Sixth Mississippi State Conference on Differential Equations and
Computational Simulations.
Electronic Journal of Differential Equations,
Conference 15 (2007), pp. 163-173.
Title: Approximations of continuous Newton's method:
An extension of Cayley's problem
Authors: Jon Jacobsen (Harvey Mudd College, Claremont, CA, USA)
Owen Lewis (Portland, OR, USA
Bradley Tennis (Stanford Univ., Stanford, CA, USA)
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.