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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Numerical Verifications of Theoretical Results about the Weighted Diaphony of the Generalized Van der Corput Sequence
verfasst von : Vesna Dimitrievska Ristovska, Vassil Grozdanov
Erschienen in: ICT Innovations 2012
Verlag: Springer Berlin Heidelberg
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The weighted
$({\cal W}(b);\gamma)-$
diaphony is a new quantitative measure for the irregularity of distribution of sequences. In previous works of the authors it has been found the exact order
${\cal O}\left({1 \over N}\right)$
of the weighted
$({\cal W}(b);\gamma)-$
diaphony of the generalized Van der Corput sequence. Here, we give an upper bound of the weighted
$({\cal W}(b);\gamma)-$
diaphony, which is an analogue of the classical Erdös-Turán-Koksma inequality, with respect to this kind of the diaphony. This permits us to make a computational simu-lations of the weighted
$({\cal W}(b);\gamma)-$
diaphony of the generalized Van der Corput sequence. Different choices of sequences of permutations of the set {0,1, …,
b
− 1} are practically realized and the
$({\cal W}(b);\gamma)-$
diaphony of the corresponding generalized Van der Corput sequences is numerically calculated and discussed.