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Cubo (Temuco)

On-line version ISSN 0719-0646

Abstract

ARGYROS, Ioannis K  and  HILOUT, Saïd. On the semilocal convergence of Newton-type methods, when the derivative is not continuously invertible. Cubo [online]. 2011, vol.13, n.3, pp.1-15. ISSN 0719-0646.  http://dx.doi.org/10.4067/S0719-06462011000300001.

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 Ώ]-[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.

Keywords : Newton-type methods; Banach space; small divisors; non-invertible operators; semilocal convergence; Newton-Kantorovich-type hypothesis..

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