Publication:
Basins of attraction for several methods to find simple roots of nonlinear equations

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Authors
Neta, Beny
Scott, Melvin
Chun, Changbum
Subjects
Basin of attraction
Simple roots
Nonlinear equations
Modified super Halley method
King’s family of methods
Halley method
Super Halley method
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Date of Issue
2012
Date
2012
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Abstract
There are many methods for solving a nonlinear algebraic equation. The methods are clas- sified 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 third and fourth order methods to find simple zeros. The relationship between the basins of attraction and the corresponding conjugacy maps will be discussed in numerical experiments. The effect of the extraneous roots on the basins is also discussed.
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The article of record as published may be located at http://dx.doi.org/10.1016/j.amc.2010.04.017
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Applied Mathematics
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Citation
B. Neta, C. Chun, "Basins of attraction for several methods to find simple roots of nonlinear equations," Applied Mathematics and Computation,v. 218 (2012), pp. 10548–10556.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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