Table of Contents
Chinese Journal of Mathematics
Volume 2014, Article ID 369713, 7 pages
http://dx.doi.org/10.1155/2014/369713
Research Article

A New Optimal Eighth-Order Ostrowski-Type Family of Iterative Methods for Solving Nonlinear Equations

1Department of Applied Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 65138, Iran
2Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan 987-98155, Iran

Received 6 September 2013; Accepted 2 October 2013; Published 13 March 2014

Academic Editors: Q. Guo and Z.-Y. Li

Copyright © 2014 Taher Lotfi and Tahereh Eftekhari. 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

Based on Ostrowski's method, a new family of eighth-order iterative methods for solving nonlinear equations by using weight function methods is presented. Per iteration the new methods require three evaluations of the function and one evaluation of its first derivative. Therefore, this family of methods has the efficiency index which equals 1.682. Kung and Traub conjectured that a multipoint iteration without memory based on evaluations could achieve optimal convergence order . Thus, we provide a new class which agrees with the conjecture of Kung-Traub for . Numerical comparisons are made to show the performance of the presented methods.