A UNIFIED APPROACH FOR ENLARGING THE RADIUS OF CONVERGENCE FOR NEWTON'S METHOD AND APPLICATIONS

Abstract

Local convergence theorems are provided for Newton's method in a Banach space setting. Our conditions are very general and in special cases provide larger convergence radius than before, which in turn allows a wider choice of initial guesses for Newton's method. This observations is important in numerical analysis and finds applications in step length selection in predictor-corrector continuation procedures.