Study of the dynamics of third-order iterative methods on quadratic polynomials
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Otros documentos de la autoría: Cordero Barbero, Alicia; Torregrosa, Juan R.; Vindel, Pura
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Título
Study of the dynamics of third-order iterative methods on quadratic polynomialsFecha de publicación
2012Editor
Taylor & FrancisISSN
0020-7160; 1029-0265Cita bibliográfica
International Journal of Computer Mathematics Volume 89, Issue 13-14, 2012 Special Issue: COMPUTATIONAL AND MATHEMATICAL METHODS IN SCIENCE AND ENGINEERINGTipo de documento
info:eu-repo/semantics/articleVersión de la editorial
http://www.tandfonline.com/doi/abs/10.1080/00207160.2012.687446#.UYJlC5NA1uIVersión
info:eu-repo/semantics/sumittedVersionPalabras clave / Materias
Resumen
In this paper, we analyse the dynamical behaviour of the operators associated with multi-point interpolation iterative methods and frozen derivative methods, for solving nonlinear equations, applied on second-degree ... [+]
In this paper, we analyse the dynamical behaviour of the operators associated with multi-point interpolation iterative methods and frozen derivative methods, for solving nonlinear equations, applied on second-degree complex polynomials. We obtain that, in both cases, the Julia set is connected and separates the basins of attraction of the roots of the polynomial. Moreover, the Julia set of the operator associated with multi-point interpolation methods is the same as the Newton operator, although it is more complicated for the frozen derivative operator. We explain these differences by obtaining the conjugacy function of each method and by showing that the operators associated with Newton's method and multi-point interpolation methods are both conjugate to powers of z. [-]
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International Journal of Computer Mathematics, 2012,vol. 89, núm. 13-14Derechos de acceso
© Informa UK Limited, an Informa Group Company
This is an Author's Original Manuscript of an article submitted for consideration in the INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS [copyright Taylor & Francis]; INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS is available online at http://www.tandfonline.com/10.1080/00207160.2012.687446
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info:eu-repo/semantics/openAccess
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