Variants of the Koksma-Hlawka inequality for vertex-modified quasi-Monte Carlo integration rules

  • Authors:

  • H. Niederreiter;I. H. Sloan

  • Affiliations:

  • Institute for Information Processing, Austrian Academy of Sciences Sonnenfelsgasse 19, A-1010 Vienna, Austria;School of Mathematics, University of New South Wales Sydney 2052, Australia

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 1996

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Abstract

Vertex-modified rules have recently been introduced by the authors as a way of improving the performance of quasi-Monte Carlo methods for numerical integration. In this paper, we establish variants of the Koksma-Hlawka inequality for vertex-modified rules, and we show that there are choices for the vertex weights which, in general, yield smaller error bounds than the classical Koksma-Hlawka bound. Low-discrepancy point sets for which the local discrepancy has constant sign emerge as interesting objects of study.