On the fixed volume discrepancy of the Korobov point sets

A. S. Rubtsova^ab, K. S. Ryutin^ab, V. N. Temlyakov<sup>cdab

a</sup> 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

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.

UDC: 517.518

MSC: Primary 30C65, 30L10, 58C06; Secondary 31C12, 31C15, 31B15, 30D45

Received: 31.03.2020 and 22.03.2021

DOI: 10.4213/sm9420

 English version: Sbornik: Mathematics, 2021, 212:8, 1180–1192

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