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Algorithms 2015, 8(2), 309-320; doi:10.3390/a8020309

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

University Institute of Engineering and Technology, Panjab University, Chandigarh 160-014, India
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Author to whom correspondence should be addressed.
Academic Editor: Alicia Cordero
Received: 25 April 2015 / Accepted: 8 June 2015 / Published: 15 June 2015
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
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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. View Full-Text
Keywords: Steffensen-type methods; Kung-Traub conjecture; optimal order of convergence; efficiency index Steffensen-type methods; Kung-Traub conjecture; optimal order of convergence; efficiency index
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Kansal, M.; Kanwar, V.; Bhatia, S. An Optimal Eighth-Order Derivative-Free Family of Potra-Pták’s Method. Algorithms 2015, 8, 309-320.

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