ABSTRACT
Secant method SM is an alternative method of Newton's method NM studied in chapter 2. We study in this chapter the convergence of SM under various conditions and space settings.
We establish in this section new sucient convergence conditions for Secant method to a locally unique solution of a nonlinear equation in a Banach space. Using our new concept of recurrent functions and combining Lipschitz and center{Lipschitz conditions on the divided dierence operator, we obtain a new semilocal convergence analysis of the Secant method. Moreover, our sucient convergence conditions expand the applicability of the Secant method in cases not covered before (cf. [313], [427], [496], [596], [600], [668], [770]).
