Extending the applicability of the local and semilocal convergence of Newton's method
Argyros, Ioannis K
Magreñán, Á. Alberto (1)
Tipo de Ítem:Articulo Revista Indexada
We present a local as well a semilocal convergence analysis for Newton's method in a Banach space setting. Using the same Lipschitz constants as in earlier studies, we extend the applicability of Newton's method as follows: local case: a larger radius is given as well as more precise error estimates on the distances involved. Semilocal case: the convergence domain is extended; the error estimates are tighter and the information on the location of the solution is at least as precise as before. Numerical examples further justify the theoretical results.
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 ...