Diophantine Approximation via the ILLL Algorithm

Abstract

We are studying the Iterated LLL algorithm (or ILLL algorithm) due to W. Bosma and I. Smeets. For a given list of irrational numbers, the ILLL algorithm returns a series of efficient rational approximations to the numbers. The central aim of our on-going project is to develop a new version of ILLL that will incorporate the continued fraction algorithm for storing real numbers for preprocessing. Since the continued fraction algorithm is optimal, we expect that our planned implementation will give us new insight into the overall performance of the ILLL algorithm.