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Good Lattice Rules with a Composite Number of Points Based on the Product Weighted Star Discrepancy

In: Monte Carlo and Quasi-Monte Carlo Methods 2006

Author

Listed:
  • Vasile Sinescu

    (University of Waikato, Department of Mathematics)

  • Stephen Joe

    (University of Waikato, Department of Mathematics)

Abstract

Summary Rank-1 lattice rules based on a weighted star discrepancy with weights of a product form have been previously constructed under the assumption that the number of points is prime. Here, we extend these results to the non-prime case. We show that if the weights are summable, there exist lattice rules whose weighted star discrepancy is O(n −1+δ ), for any δ > 0, with the implied constant independent of the dimension and the number of lattice points, but dependent on δ and the weights. Then we show that the generating vector of such a rule can be constructed using a component-by-component (CBC) technique. The cost of the CBC construction is analysed in the final part of the paper.

Suggested Citation

  • Vasile Sinescu & Stephen Joe, 2008. "Good Lattice Rules with a Composite Number of Points Based on the Product Weighted Star Discrepancy," Springer Books, in: Alexander Keller & Stefan Heinrich & Harald Niederreiter (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2006, pages 645-658, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-74496-2_39
    DOI: 10.1007/978-3-540-74496-2_39
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