论文标题
AGM计算的数字揭示了反函数的周期性
Computed multivalues of AGM reveal periodicities of inverse functions
论文作者
论文摘要
本文显示，每当计算几何均值时，如何进行两种选择，而当选择在评估算术几何平均值的第一n步骤中，此过程的重复总体屈服2到幂n不同的值。这不仅发生在计算第一类完整椭圆积分的简单股东大会上，而且还以类似的方法来计算第一和第二类的完整椭圆形积分。
The article shows how two choices are possible whenever computing the geometric mean, and the repetition of this process can in general yield 2-to-the power N different values when the choices are compounded in the first N steps of evaluation of the arithmetic-geometric mean. This happens not only in the simple AGM involved in the computation of the complete elliptic integral of the first kind, but also in analogous methods for the computation of the complete and incomplete elliptic integrals of the first and second kind.
