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- Title
New Families of Third-Order Iterative Methods for Finding Multiple Roots.
- Authors
Lin, R. F.; Ren, H. M.; Šmarda, Z.; Wu, Q. B.; Khan, Y.; Hu, J. L.
- Abstract
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-ordermethods for findingmultiple roots, such as the known Dong'smethods andNeta'smethod. 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 obtainedmethods 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.
- Subjects
ITERATIVE methods (Mathematics); MULTIPLES (Mathematics); NONLINEAR equations; STOCHASTIC convergence; MATHEMATICAL analysis; NUMERICAL analysis
- Publication
Journal of Applied Mathematics, 2014, p1
- ISSN
1110-757X
- Publication type
Article
- DOI
10.1155/2014/812072