Approximations of Continuous Newton's Method: An Extension of Cayley's Problem

Authors

Jon T. Jacobsen, Harvey Mudd CollegeFollow
Owen Lewis '05, Harvey Mudd CollegeFollow
Bradley Tennis '06, Harvey Mudd CollegeFollow

Student Co-author

HMC Undergraduate

Document Type

Article

Department

Mathematics (HMC)

Publication Date

2-2007

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

Comments

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.

Rights Information

© 2007 Texas State University -- San Marcos

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Recommended Citation

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.