ON THE SECANT METHOD FOR SOLVING NONSMOOTH EQUATIONS AND NONDISCRETE INDUCTION

Abstract

In this study we are concerned with the problem of approximating a locallyunique solution of an operator equation in Banach space using the Secant method, and nondiscrete mathematical induction. The differentiability of the operator involved is not assumed. Using a flexible point-based approximation we provide a local as well as a semilocalconvergence analysis for the Secant method. Our results are justified by numerical examplesthat cannot be handled with earlier works.