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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)
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.
Received: 04.07.2021 Accepted: 21.12.2021
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
Linking options:
https://www.mathnet.ru/eng/cheb1142 https://www.mathnet.ru/eng/cheb/v22/i5/p365
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Abstract page: | 101 | Full-text PDF : | 21 | References: | 17 |
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