Geodesic
On the accuracy of quadrature formulas with optimal parallelepipedal grids
Čebyševskij sbornik, Tome 24 (2023) no. 4, pp. 335-340.

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The paper obtained a new estimate for the error of quadrature formulas with optimal parallelepipedal meshes modulo $N$.
Keywords: parallelepipedal grid, quadrature formulas, method of optimal coefficients. 
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M. N. Dobrovol'skii; N. N. Dobrovol'skii; N. M. Dobrovol'skii. On the accuracy of quadrature formulas with optimal parallelepipedal grids. Čebyševskij sbornik, Tome 24 (2023) no. 4, pp. 335-340. http://geodesic.mathdoc.fr/item/CHEB_2023_24_4_a19/

[1] Vronskaya, G.T., Dobrovol'skii, N.M., Rodionova, O.V., “Comparisons, sums and products on the reduced system of deductions”, Izvestiya TulGU. Seriya Matematika. Mekhanika. Informatika, 8:1 (2002), 10–28 | MR

[2] Dobrovol'skii, N. M., Korobov, N. M., “On the error estimation of quadrature formulas with optimal parallelepipedal grids”, Chebyshevskii sbornik, 3:1(3) (2002), 41–48 | MR | Zbl

[3] N. N. Dobrovol'skii, N. M. Dobrovol'skii, I. Yu. Rebrova, A. V. Rodionov, “Monoids of natural numbers in the numerical-theoretical method in the approximate analysis”, Chebyshevskii sbornik, 20:1 (2019), 164–179 | DOI

[4] Korobov, N.M., Number-theoretic methods in approximate analysis, Fizmatgiz, Moscow, Russia, 1963

[5] N. M. Korobov, M. N. Dobrovol'skii, N. N. Dobrovol'skii, N. M. Dobrovol'skii, “On the estimation of the error of quadrature formulas with optimal parallelepipedal grids II”, Chebyshevskii sbornik, 24:4 (2023), 345–353 | MR