论文信息 - Efficient computing of n-dimensional simultaneous Diophantine approximation problems

Efficient computing of n-dimensional simultaneous Diophantine approximation problems

Abstract 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.

Norbert Tihanyi | Norbert Tihanyi | Attila L. Kovács | A. Kovács

[1] G. Szekeres,et al. Rational approximation vectors , 1988 .

[2] Jeffrey C. Lagarias,et al. Best simultaneous Diophantine approximations. II. Behavior of consecutive best approximations , 1982 .

[3] András Frank,et al. An application of simultaneous diophantine approximation in combinatorial optimization , 1987, Comb..

[4] Jeffrey C. Lagarias. The Computational Complexity of Simultaneous Diophantine Approximation Problems , 1985, SIAM J. Comput..

[5] László Lovász,et al. Factoring polynomials with rational coefficients , 1982 .

[6] Kim,et al. Simultaneous rational approximations in the study of dynamical systems. , 1986, Physical review. A, General physics.

[7] Frederik Armknecht,et al. Using the Inhomogeneous Simultaneous Approximation Problem for Cryptographic Design , 2011, AFRICACRYPT.

[8] Mukarram Ahmad,et al. Continued fractions , 2019, Quadratic Number Theory.

[9] Jeffrey C. Lagarias,et al. Best simultaneous Diophantine approximations. I. Growth rates of best approximation denominators , 1982 .

[10] Tadej Kotnik,et al. Computational estimation of the order of zeta (1/2 + it) , 2003, Math. Comput..