Two New Iterated Maps for Numerical Nth Root Evaluation

• 作者: Charles Corrêa Dias Fernanda Jaiara Dellajustina Luciano Camargo Martins
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: ITERATED Map Nth ROOT of a Real Number NUMERICAL METHOD NEWTON-RAPHSON METHOD Dynamical System
• 年，卷（期）: 2014,（19）
• 页码范围: 2974-2981
• 页数: 8页
• 分类号: O1

摘要

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.