Mathematics (Oct 2022)

Convergence of Uniformity Criteria and the Application in Numerical Integration

  • Yang Huang,
  • Yongdao Zhou

DOI
https://doi.org/10.3390/math10193717
Journal volume & issue
Vol. 10, no. 19
p. 3717

Abstract

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Quasi-Monte Carlo (QMC) methods have been successfully used for the estimation of numerical integrations arising in many applications. In most QMC methods, low-discrepancy sequences have been used, such as digital nets and lattice rules. In this paper, we derive the convergence rates of order of some improved discrepancies, such as centered L2-discrepancy, wrap-around L2-discrepancy, and mixture discrepancy, and propose a randomized QMC method based on a uniform design constructed by the mixture discrepancy and Baker’s transformation. Moreover, the numerical results show that the proposed method has better approximation than the Monte Carlo method and many other QMC methods, especially when the number of dimensions is less than 10.

Keywords