Fractal Basins of Attraction Associated with a Damped Newton's Method
Abstract
An intriguing and unexpected result for students learning numerical analysis is that Newton's method, applied to the simple polynomial z3 - 1 = 0 in the complex plane, leads to intricately interwoven basins of attraction of the roots. As an example of an interesting open question that may help to stimulate student interest in numerical analysis, we investigate the question of whether a damping method, which is designed to increase the likelihood of convergence for Newton's method, modifies the fractal structure of the basin boundaries. The overlap of the frontiers of numerical analysis and nonlinear dynamics provides many other problems that can help to make numerical analysis courses interesting.
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SIAM Review
Pages: 102 - 109
ISSN (online): 1095-7200
Copyright
Copyright © 1998 Society for Industrial and Applied Mathematics.
History
Published online: 4 August 2006
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