Optimizing the applicability of a theorem by F. Potra for Newton-like methods
Magreñán, Á. Alberto (1)
Argyros, Ioannis K
Tipo de Ítem:Articulo Revista Indexada
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 methods in cases not covered in other studies such as Dennis (1971) , Ezquerro et al. (2000, 2010) [13,14], Kornstaedt (1975) , Potra and Ptak (1984) , Potra (1985, 1979, 1982, 1981, 1984) [23,25,26,27,28], Proinov (2010) , Schmidt (1978)  or Yamamoto (1987) . The advantages of our approach also include a tighter convergence analysis under the same computational cost. Applications, where the older convergence criteria are not satisfied but the new convergence criteria are satisfied are also given in this study. (C) 2014 Elsevier Inc. All rights reserved.
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 ...
A study on the local convergence and the dynamics of Chebyshev–Halley–type methods free from second derivative Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Numerical Algorithms, 01/2016)We study the local convergence of Chebyshev-Halley-type methods of convergence order at least five to approximate a locally unique solution of a nonlinear equation. Earlier studies such as Behl (2013), Bruns and Bailey ...