An Optimal Eighth-Order Derivative-Free Family of Potra-Pták’s Method

Abstract

In this paper, we present a new three-step derivative-free family based on Potra-Pták’s method for solving nonlinear equations numerically. In terms of computational cost, each member of the proposed family requires only four functional evaluations per full iteration to achieve optimal eighth-order convergence. Further, computational results demonstrate that the proposed methods are highly efficient as compared with many well-known methods.

Keywords

• Steffensen-type methods
• Kung-Traub conjecture
• optimal order of convergence
• efficiency index