Extended convergence results for the Newton–Kantorovich iteration
Argyros, Ioannis K
Magreñán, Á. Alberto (UNIR)
Tipo de Ítem:Articulo Revista Indexada
We present new semilocal and local convergence results for the Newton–Kantorovich method. These new results extend the applicability of the Newton–Kantorovich method on approximate zeros by improving the convergence domain and ratio given in earlier studies by Argyros (2003), Cianciaruso (2007), Smale (1986) and Wang (1999). These advantages are also obtained under the same computational cost. Numerical examples where the old sufficient convergence criteria are not satisfied but the new convergence criteria are satisfied are 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 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) (Journal of Mathematical Chemistry, 08/2016)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 ...
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 ...