On the semilocal convergence of Newton–type methods, when the derivative is not continuously invertible
Author
Argyros, Ioannis K.
Hilout, Saïd
Full text
https://revistas.ufro.cl/ojs/index.php/cubo/article/view/135910.4067/S0719-06462011000300001
Abstract
We provide a semilocal convergence analysis for Newton–type methods to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The Fr´echet– derivative of the operator involved is not necessarily continuous invertible. This way we extend the applicability of Newton–type methods [1]–[12]. We also provide weaker sufficient convergence conditions, and finer error bound on the distances involved (under the same computational cost) than [1]–[12], in some intersting cases. Numerical examples are also provided in this study.