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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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     title = {About the partial quotients of one of the continued fractions},
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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/

[1] Vronskaya G. T., Dobrovol'skii N. N., Deviations of flat grids, monograph, ed. N. M. Dobrovol'skii, Tula, 2012

[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