The Mathematical Institute, University of Oxford, Eprints Archive

On the fractal characteristics of a stabilised Newton method

Drexler, Michael and Sobey, Ian and Bracher, C. (1995) On the fractal characteristics of a stabilised Newton method. Technical Report. Unspecified. (Submitted)

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Abstract

In this report, we present a complete theory for the fractal that is obtained when applying Newton's Method to find the roots of a complex cubic. We show that a modified Newton's Method improves convergence and does not yield a fractal, but basins of attraction with smooth borders. Extensions to higher-order polynomials and the numerical relevance of this fractal analysis are discussed.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1332
Deposited By:Lotti Ekert
Deposited On:12 Jun 2011 09:53
Last Modified:12 Jun 2011 09:53

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