TITLE:
Two New Iterated Maps for Numerical Nth Root Evaluation
AUTHORS:
Charles Corrêa Dias, Fernanda Jaiara Dellajustina, Luciano Camargo Martins
KEYWORDS:
Iterated Map, Nth Root of a Real Number, Numerical Method, Newton-Raphson Method, Dynamical System
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.19,
November
5,
2014
ABSTRACT: In this paper we propose two original iterated maps to numerically approximate the nth root of a real number. Comparisons between the new maps and the famous Newton-Raphson method are carried out, including fixed point determination, stability analysis and measure of the mean convergence time, which is confirmed by our analytical convergence time model. Stability of solutions is confirmed by measuring the Lyapunov exponent over the parameter space of each map. A generalization of the second map is proposed, giving rise to a family of new maps to address the same problem. This work is developed within the language of discrete dynamical systems.