Analysis of Traub’s Method for Cubic Polynomials

Abstract

The dynamical analysis of Kurchatov’s scheme is extended to Traub’s method. The difference here is that Traub’s method requires two additional starting points. Therefore, the map is three-dimensional instead of 2-D. We obtain a complete description of the dynamical planes and show that the method is stable for cubic polynomials.

Keywords

• nonlinear equations
• simple roots
• derivative-free methods