On Hermite's Algorithm

Abstract

In this thesis, I discuss Hermite's continued fraction algorithm. First, I talk about the ordinary continued fraction algorithm and some of its properties. After that, I treat Hermite's algorithm, visualize it and deduce some of its properties. Then, I compare the two algorithms, by both comparing the properties and actually calculating approximations using both algorithms in Mathematica. It turns out that for most numbers, Hermite's algorithm gives a more precise approximation than the ordinary continued fraction algorithm. However, the ordinary algorithm is easier to execute by hand and is more intuitive.