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)
Tipo de Ítem:Articulo Revista Indexada
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 compare the new result with an older one and see that the former improves the latter. (C) 2018 Elsevier B.V. All rights reserved.
Este ítem aparece en la(s) siguiente(s) colección(es)
Mostrando ítems relacionados por Título, autor o materia.
Convergence of Newton's method under Vertgeim conditions: new extensions using restricted convergence domains Argyros, Ioannis K; Ezquerro, J A; Hernández-Verón, M A; Magreñán, Á. Alberto (1) (Journal of Mathematical Chemistry, 08/2017)We present new sufficient convergence conditions for the semilocal convergence of Newton’s method to a locally unique solution of a nonlinear equation in a Banach space. We use Hölder and center Hölder conditions, instead ...
Argyros, Ioannis K; Ezquerro, J A; Hernández-Verón, M A; Hilout, S; Magreñán, Á. Alberto (1) (Taiwanese Journal of Mathematics, 04/2015)We present two new semilocal convergence analyses for secant-like methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. These methods include the secant, Newton's ...
Ezquerro, J A; Hernández-Verón, M A; Magreñán, Á. Alberto (1) (Journal of Computational and Applied Mathematics, 03/2018)We analyze the semilocal convergence of Newton's method under a center Lipschitz condition for the second derivative of the operator involved different from that used by other authors until now. In particular, we propose ...