Attractor basins of various root-finding methods
Publisher: Naval Postgraduate School; Available from National Technical Information Service
Published: 2001
Place of publication: Monterey, Calif; Springfield, Va
Language: eng
Number of pages: 67
Description: 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.
Notes: Thesis advisors, David Canright, Carlos F. Borges.

Thesis (M.S. in Applied Mathematics) Naval Postgraduate School, June 2001.

Includes bibliographical references (p. 59)

Also available online.

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dk/dk cc:9116 1/17/02