Geodesic
Quality function for the approximation of quadratic algebraic nets
Čebyševskij sbornik, Tome 20 (2019) no. 1, pp. 307-312.

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This work is devoted to the construction of fast algorithms for calculating the quality function of rational grids approximating quadratic algebraic nets. It is shown that the generalized parallelepipedal net approximating the quadratic algebraic net is parallelepiped.As a consequence, an algorithm for calculating the quality function for $O\left(\ln{N}\right)$ arithmetic operations is constructed.
Keywords: quadratic fields, approximation of algebraic grids, quality function, generalized parallelepipedal grid. 
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     author = {A. V. Mikhlyaeva},
     title = {Quality function for the approximation of quadratic algebraic nets},
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     url = {http://geodesic.mathdoc.fr/item/CHEB_2019_20_1_a20/}
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A. V. Mikhlyaeva. Quality function for the approximation of quadratic algebraic nets. Čebyševskij sbornik, Tome 20 (2019) no. 1, pp. 307-312. http://geodesic.mathdoc.fr/item/CHEB_2019_20_1_a20/

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

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