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Advances in Numerical Analysis
Volume 2012 (2012), Article ID 346420, 18 pages
http://dx.doi.org/10.1155/2012/346420
Research Article

An Efficient Family of Root-Finding Methods with Optimal Eighth-Order Convergence

1Department of Applied Sciences, DAV Institute of Engineering and Technology, Kabirnagar 144008, India
2Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal 148106, India

Received 21 May 2012; Accepted 4 September 2012

Academic Editor: Nils Henrik Risebro

Copyright © 2012 Rajni Sharma and Janak Raj Sharma. 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 derive a family of eighth-order multipoint methods for the solution of nonlinear equations. In terms of computational cost, the family requires evaluations of only three functions and one first derivative per iteration. This implies that the efficiency index of the present methods is 1.682. Kung and Traub (1974) conjectured that multipoint iteration methods without memory based on n evaluations have optimal order . Thus, the family agrees with Kung-Traub conjecture for the case . Computational results demonstrate that the developed methods are efficient and robust as compared with many well-known methods.