Ionica Smeets (Universiteit Leiden): Multidimensional continued fractions and the LLL-algorithm

There are many different algorithms for finding multidimensional continued fractions, but none of them can efficiently find an infinite sequence of simultaneous approximations of prescribed magnitude and quality. We use a dynamic version of the well-known LLL-algorithm for lattice reduction to attack this problem. In this talk we explain how to use the LLL-algorithm to find these simultaneous approximations.