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Numerical Verifications of Theoretical Results about the Weighted \(({\cal W}(b);\gamma)-\) Diaphony of the Generalized Van der Corput Sequence

  • Vesna Dimitrievska Ristovska
  • Vassil Grozdanov
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 207)

Abstract

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.

Keywords

Uniform distribution of sequences Diaphony Generalized Van der Corput sequence 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Vesna Dimitrievska Ristovska
    • 1
  • Vassil Grozdanov
    • 2
  1. 1.FINKIUniversity “Ss Cyril and Methodius”SkopjeMacedonia
  2. 2.Department of MathematicsSouth-West University “Neophit Rilsky”BlagoevgradBulgaria

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