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Sbornik: Mathematics, 2021, Volume 212, Issue 8, Pages 1180–1192
DOI: https://doi.org/10.1070/SM9420 (Mi sm9420) 		 
On the fixed volume discrepancy of the Korobov point sets

A. S. Rubtsovaab, K. S. Ryutinab, V. N. Temlyakovcdab

a Laboratory "High-Dimensional Approximation and Applications", Lomonosov Moscow State University, Moscow, Russia
b Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia
c University of South Carolina, Columbia, SC, USA
d Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
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DOI: https://doi.org/10.1070/SM9420
Abstract: This paper is devoted to the study of a discrepancy-type characteristic – the fixed volume discrepancy – of Korobov point sets in the unit cube. It has been observed recently that this new characteristic allows us to obtain an optimal rate of dispersion decay. This observation has motivated us to study this new version of discrepancy thoroughly; it also seems to have independent interest. This paper extends recent results due to Temlyakov and Ullrich on the fixed volume discrepancy of Fibonacci point sets.
Bibliography: 23 titles.
Keywords: Korobov cubature formulae, discrepancy, dispersion.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.W03.31.0031
This work was carried out with the support of a grant for state support of scientific research conducted under the auspices of leading scientists of the Government of the Russian Federation (project no. 14.W03.31.0031).
Received: 31.03.2020 and 22.03.2021
Russian version:
Matematicheskii Sbornik, 2021, Volume 212, Number 8, Pages 151–164
DOI: https://doi.org/10.4213/sm9420
Bibliographic databases:
Document Type: Article
UDC: 517.518
MSC: Primary 30C65, 30L10, 58C06; Secondary 31C12, 31C15, 31B15, 30D45
Language: English
Original paper language: Russian
Citation: A. S. Rubtsova, K. S. Ryutin, V. N. Temlyakov, “On the fixed volume discrepancy of the Korobov point sets”, Mat. Sb., 212:8 (2021), 151–164; Sb. Math., 212:8 (2021), 1180–1192
Citation in format AMSBIB
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