Computational investigations of scrambled Faure sequences

Bart Vandewoestyne, Hongmei Chi and Ronald Cools

Mathematics and Computers in Simulation (MATCOM), 2010, vol. 81, issue 3, 522-535

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.

Keywords: Faure sequence; Low-discrepancy sequences; (quasi)-Monte Carlo; Linear scrambling; Nonlinear scrambling (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:81:y:2010:i:3:p:522-535

DOI: 10.1016/j.matcom.2009.09.007

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