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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 2, Pages 212–219
(Mi zvmmf178)
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This article is cited in 5 scientific papers (total in 5 papers)
Construction of lattice rules with a trigonometric $d$-property on the basis of extreme lattices
N. N. Osipov Krasnoyarsk State Technical University, ul. Kirenskogo 26, Krasnoyarsk, 660074, Russia
Abstract:
Lattice rules with the trigonometric $d$-property that are optimal with respect to the number of points are constructed for the approximation of integrals over an $n$-dimensional unit cube. An extreme lattice for a hyperoctahedron at $n=4$ is used to construct lattice rules with the trigonometric $d$-property and the number of points
$$
0.80822\ldots\cdot\Delta^4(1+o(1)),\quad\Delta\to\infty
$$
($d=2\Delta-1\ge3$ is an arbitrary odd number). With few exceptions, the resulting lattice rules have the highest previously known effectiveness factor.
Key words:
attice rules, lattice rules optimal with respect to the number of points, trigonometric $d$-property.
Received: 28.06.2007
Citation:
N. N. Osipov, “Construction of lattice rules with a trigonometric $d$-property on the basis of extreme lattices”, Zh. Vychisl. Mat. Mat. Fiz., 48:2 (2008), 212–219; Comput. Math. Math. Phys., 48:2 (2008), 201–208
Linking options:
https://www.mathnet.ru/eng/zvmmf178 https://www.mathnet.ru/eng/zvmmf/v48/i2/p212
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Abstract page: | 241 | Full-text PDF : | 94 | References: | 56 | First page: | 2 |
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