ABSTRACT
Gauss{Newton method is also an alternative method for Newton's method. We study in this chapter the convergence of Gauss{Newton method under Lipschitz and average Lipschitz{type conditions.
We establish in this section a new semilocal convergence analysis of the Gauss{Newton method GNM for solving nonlinear equation in the Euclidean space. Using our new idea of recurrent functions and a combination of center{Lipschitz, Lipschitz conditions, we provide under the same or weaker hypotheses than before (cf. [226], [469]), a tighter convergence analysis. The results can be extented in case outer or generalized inverses are used.
