On the Gauss-Newton method for solving equations

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