Attractor basins of various root-finding methods
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Authors
Stewart, Bart D.
Subjects
Advisors
Canright, David
Borges, Carlos F.
Date of Issue
2001-06
Date
June 2001
Publisher
Monterey, California. Naval Postgraduate School
Language
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.
Type
Thesis
Description
Series/Report No
Department
Applied Mathematics
Organization
Identifiers
NPS Report Number
Sponsors
Funder
Format
xii, 67 p. : ill. 28 cm.
Citation
Distribution Statement
Rights
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.