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Constructing a new class of low-discrepancy sequences by using the β-adic transformation

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  • Ninomiya, Syoiti

Abstract

It is well known that low-discrepancy sequences and their discrepancy play essential roles in quasi Monte Carlo methods [5]. In this paper, a new class of low-discrepancy sequences Nβ is constructed by using the ergodic theoretical transformation which is called β-adic transformation [7, 8]. Here, β is a real number greater than 1. When β is an integer greater than 2, Nβ becomes the classical van der Corput sequence in base β. Therefore, the class Nβ can be regarded as a generalization of the van der Corput sequence. It is shown that for some special β, the discrepancy of this sequence decreases in the fastest order O(N−1logN). We give the numerical results of discrepancy of Nβ for some βs. Pagès [6] also generalized van der Corput sequence in a different direction by using an ergodic transformation.

Suggested Citation

  • Ninomiya, Syoiti, 1998. "Constructing a new class of low-discrepancy sequences by using the β-adic transformation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(2), pages 403-418.
    • Handle: RePEc:eee:matcom:v:47:y:1998:i:2:p:403-418
    DOI: 10.1016/S0378-4754(98)00115-3
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    Cited by:

    1. Mori, Makoto, 2001. "Pseudo random sequences generated by piecewise linear maps from the view point of dynamical system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 55(1), pages 177-189.
    2. Carbone, Ingrid, 2015. "Extension of van der Corput algorithm to LS-sequences," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 207-213.
    3. Hofer, Roswitha, 2018. "Halton-type sequences in rational bases in the ring of rational integers and in the ring of polynomials over a finite field," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 143(C), pages 78-88.

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