Improved convergence analysis for Newton-like methods
Magreñán, Á. Alberto (1)
Argyros, Ioannis K
Tipo de Ítem:Articulo Revista Indexada
We present a new semilocal convergence analysis for Newton-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. This way, we expand the applicability of these methods in cases not covered in earlier studies. The advantages of our approach include a more precise convergence analysis under the same computational cost on the Lipschitz constants involved. Applications are also given in this study to show that our estimates on the distances involved are tighter than the older ones.
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 ...
Magreñán, Á. Alberto (1); Argyros, Ioannis K (Applied Mathematics and Computation, 09/2014)We present a new sufficient semilocal convergence conditions for Newton-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. This way, we expand the applicability of these ...