Tractability properties of the weighted star discrepancy

  • Authors:

  • Aicke Hinrichs;Friedrich Pillichshammer;Wolfgang Ch. Schmid

  • Affiliations:

  • FSU Jena, Institut für Mathematik und Informatik, Ernst-Abbe-Platz 2, D-07743 Jena, Germany;Institut für Finanzmathematik, Universität Linz, Altenbergstraße 69, A-4040 Linz, Austria;Fachbereich Mathematik, Universität Salzburg, Hellbrunnerstraße 34, A-5020, Austria

  • Venue:
  • Journal of Complexity
  • Year:
  • 2008

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Abstract

Tractability properties of various notions of discrepancy have been intensively studied in the last decade. In this paper we consider the so-called weighted star discrepancy which was introduced by Sloan and Wozniakowski. We show that under a very mild condition on the weights one can obtain tractability with s-exponent zero (s is the dimension of the point set). In the case of product weights we give a condition such that the weighted star discrepancy is even strongly tractable. Furthermore, we give a lower bound for the weighted star discrepancy for a large class of weights. This bound shows that for such weights one cannot obtain strong tractability.