Sixth Mississippi State Conference on Differential Equations and Computational Simulations.
Electron. J. Diff. Eqns., Conference 15 (2007), pp. 163-173.

Approximations of continuous Newton's method: An extension of Cayley's problem

Jon Jacobsen, Owen Lewis, Bradley Tennis

Continuous Newton's Method refers to a certain dynamical system whose associated flow generically tends to the roots of a given polynomial. An Euler approximation of this system, with step size h=1, yields the discrete Newton's method algorithm for finding roots. In this note we contrast Euler approximations with several different approximations of the continuous ODE system and, using computer experiments, consider their impact on the associated fractal basin boundaries of the roots.

Published February 28, 2007.
Math Subject Classifications: 34C35, 58C15, 28A80, 65H10.
Key Words: Newton's method; damping; fractal basins of attraction.

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Jon Jacobsen
Mathematics Department, Harvey Mudd College
301 Platt Blvd
Claremont, CA 91711, USA
Owen Lewis
4047 North Castle Ave.
Portland, OR 97227, USA
Bradley Tennis
Computer Science Department, Stanford University
Stanford, CA 94305, USA

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