Vol. 1, Issue 4, Part B (2015)

Abstract
Polynomial root finding is the origin of some fundamental discoveries in Mathematics and Sciences. Where analytical or exact method fails, numerical approximation methods often succeed. We will investigate the numerical root finding method of Newton from a dynamical system perspective. Consider a complex valued function f on the Riemann Sphere. For in the Sphere, we have sequence, f ( ), f ² ( ), . . . which becomes a dynamical system. We are essentially interested in the long term behavior of this system. We address the connection between behavior of Halley’s methods with Voronoi diagram of the roots of the underlying polynomial