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.