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Integration With Quasirandom Sequences: Numerical Experience

Author

Listed:
  • ILYA M. SOBOL’

    (Institute for Mathematical Modelling of the Russian Academy of Sciences, 4 Miusskaya Square, Moscow 125047, Russia)

  • BORIS V. SHUKHMAN

    (School of Computer Science, McGill University, 3480 University Street, Montreal Quebec, Canada H3A 2A7, Canada)

Abstract

Numerical experiments with two multivariable integrands and various quasirandom sequences are described. The integrands were introduced as models of Monte Carlo algorithms for particle tracking with or without statistical weights. Though analytically both integrands are very similar, the corresponding integration errors behave quite differently.From these experiments together with earlier ones (that are briefly summarized in the paper) several non-standard conclusions are drawn both on quasirandom sequences and on types of integrands.

Suggested Citation

  • Ilya M. Sobol’ & Boris V. Shukhman, 1995. "Integration With Quasirandom Sequences: Numerical Experience," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 263-275.
    • Handle: RePEc:wsi:ijmpcx:v:06:y:1995:i:02:n:s0129183195000204
    DOI: 10.1142/S0129183195000204
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    Citations

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    Cited by:

    1. Sobol, I.M., 1998. "On quasi-Monte Carlo integrations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(2), pages 103-112.
    2. Sobol Ilya M. & Shukhman Boris V., 2014. "Quasi-Monte Carlo: A high-dimensional experiment," Monte Carlo Methods and Applications, De Gruyter, vol. 20(3), pages 167-171, September.
    3. Sobol’, I.M & Asotsky, D.I, 2003. "One more experiment on estimating high-dimensional integrals by quasi-Monte Carlo methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(3), pages 255-263.

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