Local Convergence and Radius of Convergence for Modified Newton Method

We investigate the local convergence of modified Newton method, i.e., the classical Newton method in which the derivative is periodically re-evaluated. Based on the convergence properties of Picard iteration for demicontractive mappings, we give an algorithm to estimate the local radius of convergence for considered method. Numerical experiments show that the proposed algorithm gives estimated radii which are very close to or even equal with the best ones.