On the L p discrepancy of two-dimensional folded Hammersley point sets
نویسندگان
چکیده
منابع مشابه
Lp discrepancy of generalized two-dimensional Hammersley point sets
We determine the Lp discrepancy of the two-dimensional Hammersley point set in base b. These formulas show that the Lp discrepancy of the Hammersley point set is not of best possible order with respect to the general (best possible) lower bound on Lp discrepancies due to Roth and Schmidt. To overcome this disadvantage we introduce permutations in the construction of the Hammersley point set and...
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We generalize to arbitrary bases recent results on the star discrepancy of digitally shifted two-dimensional Hammersley point sets in base 2 by Kritzer, Larcher and Pillichshammer. The key idea is to link our fundamental formula for the discrepancy function of generalized van der Corput sequences to the corresponding quantity for generalized two-dimensional Hammersley point sets. In that way, w...
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We generalize to arbitrary bases recent results on the star extreme discrepancy of digitally shifted two-dimensional Hammersley point sets in base 2 by Kritzer, Larcher and Pillichshammer. The key idea is to link our fundamental formula for the discrepancy function of generalized van der Corput sequences to the corresponding quantity for generalized two-dimensional Hammersley point sets. In tha...
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We give an exact formula for the L2 discrepancy of two-dimensional digitally shifted Hammersley point sets in base b. This formula shows that for certain bases b and certain shifts the L2 discrepancy is of best possible order with respect to the general lower bound due to Roth. Hence, for the first time, it is proved that, for a thin, but infinite subsequence of bases b starting with 5, 19, 71,...
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The L2 discrepancy is a quantitative measure for the irregularity of distribution of a finite point set. In this paper we consider the L2 discrepancy of so-called generalized Hammersley point sets which can be obtained from the classical Hammersley point sets by introducing some permutations on the base b digits. While for the classical Hammersley point set it is not possible to achieve the opt...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2014
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-014-0698-1