ABSTRACT
We are concerned in this section with the problem of approximating a locally unique solution x? of (2.1). We revisit in this section Werner's method (cf. [600], [766]) given by
xn+1 = xn A1n F (xn); An = F 0 xn + yn
yn+1 = xn+1 A1n F (xn+1) (n 0; x0; y0 2 D): (8.1)
The local convergence of Werner's method (8.1) was given in (cf. [600], [766]) under Lipschitz conditions on the rst and second Frechet{derivatives given in non{ane invariant form (see (8.53) and (8.54)). The order of convergence of Werner's method (8.1) is 1 +
p 2. The derivation of this method and its
importance has well been explained in (cf. [600], [766]) (see also (cf. [139])). The two{step method uses one inverse and two function evaluations. Note that if x0 = y0, then, (8.1) becomes Newton's method (cf. [78], [792]).
