Two New Iterated Maps for Numerical Nth Root Evaluation

Autor:	Fernanda Jaiara Dellajustina, Luciano Camargo Martins, Charles Corrêa Dias
Rok vydání:	2014
Předmět:	symbols.namesake Dynamical systems theory Iterated function Mathematical analysis symbols General Medicine Lyapunov exponent Fixed point Dynamical system Newton's method nth root Measure (mathematics) Mathematics
Zdroj:	Applied Mathematics. :2974-2981
ISSN:	2152-7393 2152-7385
DOI:	10.4236/am.2014.519283
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::8e71feb8c5523a369557b055c6c3d5c2 https://doi.org/10.4236/am.2014.519283 Zobrazit plný text záznamu