Geodesic
On generalized non-uniform Korobov grids
Čebyševskij sbornik, Tome 22 (2021) no. 5, pp. 365-373 Cet article a éte moissonné depuis la source Math-Net.Ru

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Generalized non-uniform Korobov grids are considered in the paper. Three new constructions are considered: the product of non-uniform grids by mutually simple modules; modified non-uniform grids; the product of an uneven grid and a parallelepipedal grid by a mutually simple module. A paradoxical result is established about the value of the mathematical expectation of the error of approximate integration over modified non-uniform grids. It is shown that the algorithm of approximate integration using the product of an uneven grid and a parallelepipedal grid in a mutually simple module is unsaturated with the order $\frac{\alpha}{2}$.
Keywords: hyperbolic zeta function of the grid, uneven Korobov grids, hyperbolic zeta function of the lattice. 
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     title = {On generalized non-uniform {Korobov} grids},
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N. N. Dobrovol'skii; I. Yu. Rebrova; N. M. Dobrovol'skii. On generalized non-uniform Korobov grids. Čebyševskij sbornik, Tome 22 (2021) no. 5, pp. 365-373. http://geodesic.mathdoc.fr/item/CHEB_2021_22_5_a27/

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