### Local convergence theorems for Newton's method from data at one point

Ioannis K. Argyros (2002)

Applicationes Mathematicae

Similarity:

We provide local convergence theorems for the convergence of Newton's method to a solution of an equation in a Banach space utilizing only information at one point. It turns out that for analytic operators the convergence radius for Newton's method is enlarged compared with earlier results. A numerical example is also provided that compares our results favorably with earlier ones.