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The Scientific World Journal
Volume 2015 (2015), Article ID 934260, 12 pages
http://dx.doi.org/10.1155/2015/934260
Research Article

A General Class of Derivative Free Optimal Root Finding Methods Based on Rational Interpolation

Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan

Received 22 May 2014; Accepted 18 August 2014

Academic Editor: S. A. Mohiuddine

Copyright © 2015 Fiza Zafar et al. 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.

Abstract

We construct a new general class of derivative free -point iterative methods of optimal order of convergence using rational interpolant. The special cases of this class are obtained. These methods do not need Newton’s iterate in the first step of their iterative schemes. Numerical computations are presented to show that the new methods are efficient and can be seen as better alternates.