Resumo

ARGYROS, Ioaniss K  e  HITLOUT, Saïd. On the Gauss-Newton method for solving equations. Proyecciones (Antofagasta) [online]. 2012, vol.31, n.1, pp. 11-24. ISSN 0716-0917.  doi: 10.4067/S0716-09172012000100002.

We use a combination of the center-Lipschitz condition with the Lipschitz condition condition on the Frechet-derivative of the operator involved to provide a semilocal convergence analysis of the Gauss-Newton method to a solution of an equation. Using more precise estimates on the distances involved, under weaker hypotheses, and under the same computational cost, we provide an analysis of the Gauss- Newton method with the following advantages over the corresponding results in [8]: larger convergence domain; finer error estimates on the distances involved, and an at least as precise information on the location ofthe solution

Palavras-chave : Gauss-Newton method; semilocal convergence; Frechet- derivative; Lipschitz/center-Lipschitz condition; convergence domain.