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

Algorithms

Munish Kansal²  Vinay Kanwar¹  Saurabh Bhatia² 

[1] University Institute of Engineering and Technology, Panjab University, Chandigarh 160-014, India;

关键词: Steffensen-type methods;    Kung-Traub conjecture;    optimal order of convergence;    efficiency index;   

DOI  :  10.3390/a8020309

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland