International Journal of Applied Research
Vol. 1, Issue 3, Part C (2015)
Newton’s method and voronoi diagram
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 and pick x0 in the domain of f. If we iterate this function around x0, then we have sequence x0, f (x0), f ² (x0), . . . which becomes a dynamical system. We are essentially interested in the long term behavior of this system. We address the connection between behavior of both Newton’s and Halley’s methods with Voronoi diagram of underlying polynomial roots.
How to cite this article:
Anudeep Nain. Newton’s method and voronoi diagram. Int J Appl Res 2015;1(3):129-134.