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
© 2007 Texas State University -- San Marcos
J. Jacobsen, B. Tennis and O. Lewis. "Approximations of Continuous Newton's Method: An Extension of Cayley's Problem," Electronic Journal of Differential Equations, 15, (2007), pp. 163-173.
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This article is also available from the Electronic Journal of Differential Equations at ftp://ejde.math.txstate.edu/pub/EJDE/conf-proc/15/j1/abstr.html.