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Journal of Applied Mathematics
Volume 2013, Article ID 369067, 7 pages
Research Article

A Two-Parameter Family of Fourth-Order Iterative Methods with Optimal Convergence for Multiple Zeros

Department of Applied Mathematics, Dankook University, Cheonan 330-714, Republic of Korea

Received 25 October 2012; Revised 2 December 2012; Accepted 19 December 2012

Academic Editor: Fazlollah Soleymani

Copyright © 2013 Young Ik Kim and Young Hee Geum. 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.


We develop a family of fourth-order iterative methods using the weighted harmonic mean of two derivative functions to compute approximate multiple roots of nonlinear equations. They are proved to be optimally convergent in the sense of Kung-Traub’s optimal order. Numerical experiments for various test equations confirm well the validity of convergence and asymptotic error constants for the developed methods.