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Journal of Applied Mathematics
Volume 2014, Article ID 812072, 9 pages
Research Article

New Families of Third-Order Iterative Methods for Finding Multiple Roots

1Department of Mathematics, Taizhou University, Linhai, Zhejiang 317000, China
2College of Information and Engineering, Hangzhou Polytechnic, Hangzhou, Zhejiang 311402, China
3Department of Mathematics, Brno University of Technology, Brno, Czech Republic
4Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, China
5Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China

Received 5 February 2014; Revised 19 May 2014; Accepted 20 May 2014; Published 15 June 2014

Academic Editor: Alicia Cordero

Copyright © 2014 R. F. Lin 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.


Two families of third-order iterative methods for finding multiple roots of nonlinear equations are developed in this paper. Mild conditions are given to assure the cubic convergence of two iteration schemes (I) and (II). The presented families include many third-order methods for finding multiple roots, such as the known Dong's methods and Neta's method. Some new concrete iterative methods are provided. Each member of the two families requires two evaluations of the function and one of its first derivative per iteration. All these methods require the knowledge of the multiplicity. The obtained methods are also compared in their performance with various other iteration methods via numerical examples, and it is observed that these have better performance than the modified Newton method, and demonstrate at least equal performance to iterative methods of the same order.