Fractal basins of attraction associated with a damped Newton's method

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Epureanu, BI; Greenside, HS

Published Date

  • January 1, 1998

Published In

Volume / Issue

  • 40 / 1

Start / End Page

  • 102 - 109

International Standard Serial Number (ISSN)

  • 0036-1445

Digital Object Identifier (DOI)

  • 10.1137/S0036144596310033

Citation Source

  • Scopus