A method for recursively generating sequential rational approximations to $\sqrt[n]{k}$
Dynamical Systems
2011-11-15 v1
Abstract
The goal of this paper is to derive a simple recursion that generates a sequence of fractions approximating with increasing accuracy. The recursion is defined in terms of a series of first-order non-linear difference equations and then analyzed as a discrete dynamical system. Convergence behavior is then discussed in the language of initial trajectories and eigenvectors, effectively proving convergence without notions from standard analysis of infinitesimals.
Cite
@article{arxiv.1111.2985,
title = {A method for recursively generating sequential rational approximations to $\sqrt[n]{k}$},
author = {Joe Nance},
journal= {arXiv preprint arXiv:1111.2985},
year = {2011}
}