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Chebyshevskii Sbornik, 2022, Volume 23, Issue 2, Pages 56–73
DOI: https://doi.org/10.22405/2226-8383-2022-23-2-56-73
(Mi cheb1177)
 

This article is cited in 2 scientific papers (total in 2 papers)

The final deviation and the main quality measure for Korobov grids

N. N. Dobrovol'skiiab, M. N. Dobrovol'skiic, I. Yu. Rebrovaa, N. M. Dobrovol'skiia

a Tula State Lev Tolstoy Pedagogical University (Tula)
b Tula State University (Tula)
c Geophysical centre of RAS (Moscow)
Full-text PDF (701 kB) Citations (2)
References:
Abstract: The paper considers four new concepts: a modified basic measure of the quality of a set of coefficients, absolutely optimal coefficients of the index $s$, the mathematical expectation of the local deviation of the parallelepipedal grid and the variance of the local deviation of the parallelepipedal grid.
It is shown that at least $\frac{(p-1)^s}{2}$ of different sets $(a_1,\ldots,a_s)$ integers mutually prime with the module $p$ will be absolutely optimal sets of the index $s$ with the constant $B=2s$.
It is established that any absolutely optimal set of optimal coefficients of the $s$ index is an optimal set of optimal coefficients of the $s$ index, while any subset of its $s_1$ coefficients is an optimal set of optimal coefficients of the $s_1$ index.
For the finite deviation introduced by N. M. Korobov in 1967, new formulas and estimates are obtained for parallelepipedal grids.
In this paper, for the first time, the concept of the mathematical expectation of a local deviation is considered and a convenient formula for its calculation is found.
The concept of local deviation variance is also considered for the first time.
The paper outlines the directions of further research on this topic.
Keywords: finite deviation, the main measure of quality, Korobov grids, finite Fourier series.
Funding agency Grant number
Russian Foundation for Basic Research 19-41-710004_р_а
This work was prepared under a grant from the RFBR № 19-41-710004 _r_а. The work was supported financially by a grant from the Government of the Tula Region under Contract ДС/294 dated November 16, 2021.
Received: 12.03.2022
Accepted: 22.06.2022
Document Type: Article
UDC: 511.3+511.43
Language: Russian
Citation: N. N. Dobrovol'skii, M. N. Dobrovol'skii, I. Yu. Rebrova, N. M. Dobrovol'skii, “The final deviation and the main quality measure for Korobov grids”, Chebyshevskii Sb., 23:2 (2022), 56–73
Citation in format AMSBIB
\Bibitem{DobDobReb22}
\by N.~N.~Dobrovol'skii, M.~N.~Dobrovol'skii, I.~Yu.~Rebrova, N.~M.~Dobrovol'skii
\paper The final deviation and the main quality measure for Korobov grids
\jour Chebyshevskii Sb.
\yr 2022
\vol 23
\issue 2
\pages 56--73
\mathnet{http://mi.mathnet.ru/cheb1177}
\crossref{https://doi.org/10.22405/2226-8383-2022-23-2-56-73}
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  • https://www.mathnet.ru/eng/cheb/v23/i2/p56
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Full-text PDF :19
    References:15
     
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