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Computational investigations of scrambled Faure sequences

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  • Vandewoestyne, Bart
  • Chi, Hongmei
  • Cools, Ronald

Abstract

The Faure sequence is one of the well-known quasi-random sequences used in quasi-Monte Carlo applications. In its original and most basic form, the Faure sequence suffers from correlations between different dimensions. These correlations result in poorly distributed two-dimensional projections. A standard solution to this problem is to use a randomly scrambled version of the Faure sequence. We analyze various scrambling methods and propose a new nonlinear scrambling method, which has similarities with inversive congruential methods for pseudo-random number generation. We demonstrate the usefulness of our scrambling by means of two-dimensional projections and integration problems.

Suggested Citation

  • Vandewoestyne, Bart & Chi, Hongmei & Cools, Ronald, 2010. "Computational investigations of scrambled Faure sequences," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(3), pages 522-535.
    • Handle: RePEc:eee:matcom:v:81:y:2010:i:3:p:522-535
    DOI: 10.1016/j.matcom.2009.09.007
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    References listed on IDEAS

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    1. Chi, H. & Mascagni, M. & Warnock, T., 2005. "On the optimal Halton sequence," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(1), pages 9-21.
    2. Tan, Ken Seng & Boyle, Phelim P., 2000. "Applications of randomized low discrepancy sequences to the valuation of complex securities," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1747-1782, October.
    3. Pierre L’Ecuyer & Christiane Lemieux, 2002. "Recent Advances in Randomized Quasi-Monte Carlo Methods," International Series in Operations Research & Management Science, in: Moshe Dror & Pierre L’Ecuyer & Ferenc Szidarovszky (ed.), Modeling Uncertainty, chapter 0, pages 419-474, Springer.
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