International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 979245, 13 pages
http://dx.doi.org/10.1155/2012/979245
Research Article

On a 4-Point Sixteenth-Order King Family of Iterative Methods for Solving Nonlinear Equations

Diyashvir Kreetee Rajiv Babajee1 and Rajinder Thukral2

1Department of Applied Mathematical Sciences, School of Innovative Technologies and Engineering, University of Technology, Mauritius, La Tour Koenig, Pointe aux Sables, Mauritius
2Padé Research Centre, 39 Deanswood Hill, Leeds, West Yorkshire LS17 5JS, UK

Received 23 March 2012; Accepted 14 May 2012

Academic Editor: Songxiao Li

Copyright © 2012 Diyashvir Kreetee Rajiv Babajee and Rajinder Thukral. 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

A one-parameter 4-point sixteenth-order King-type family of iterative methods which satisfy the famous Kung-Traub conjecture is proposed. The convergence of the family is proved, and numerical experiments are carried out to find the best member of the family. In most experiments, the best member was found to be a sixteenth-order Ostrowski-type method.