Improving the domain of parameters for Newton's method with applications
Argyros, Ioannis K
Magreñán, Á. Alberto (1)
Sicilia, Juan Antonio (1)
Tipo de Ítem:Articulo Revista Indexada
We present a new technique to improve the convergence domain for Newton’s method both in the semilocal and local case. It turns out that with the new technique the sufficient convergence conditions for Newton’s method are weaker, the error bounds are tighter and the information on the location of the solution is at least as precise as in earlier studies. Numerical examples are given showing that our results apply to solve nonlinear equations in cases where the old results cannot apply.
Este ítem aparece en la(s) siguiente(s) colección(es)
Mostrando ítems relacionados por Título, autor o materia.
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 ...
Argyros, Ioannis K; Magreñán, Á. Alberto (1); Orcos, Lara (1); Sicilia, Juan Antonio (1) (Journal of Mathematical Chemistry, 08/2017)We present a local convergence analysis for a relaxed two-step Newton-like method. We use this method to approximate a solution of a nonlinear equation in a Banach space setting. Hypotheses on the first Fr,chet derivative ...
Magreñán, Á. Alberto (1); Argyros, Ioannis K; Sicilia, Juan Antonio (1) (Journal of Mathematical Chemistry, 08/2017)We present a new semilocal convergence analysis for Newton-like methods using restricted convergence domains in a Banach space setting. The main goal of this study is to expand the applicability of these methods in cases ...