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Point sets with low $Lp$-discrepancy

In: Mathematica Slovaca, vol. 57, no. 1
Peter Kritzer - Friedrich Pillichshammer

Details:

Year, pages: 2007, 11 - 32
About article:
In this paper we study the $Lp$-discrepancy of digitally shifted Hammersley point sets. While it is known that the (unshifted) Hammersley point set (which is also known as Roth net) with $N$ points has $Lp$-discrepancy ($p$ an integer) of order $( log N)/N$, we show that there always exists a shift such that the digitally shifted Hammersley point set has $Lp$-discrepancy ($p$ an even integer) of order $\sqrt{ log N}/N$ which is best possible by a result of W. Schmidt. Further we concentrate on the case $p=2$. We give very tight lower and upper bounds for the $L2$-discrepancy of digitally shifted Hammersley point sets which show that the value of the $L2$-discrepancy of such a point set mostly depends on the number of zero coordinates of the shift and not so much on the position of these.
How to cite:
ISO 690:
Kritzer, P., Pillichshammer, F. 2007. Point sets with low $Lp$-discrepancy. In Mathematica Slovaca, vol. 57, no.1, pp. 11-32. 0139-9918.

APA:
Kritzer, P., Pillichshammer, F. (2007). Point sets with low $Lp$-discrepancy. Mathematica Slovaca, 57(1), 11-32. 0139-9918.