Geodesic
On generalized non-uniform Korobov grids
Čebyševskij sbornik, Tome 22 (2021) no. 5, pp. 365-373.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{CHEB_2021_22_5_a27,
     author = {N. N. Dobrovol'skii and I. Yu. Rebrova and N. M. Dobrovol'skii},
     title = {On generalized non-uniform {Korobov} grids},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {365--373},
     publisher = {mathdoc},
     volume = {22},
     number = {5},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2021_22_5_a27/}
}
TY  - JOUR
AU  - N. N. Dobrovol'skii
AU  - I. Yu. Rebrova
AU  - N. M. Dobrovol'skii
TI  - On generalized non-uniform Korobov grids
JO  - Čebyševskij sbornik
PY  - 2021
SP  - 365
EP  - 373
VL  - 22
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2021_22_5_a27/
LA  - ru
ID  - CHEB_2021_22_5_a27
ER  - 
%0 Journal Article
%A N. N. Dobrovol'skii
%A I. Yu. Rebrova
%A N. M. Dobrovol'skii
%T On generalized non-uniform Korobov grids
%J Čebyševskij sbornik
%D 2021
%P 365-373
%V 22
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2021_22_5_a27/
%G ru
%F CHEB_2021_22_5_a27
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/

[1] Dobrovolskaya L. P., Dobrovolskii N. M., Simonov A. S., “O pogreshnosti priblizhennogo integrirovaniya po modifitsirovannym setkam”, Chebyshevskii sbornik, 9:1(25) (2008), 185–223 | MR | Zbl

[2] Dobrovolskii N. M., O kvadraturnykh formulakh na klassakh $E^\alpha_s(c)$ i $H^\alpha_s(c)$, Dep. v VINITI 24.08.84, No6091–84

[3] Korobov N. M., Teoretiko-chislovye metody v priblizhennom analize, Fizmatgiz, M., 1963

[4] Korobov N. M., Teoretiko-chislovye metody v priblizhennom analize, vtoroe izdanie, MTsNMO, M., 2004, 288 pp.