On the semilocal convergence of Newton-type methods, when the derivative is not continuously invertible

摘要

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 Frechet-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.