Expanding the Applicability of High-Order Traub-Type Iterative Procedures

We propose a collection of hybrid methods combining Newton's method with frozen derivatives and a family of high-order iterative schemes. We present semilocal convergence results for this collection on a Banach space setting. Using a more precise majorizing sequence and under the same or weaker convergence conditions than the ones in earlier studies, we expand the applicability of these iterative procedures. © 2013 Springer Science+Business Media New York.