递归生成$\sqrt[n]{k}$序列有理逼近的一种方法
A method for recursively generating sequential rational approximations to $\sqrt[n]{k}$
摘要：
本文的目标是得到一个简单的递归，产生一个序列的分数近似$\sqrt[n]{k}$的精度不断提高。该递归被定义为一系列的一阶非线性差分方程，然后分析作为一个离散的动力系统。收敛行为，然后讨论的语言的初始轨迹和特征向量，有效地证明收敛没有概念的标准分析的无穷小。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
