Attractor Basins of Various Root-Finding Methods
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 2001
- Accession Number
- ADA397512
Entities
People
- Bart D. Stewart
Organizations
- Naval Postgraduate School