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Fixed volume discrepancy in the periodic case

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arxiv 1710.11499 v1 pith:LE5MHUWE submitted 2017-10-30 math.NA cs.NA

V.N. Temlyakov This is my paper · ORCID
classification math.NAcs.NA
keywords periodicdiscrepancycasefixedsmoothvolumesetsadjusted
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abstract

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.

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  1. On the fixed volume discrepancy of the Fibonacci sets in the integral norms

    math.NA 2019-08 accept novelty 6.0 of 10

    For finite p, the periodic r-smooth fixed volume L_p discrepancy of the Fibonacci point set with b_n points is O(sqrt(log(b_n v)) / b_n^r); for p=∞ it is O(log(b_n v)/b_n^r).

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