Geodesic
About the partial quotients of one of the continued fractions
Čebyševskij sbornik, Tome 20 (2019) no. 1, pp. 298-306

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This paper is devoted to the computation of partial quotiens of decomposition of $\frac{a_m}{N_m}$ into a continued fraction, where ${a_m}$ and ${N_m}$ are parameters of a parallelepipedal grid, which is an approximation of a quadratic algebraic grid by a rational grid. The results of this work allow us to implement fast algorithms for calculating the quality function of these rational approximations.
Keywords: quadratic fields, approximation of algebraic grids, quality function, generalized parallelepipedal grid. 
A. N. Kormacheva. About the partial quotients of one of the continued fractions. Čebyševskij sbornik, Tome 20 (2019) no. 1, pp. 298-306. http://geodesic.mathdoc.fr/item/CHEB_2019_20_1_a19/
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[2] Davenport H., The higher arithmetic, Nauka, M., 1965, 176 pp.

[3] A. V. Mikhlyaeva, “Approximation of quadratic algebraic lattices and nets by integer lattices and rational nets”, Chebyshevskii sbornik, 19:3 (2018), 241–256 | Zbl

[4] Mikhlyaeva A. V., “Quality function for the approximation of quadratic algebraic nets”, Chebyshevskii sbornik, 20:1 (2019), 307–312 | Zbl