Journal of Numerical Analysis and Approximation Theory (Sep 2017)
On Newton's method for subanalytic equations
Abstract
We present local and semilocal convergence results for Newton’s method in order to approximate solutions of subanalytic equations. The local convergence results are given under weaker conditions than in earlier studies such as [9], [10], [14], [15], [24], [25], [26], resulting to a larger convergence ball and a smaller ratio of convergence. In the semilocal convergence case contravariant conditions not used before are employed to show the convergence of Newton’s method. Numerical examples illustrating the advantages of our approach are also presented in this study.