Dynamics of a higher-order family of iterative methods

We study the dynamics of a higher-order family of iterative methods for solving non-linear equations. We show that these iterative root-finding methods are generally convergent when extracting radicals. We examine the Julia sets of these methods with particular polynomials. The examination takes pla...

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Bibliographic Details
Published in:Journal of Complexity 2011-04, Vol.27 (2), p.221-229
Main Authors: Honorato, Gerardo, Plaza, Sergio, Romero, Natalia
Format: Article
Language:English
Subjects:
General convergence
Iterative processes
Julia sets
Non-linear equations
Order of convergence
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Summary:We study the dynamics of a higher-order family of iterative methods for solving non-linear equations. We show that these iterative root-finding methods are generally convergent when extracting radicals. We examine the Julia sets of these methods with particular polynomials. The examination takes place in the complex plane.
ISSN:0885-064X
1090-2708
DOI:10.1016/j.jco.2010.10.005