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.
@article{1359,
title = {On the semilocal convergence of Newton--type methods, when the derivative is not continuously invertible},
journal = {CUBO, A Mathematical Journal},
volume = {13},
year = {2011},
language = {en},
url = {http://dml.mathdoc.fr/item/1359}
}
Argyros, Ioannis K.; Hilout, Sa¨ıd. On the semilocal convergence of Newton–type methods, when the derivative is not continuously invertible. CUBO, A Mathematical Journal, Tome 13 (2011) . http://gdmltest.u-ga.fr/item/1359/