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Acta Universitatis Sapientiae, Informatica

The Journal of "Sapientia" Hungarian University of Transylvania

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Efficient computing of n-dimensional simultaneous Diophantine approximation problems

Attila Kovács / Norbert Tihanyi
Published Online: 2014-05-30 | DOI: https://doi.org/10.2478/ausi-2014-0002


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.

Keywords : Diophantine approximation


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About the article

Received: 2013-04-10

Revised: 2013-06-08

Published Online: 2014-05-30

Published in Print: 2013-07-01

Citation Information: Acta Universitatis Sapientiae, Informatica, Volume 5, Issue 1, Pages 16–34, ISSN (Online) 2066-7760, DOI: https://doi.org/10.2478/ausi-2014-0002.

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© 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. BY-NC-ND 3.0

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