date.issued 2017 es_ES
dc.identifier.issn 0924-090X es_ES
dc.identifier.uri http://hdl.handle.net/10251/102246
dc.description.abstract [EN] In this work, we analyze the dynamical behavior on quadratic polynomials of a class of derivative-free optimal parametric iterative methods, designed by Khattri and Steihaug. By using their parameter as an accelerator, we develop different methods with memory of orders three, six and twelve, without adding new functional evaluations. Then a dynamical approach is made, comparing each of the proposed methods with the original ones without memory, with the following empiric conclusion: Basins of attraction of iterative schemes with memory are wider and the behavior is more stable. This has been numerically checked by estimating the solution of a practical problem, as the friction factor of a pipe and also of other nonlinear academic problems. es_ES
dc.description.sponsorship This research was supported by Islamic Azad University, Hamedan Branch, Ministerio de Economia y Competitividad MTM2014-52016-C02-2-P and Generalitat Valenciana PROMETEO/2016/089. en_EN
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Nonlinear Dynamics es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Multi-point iterative methods es_ES
dc.subject Dynamical plane es_ES
dc.subject Basin of attraction es_ES
dc.subject With and without memory methods es_ES
dc.subject Kung and Traub's conjecture es_ES
dc.subject Efficiency index es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Widening basins of attraction of optimal iterative methods es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s11071-016-3089-2 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.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 Bakhtiari, P.; Cordero Barbero, A.; Lotfi, T.; Mahdiani, K.; Torregrosa Sánchez, JR. (2017). Widening basins of attraction of optimal iterative methods. Nonlinear Dynamics. 87(2):913-938. https://doi.org/10.1007/s11071-016-3089-2 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s11071-016-3089-2 es_ES
dc.description.upvformatpinicio 913 es_ES
dc.description.upvformatpfin 938 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 87 es_ES
dc.description.issue 2 es_ES
dc.relation.pasarela S\324460 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Ministerio de Economía, Industria y Competitividad es_ES
dc.description.references Amat, S., Busquier, S., Bermúdez, C., Plaza, S.: On two families of high order Newton type methods. Appl. Math. Lett. 25, 2209–2217 (2012) es_ES
dc.description.references Amat, S., Busquier, S., Bermúdez, C., Magreñán, Á.A.: On the election of the damped parameter of a two-step relaxed Newton-type method. Nonlinear Dyn. 84(1), 9–18 (2016) es_ES
dc.description.references Chun, C., Neta, B.: An analysis of a family of Maheshwari-based optimal eighth order methods. Appl. Math. Comput. 253, 294–307 (2015) es_ES
dc.description.references Babajee, D.K.R., Cordero, A., Soleymani, F., Torregrosa, J.R.: On improved three-step schemes with high efficiency index and their dynamics. Numer. Algorithms 65(1), 153–169 (2014) es_ES
dc.description.references Argyros, I.K., Magreñán, Á.A.: On the convergence of an optimal fourth-order family of methods and its dynamics. Appl. Math. Comput. 252, 336–346 (2015) es_ES
dc.description.references Petković, M., Neta, B., Petković, L., Džunić, J.: Multipoint Methods for Solving Nonlinear Equations. Academic Press, London (2013) es_ES
dc.description.references Ostrowski, A.M.: Solution of Equations and System of Equations. Prentice-Hall, Englewood Cliffs, NJ (1964) 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 Khattri, S.K., Steihaug, T.: Algorithm for forming derivative-free optimal methods. Numer. Algorithms 65(4), 809–824 (2014) 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 Cordero, A., Soleymani, F., Torregrosa, J.R., Shateyi, S.: Basins of Attraction for Various Steffensen-Type Methods. J. Appl. Math. 2014, 1–17 (2014) es_ES
dc.description.references Devaney, R.L.: The Mandelbrot Set, the Farey Tree and the Fibonacci sequence. Am. Math. Mon. 106(4), 289–302 (1999) es_ES
dc.description.references McMullen, C.: Families of rational maps and iterative root-finding algorithms. Ann. Math. 125(3), 467–493 (1987) es_ES
dc.description.references Chicharro, F., Cordero, A., Gutiérrez, J.M., Torregrosa, J.R.: Complex dynamics of derivative-free methods for nonlinear equations. Appl. Math. Comput. 219, 70237035 (2013) es_ES
dc.description.references Magreñán, Á.A.: Different anomalies in a Jarratt family of iterative root-finding methods. Appl. Math. Comput. 233, 29–38 (2014) es_ES
dc.description.references Neta, B., Chun, C., Scott, M.: Basins of attraction for optimal eighth order methods to find simple roots of nonlinear equations. Appl. Math. Comput. 227, 567–592 (2014) es_ES
dc.description.references Lotfi, T., Magreñán, Á.A., Mahdiani, K., Rainer, J.J.: A variant of Steffensen–King’s type family with accelerated sixth-order convergence and high efficiency index: dynamic study and approach. Appl. Math. Comput. 252, 347–353 (2015) 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, 1–11 (2013) es_ES
dc.description.references Cordero, A., Lotfi, T., Torregrosa, J.R., Assari, P., Mahdiani, K.: Some new bi-accelerator two-point methods for solving nonlinear equations. Comput. Appl. Math. 35(1), 251–267 (2016) es_ES
dc.description.references Cordero, A., Lotfi, T., Bakhtiari, P., Torregrosa, J.R.: An efficient two-parametric family with memory for nonlinear equations. Numer. Algorithms 68(2), 323–335 (2015) es_ES
dc.description.references Lotfi, T., Mahdiani, K., Bakhtiari, P., Soleymani, F.: Constructing two-step iterative methods with and without memory. Comput. Math. Math. Phys. 55(2), 183–193 (2015) es_ES
dc.description.references Cordero, A., Maimó, J.G., Torregrosa, J.R., Vassileva, M.P.: Solving nonlinear problems by Ostrowski–Chun type parametric families. J. Math. Chem. 53, 430–449 (2015) es_ES
dc.description.references Abad, M., Cordero, A., Torregrosa, J.R.: A family of seventh-order schemes for solving nonlinear systems. Bull. Math. Soc. Sci. Math. Roum. Tome 57(105), 133–145 (2014) es_ES
dc.description.references Weerakoon, S., Fernando, T.G.I.: A variant of Newton’s method with accelerated third-order convergence. Appl. Math. Lett. 13, 87–93 (2000) es_ES
dc.description.references White, F.: Fluid Mechanics. McGraw-Hill, Boston (2003) es_ES
dc.description.references Zheng, Q., Li, J., Huang, F.: An optimal Steffensen-type family for solving nonlinear equations. Appl. Math. Comput. 217, 9592–9597 (2011) es_ES
dc.description.references Soleymani, F., Babajee, D.K.R., Shateyi, S., Motsa, S.S.: Construction of optimal derivative-free techniques without memory. J. Appl. Math. (2012). doi: 10.1155/2012/497023 es_ES


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