A UNIFYING SEMI-LOCAL ANALYSIS FOR ITERATIVE ALGORITHMS OF HIGH CONVERGENCE ORDER - Argyros, I. K.; Khattri, S.K. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2013)
We present a unifying semi-local convergence analysis of two-step Newton-type methods for solving nonlinear equations in a Banach space setting. Convergence order of these methods is higher than two. Our analysis expands the applicability of these methods by providing weaker convergence criteria and a convergence analysis-which is tighter than earlier studies [see 1-4,24-34] - is also presented. Numerical examples illustrating the developed theoretical results are also given.