New Families of Third-Order Iterative Methods for Finding Multiple Roots
Joint Authors
Ren, H. M.
Hu, J. L.
Khan, Yasir
Šmarda, Zdenĕk
Wu, Qingbiao
Lin, Rongfei
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-06-15
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Lin, Rongfei& Ren, H. M.& Šmarda, Zdenĕk& Wu, Qingbiao& Khan, Yasir& Hu, J. L.. 2014. New Families of Third-Order Iterative Methods for Finding Multiple Roots. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-499976
Modern Language Association (MLA)
Lin, Rongfei…[et al.]. New Families of Third-Order Iterative Methods for Finding Multiple Roots. Journal of Applied Mathematics No. 2014 (2014), pp.1-9.
https://search.emarefa.net/detail/BIM-499976
American Medical Association (AMA)
Lin, Rongfei& Ren, H. M.& Šmarda, Zdenĕk& Wu, Qingbiao& Khan, Yasir& Hu, J. L.. New Families of Third-Order Iterative Methods for Finding Multiple Roots. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-499976
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-499976