Two New Iterated Maps for Numerical Nth Root Evaluation

Charles Corrêa Dias¹, Fernanda Jaiara Dellajustina², Luciano Camargo Martins²

¹Department of Electrical Engineering, Universidade do Estado de Santa Catarina (UDESC), Joinville, Brazil.
²Department of Physics, Universidade do Estado de Santa Catarina (UDESC), Joinville, Brazil.

DOI: 10.4236/am.2014.519283                

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.

Keywords

Iterated Map, Nth Root of a Real Number, Numerical Method, Newton-Raphson Method, Dynamical System

Conflicts of Interest

The authors declare no conflicts of interest.

References

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