A method for recursively generating sequential rational approximations to $\sqrt[n]{k}$

Details A method for recursively generating sequential rational approximations to $\sqrt[n]{k}$ A method for recursively generating sequential rational approximations to $\sqrt[n]{k}$

2011-11-13

arxiv.org/abs/1111.2985v1

Mathematics

Dynamical Systems

Scientific paper

The goal of this paper is to derive a simple recursion that generates a sequence of fractions approximating $\sqrt[n]{k}$ 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.

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