Efficient computing of n-dimensional simultaneous Diophantine approximation problems
e | 30 mag 2014
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Pubblicato online: 30 mag 2014
Pagine: 16 - 34
Ricevuto: 10 apr 2013
DOI: https://doi.org/10.2478/ausi-2014-0002
© 2014
This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper we consider two algorithmic problems of simultaneous Diophantine approximations. The first algorithm produces a full solution set for approximating an irrational number with rationals with common denominators from a given interval. The second one aims at finding as many simultaneous solutions as possible in a given time unit. All the presented algorithms are implemented, tested and the PariGP version made publicly available.