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Generation of parallel modified Kronecker sequences

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  • Chi Hongmei

    (Department of Computer and Information Sciences, Florida A& M University, Tallahassee, FL, 32307, USA)

Abstract

The generation of appropriate parallel and high-quality quasirandom sequences (low-discrepancy sequences) is crucial to the success of quasi-Monte Carlo methods. The Kronecker sequence is well known to be one of the special types of low-discrepancy sequences, and one of its important advantages is that the Kronecker sequence is easy to implement due to its definition via the fractional parts of multiples of irrationals. However, the original Kronecker sequence suffers from correlations for different dimensions. These correlations result in poorly distributed two-dimensional projections. An approach to this is to find a modified Kronecker sequence via generalizing golden ratio and generate parallel sequences. This paper presents a new algorithm for finding a modified Kronecker sequence within special choices of irrationals. This modified sequence is numerically tested and shown empirically to be superior to the other widely used quasirandom sequences. In addition, based on analysis and insight into the correlations between dimensions of the Kronecker sequence, we illustrate why our algorithm is efficient for breaking these correlations.

Suggested Citation

  • Chi Hongmei, 2013. "Generation of parallel modified Kronecker sequences," Monte Carlo Methods and Applications, De Gruyter, vol. 19(4), pages 261-271, December.
    • Handle: RePEc:bpj:mcmeap:v:19:y:2013:i:4:p:261-271:n:1
    DOI: 10.1515/mcma-2013-0008
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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. Stakhov, Alexey, 2007. "The generalized golden proportions, a new theory of real numbers, and ternary mirror-symmetrical arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 315-334.
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