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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 2, Pages 212–219 (Mi zvmmf178)  

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
Full-text PDF (810 kB) Citations (5)
References:
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
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 2, Pages 201–208
DOI: https://doi.org/10.1007/s11470-008-2004-4
Bibliographic databases:
Document Type: Article
UDC: 519.644.7
Language: Russian
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
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/zvmmf/v48/i2/p212
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    Abstract page:241
    Full-text PDF :94
    References:56
    First page:2
     
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