On the fixed volume discrepancy of the Korobov point sets

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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.

About the authors

Anastasiya Sergeevna Rubtsova

Laboratory "Multidimensional Approximation and Applications", Lomonosov Moscow State University; Moscow Center for Fundamental and Applied Mathematics

Konstantin Sergeevich Ryutin

Laboratory "Multidimensional Approximation and Applications", Lomonosov Moscow State University; Moscow Center for Fundamental and Applied Mathematics

Email: kriutin@yahoo.com
Candidate of physico-mathematical sciences

Vladimir Nikolaevich Temlyakov

University of South Carolina; Steklov Mathematical Institute of Russian Academy of Sciences; Laboratory "Multidimensional Approximation and Applications", Lomonosov Moscow State University; Moscow Center for Fundamental and Applied Mathematics

Email: temlyak@math.sc.edu
Doctor of physico-mathematical sciences, Professor

References

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