Where are the logs?

  title={Where are the logs?},
  author={Art B. Owen and Zexin Pan},
  • A. Owen, Zexin Pan
  • Published 13 October 2021
  • Mathematics, Computer Science
The commonly quoted error rates for QMC integration with an infinite low discrepancy sequence isO (n−1 log(n) ) with r = d for extensible sequences and r = d − 1 otherwise. Such rates hold uniformly over all d dimensional integrands of Hardy-Krause variation one when using n evaluation points. Implicit in those bounds is that for any sequence of QMC points, the integrand can be chosen to depend on n. In this paper we show that rates with any r < (d − 1)/2 can hold when f is held fixed as n… 


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