An Optimal Family of Fast 16th-Order Derivative-Free Multipoint Simple-Root Finders for Nonlinear Equations

Abstract

This paper investigates an optimal family of derivative-free fast 16th-order multipoint iterative methods for solving nonlinear equations using polynomial weighting functions and a real control parameter. Convergence analyses and computational properties are shown along with a comparison of the classical work done by Kung–Traub in 1974. The underlying theoretical treatment and computational advantage of faster computing time is well supported through a variety of concrete numerical examples.