Basin attractors for various methods

There are many methods for the solution of a nonlinear algebraic equation. The methods are classified by the order, informational efficiency and efficiency index. Here we consider other criteria, namely the basin of attraction of the method and its dependence on the order. We discuss several methods...

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Bibliographic Details
Published in:Applied mathematics and computation 2011-11, Vol.218 (6), p.2584-2599
Main Authors: Scott, Melvin, Neta, Beny, Chun, Changbum
Format: Article
Language:English
Subjects:
Algebra
Attraction
Basin of attraction
Basins
Computational efficiency
Computing time
Criteria
Iterative methods
Mathematical analysis
Mathematical models
Nonlinear equations
Simple roots
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Summary:There are many methods for the solution of a nonlinear algebraic equation. The methods are classified by the order, informational efficiency and efficiency index. Here we consider other criteria, namely the basin of attraction of the method and its dependence on the order. We discuss several methods of various orders and present the basin of attraction for several examples. It can be seen that not all higher order methods were created equal. Newton’s, Halley’s, Murakami’s and Neta–Johnson’s methods are consistently better than the others. In two of the examples Neta’s 16th order scheme was also as good.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.07.076