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On the best joint Dirichlet approximations

I. N. Balaba, I. N. Gavrilov, T. A. Kalinkina, N. V. Medvedeva, V. S. Solovieva, E. S. Ulchenko

Tula State Lev Tolstoy Pedagogical University (Tula)

Abstract: This paper develops a program for finding best joint approximations of the second kind for dependent irrationalities.
The results of calculations using the mathcad15 computer mathematics system are presented, confirming the conclusions of [2] that, starting from a certain point, all joint best approximations of the second kind for dependent random variables are determined by the denominators of the convergents of the fundamental irrationality, of which all others are multiples.

Keywords: joint best Dirichlet approximations.

UDC: 511.3

Received: 22.05.2025
Accepted: 17.10.2025

DOI: 10.22405/2226-8383-2025-26-4-431-436