Geodesic
Quality function for the approximation of quadratic algebraic nets~---~II
Čebyševskij sbornik, Tome 21 (2020) no. 3, pp. 223-231.

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This paper is devoted to the construction of fast algorithms for calculating the quality function of rational grids that approximate quadratic algebraic grids in the General case of the maximum lattice of integer algebraic numbers. 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. 
@article{CHEB_2020_21_3_a17,
     author = {A. V. Mikhlyaeva},
     title = {Quality function for the approximation of quadratic algebraic {nets~---~II}},
     journal = {\v{C}eby\v{s}evskij sbornik},
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     publisher = {mathdoc},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2020_21_3_a17/}
}
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A. V. Mikhlyaeva. Quality function for the approximation of quadratic algebraic nets~---~II. Čebyševskij sbornik, Tome 21 (2020) no. 3, pp. 223-231. http://geodesic.mathdoc.fr/item/CHEB_2020_21_3_a17/

[1] Vronskaya G. T., Dobrovol'skii N., Deviations of flat grids, ed. N. M. Dobrovol'skii, Tula, 2012, 193 pp.

[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

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