Open Access
2014 New Families of Third-Order Iterative Methods for Finding Multiple Roots
R. F. Lin, H. M. Ren, Z. Šmarda, Q. B. Wu, Y. Khan, J. L. Hu
J. Appl. Math. 2014(SI13): 1-9 (2014). DOI: 10.1155/2014/812072


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.


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R. F. Lin. H. M. Ren. Z. Šmarda. Q. B. Wu. Y. Khan. J. L. Hu. "New Families of Third-Order Iterative Methods for Finding Multiple Roots." J. Appl. Math. 2014 (SI13) 1 - 9, 2014.


Published: 2014
First available in Project Euclid: 1 October 2014

zbMATH: 07131885
MathSciNet: MR3226324
Digital Object Identifier: 10.1155/2014/812072

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI13 • 2014
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