Jon Jacobsen, Owen Lewis, Bradley Tennis
Abstract:
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 email: jacobsen@math.hmc.edu |
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Owen Lewis 4047 North Castle Ave. Portland, OR 97227, USA email: owen.lewis@gmail.com |
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Bradley Tennis Computer Science Department, Stanford University Stanford, CA 94305, USA email: btennis@stanford.edu |
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