Distributed computing of simultaneous Diophantine approximation problems

In this paper we present the Multithreaded Advanced Fast Rational Approximation algorithm { MAFRA { for solving n-dimensional simultaneous Dio- phantine approximation problems. We show that in some particular applications the Lenstra-Lenstra-Lov asz ( L 3 ) algorithm can be substituted by the presented one in order to reduce their practical running time. MAFRA was implemented in the following architectures: an Intel Core i5-2450M CPU, an AMD Radeon 7970 GPU card and an Intel cluster with 88 computing nodes.