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Chebyshevskii Sbornik, 2021, Volume 22, Issue 5, Pages 365–373
DOI: https://doi.org/10.22405/2226-8383-2021-22-5-365-373
(Mi cheb1142)
 

BRIEF MESSAGE

On generalized non-uniform Korobov grids

N. N. Dobrovol'skiiab, I. Yu. Rebrovab, N. M. Dobrovol'skiib

a Tula State University (Tula)
b Tula State Lev Tolstoy Pedagogical University (Tula)
References:
Abstract: 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.
Funding agency Grant number
Russian Foundation for Basic Research 19-41-710004_р_а
The reported study was funded by RFBR, project number 19-41-710004_r_a. The work was supported financially by a grant from the Government of the Tula Region under Contract ДС/294 dated November 16, 2021.
Received: 04.07.2021
Accepted: 21.12.2021
Document Type: Article
UDC: 511.3
Language: Russian
Citation: N. N. Dobrovol'skii, I. Yu. Rebrova, N. M. Dobrovol'skii, “On generalized non-uniform Korobov grids”, Chebyshevskii Sb., 22:5 (2021), 365–373
Citation in format AMSBIB
\Bibitem{DobRebDob21}
\by N.~N.~Dobrovol'skii, I.~Yu.~Rebrova, N.~M.~Dobrovol'skii
\paper On generalized non-uniform Korobov grids
\jour Chebyshevskii Sb.
\yr 2021
\vol 22
\issue 5
\pages 365--373
\mathnet{http://mi.mathnet.ru/cheb1142}
\crossref{https://doi.org/10.22405/2226-8383-2021-22-5-365-373}
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