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Attractor basins of various root-finding methods

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Author
Stewart, Bart D.
Date
2001-06
Advisor
Canright, David
Borges, Carlos F.
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Abstract
Real world phenomena commonly exhibit nonlinear relationships, complex geometry, and intricate processes. Analytic or exact solution methods only address a minor class of such phenomena. Consequently, numerical approximation methods, such as root-finding methods, can be used. The goal is, by making use of a variety of root-finding methods (Newton-Rhapson, Chebyshev, Halley and Laguerre), to gain a qualitative appreciation on how various root- finding methods address many prevailing real-world concerns, to include, how are suitable approximation methods determined; when do root finding methods converge; and how long for convergence? Answers to the questions were gained through examining the basins of attraction of the root-finding methods. Different methods generate different basins of attraction. In the end, each method appears to have its own advantages and disadvantages.
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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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http://hdl.handle.net/10945/10997
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