On the local convergence and the dynamics of Chebyshev–Halley methods with six and eight order of convergence
Magreñán, Á. Alberto (1)
Argyros, Ioannis K
Tipo de Ítem:Articulo Revista Indexada
We study the local convergence of Chebyshev–Halley methods with six and eight order of convergence to approximate a locally unique solution of a nonlinear equation. In Sharma (2015) (see Theorem 1, p. 121) the convergence of the method was shown under hypotheses reaching up to the third derivative. The convergence in this study is shown under hypotheses on the first derivative. Hence, the applicability of the method is expanded. The dynamics of these methods are also studied. Finally, numerical examples examining dynamical planes are also provided in this study to solve equations in cases where earlier studies cannot apply.
Este ítem aparece en la(s) siguiente(s) colección(es)
Mostrando ítems relacionados por Título, autor o materia.
Extending the domain of starting points for Newton's method under conditions on the second derivative Argyros, Ioannis K; Ezquerro, J A; Hernández-Verón, M A; Magreñán, Á. Alberto (1) (Journal of Computational and Applied Mathematics, 10/2018)In this paper, we propose a center Lipschitz condition for the second Frechet derivative together with the use of restricted domains in order to improve the domain of starting points for Newton's method. In addition, we ...
Amorós, Cristina (1); Argyros, Ioannis K; González-Crespo, Rubén (1); Magreñán, Á. Alberto; Orcos, Lara (1); Sarría, Iñigo (1) (Mathematics, 01/03/2019)The study of the dynamics and the analysis of local convergence of an iterative method, when approximating a locally unique solution of a nonlinear equation, is presented in this article. We obtain convergence using a ...
Argyros, Ioannis K; Legaz, M. J.; Magreñán, Á. Alberto; Moreno, D.; Sicilia, Juan Antonio (1) (Journal of Mathematical Chemistry, 05/2019)We present local convergence results for inexact iterative procedures of high convergence order in a normed space in order to approximate a locally unique solution. The hypotheses involve only Lipschitz conditions on the ...