Fixed volume discrepancy in the periodic case
arXiv:1710.114996 citationsh-index: 11
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This is an incremental theoretical result for discrepancy theory in numerical analysis.
The paper studies smooth fixed volume discrepancy in the periodic case, proving that Frolov point sets achieve optimal decay rates for this discrepancy. Upper bounds for the r-smooth periodic discrepancy are established.
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.