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Diaphony, discrepancy, spectral test and worst-case error

Author

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  • Dick, Josef
  • Pillichshammer, Friedrich

Abstract

In this paper various measures for the uniformity of distribution of a point set in the unit cube are studied. We show how the diaphony and spectral test based on Walsh functions appear naturally as the worst-case error of integration in certain Hilbert spaces which are based on Walsh functions. Furthermore, it has been shown that this worst-case error equals to the root mean square discrepancy of an Owen scrambled point set.

Suggested Citation

  • Dick, Josef & Pillichshammer, Friedrich, 2005. "Diaphony, discrepancy, spectral test and worst-case error," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(3), pages 159-171.
    • Handle: RePEc:eee:matcom:v:70:y:2005:i:3:p:159-171
    DOI: 10.1016/j.matcom.2005.06.004
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