Extensions on a local convergence result by Dennis and Schnabel for Newton's method with applications

Abstract

The aim of this article is to extend the applicability of Newton's method involving k-Fréchet differentiable operators. By using tighter majorizing functions and under the same computational cost as in earlier works, we find at least as large radius of convergence and at least as tighter error bounds on the distances involved. Numerical examples further validate the theoretical results.