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Remarks on randomization of quasi-random numbers

Author

Listed:
  • Ermakov Sergej M.

    (The Faculty of Mathematics and Mechanics, St. Petersburg State University, Bibliotechnay Sq. 2 Petrodvorets 198904, St. Petersburg, Russia)

  • Leora Svetlana N.

    (The Faculty of Mathematics and Mechanics, St. Petersburg State University, Bibliotechnay Sq. 2 Petrodvorets 198904, St. Petersburg, Russia)

Abstract

In this paper we discuss estimation of the quasi-Monte Carlo methods error in the case of calculation of high-order integrals. Quasi-random Halton sequences are considered as a special case. Randomization of these sequences by the random shift method turns out to lead to well-known random quadrature formulas with one free node. Some new properties of such formulas are pointed out. The subject is illustrated by a number of numerical examples.

Suggested Citation

  • Ermakov Sergej M. & Leora Svetlana N., 2018. "Remarks on randomization of quasi-random numbers," Monte Carlo Methods and Applications, De Gruyter, vol. 24(2), pages 139-145, June.
    • Handle: RePEc:bpj:mcmeap:v:24:y:2018:i:2:p:139-145:n:6
    DOI: 10.1515/mcma-2018-0012
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