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On a two-step optimal Steffensen-type method: Relaxed local and semi-local convergence analysis and dynamical stability.
- Source :
-
Journal of Mathematical Analysis & Applications . Dec2018, Vol. 468 Issue 1, p240-269. 30p. - Publication Year :
- 2018
-
Abstract
- Abstract In this paper, we study on the local and semi-local convergence and dynamic of an iterative optimal two-step Steffensen's method. We study local convergence by using Lipschitz conditions and continuity of differentiable function F. We also obtain semi-local convergence by using majorizing sequences. By this approach, we can obtain the convergence of the method by minimum of auxiliary sequences and few initial conditions. Moreover, we analyze the stability of the method via Julia sets and parameter planes that is a novelty for Steffensen-type methods. We extend this method for obtaining the sign function of a matrix. Numerical examples are given to confirm our theoretical results. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 468
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 131633465
- Full Text :
- https://doi.org/10.1016/j.jmaa.2018.08.007