Fixed Volume Discrepancy in the Periodic Case
The smooth fixed volume discrepancy in the periodic case is studied here. It is proved that the Frolov point sets adjusted to the periodic case have optimal in a certain sense order of decay of the smooth periodic discrepancy. The upper bounds for the r-smooth fixed volume periodic discrepancy for these sets are established.
The author would like to thank the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) at the University of Vienna for support. This paper was started when the author participated in the ESI-Semester “Tractability of High Dimensional Problems and Discrepancy,” September 11–October 13, 2017. The work was supported by the Russian Federation Government Grant No. 14.W03.31.0031.
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