Local convergence and a chemical application of derivative free root finding methods with one parameter based on interpolation
Argyros, Ioannis K
Magreñán, Á. Alberto (UNIR)
Orcos, Lara (UNIR)
Tipo de Ítem:Articulo Revista Indexada
We present a local convergence analysis of a derivative free fourth order method with one parameter based on rational interpolation in order to approximate a locally unique root of a function. The method is optimal in the sense of Traub. In earlier studies such as Steffensen (Scand Actuar J 16(1):64–72, 1933) and Zafer et al. (Sci World J, 2015. doi:10.1155/2015/934260) the convergence was based on hypotheses on the third derivative or even higher. We extend the applicability of theses methods using only the first derivative. Moreover, we provide computable radii and error bounds based on Lipschitz constants. Furthermore, the dynamics of this method are studied in order to find the best choice of the parameter in terms of convergence. An application is also presented in this study.
Este ítem aparece en la(s) siguiente(s) colección(es)
Mostrando ítems relacionados por Título, autor o materia.
Local convergence and the dynamics of a two-point four parameter Jarratt-like method under weak conditions Amat, S (UNIR); Argyros, Ioannis K; Busquier, S; Magreñán, Á. Alberto (UNIR) (Numerical Algorithms, 02/2017)We present a local convergence analysis of a two-point four parameter Jarratt-like method of high convergence order in order to approximate a locally unique solution of a nonlinear equation. In contrast to earlier studies ...
Argyros, Ioannis K; Cordero, Alicia; Magreñán, Á. Alberto (UNIR); Torregrosa, Juan Ramón (Journal of Computational and Applied Mathematics, 01/2017)In this paper, we present the study of the local convergence of a higher-order family of methods. Moreover, the dynamical behavior of this family of iterative methods applied to quadratic polynomials is studied. Some ...
On the local convergence and the dynamics of Chebyshev–Halley methods with six and eight order of convergence Magreñán, Á. Alberto (UNIR); Argyros, Ioannis K (Journal of Computational and Applied Mathematics, 05/2016)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 ...