Extending the local convergence analysis of Newton's method

Abstract

We present a new local convergence analysis of Newton's method in order to approxi-mate a locally unique solution of a non-linear equation in a Banach space setting. The new results: enlarge the radius of convergence and also improve the error bounds on the distances involved. These advantages are obtained under the same computational cost as in earlier studies. Numerical examples where our results can apply to solve equations but earlier ones cannot apply to solve these equations are also provided in this study.