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Open AccessArticle

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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Academic Editor: Alicia Cordero
Algorithms 2015, 8(2), 309-320; https://doi.org/10.3390/a8020309
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)
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
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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