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A quasirandom or low discrepancy sequence, such as the Faure, Halton, Hammersley, Niederreiter or Sobol sequences

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Sobol Quasirandom Sequence

A quasirandom or low discrepancy sequence, such as the Faure, Halton, Hammersley, Niederreiter or Sobol sequences, is "less random" than a pseudorandom number sequence, but more useful for such tasks as approximation of integrals in higher dimensions, and in global optimization. This is because low discrepancy sequences tend to sample space "more uniformly" than random numbers. Algorithms that use such sequences may have superior convergence.

Author:

Original FORTRAN77 version by Bennett Fox; C++ version by John Burkardt.

Reference:

IA Antonov, VM Saleev, An Economic Method of Computing LP Tau-Sequences, USSR Computational Mathematics and Mathematical Physics, Volume 19, 1980, pages 252-256. Paul Bratley, Bennett Fox, Algorithm 659: Implementing Sobol's Quasirandom Sequence Generator, ACM Transactions on Mathematical Software, Volume 14, Number 1, March 1988, pages 88-100. Paul Bratley, Bennett Fox, Harald Niederreiter, Implementation and Tests of Low Discrepancy Sequences, ACM Transactions on Modeling and Computer Simulation, Volume 2, Number 3, July 1992, pages 195-213. Paul Bratley, Bennett Fox, Linus Schrage, A Guide to Simulation, Second Edition, Springer, 1987, ISBN: 0387964673, LC: QA76.9.C65.B73. Bennett Fox, Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators, ACM Transactions on Mathematical Software, Volume 12, Number 4, December 1986, pages 362-376. Stephen Joe, Frances Kuo, Remark on Algorithm 659: Implementing Sobol's Quasirandom Sequence Generator, ACM Transactions on Mathematical Software, Volume 29, Number 1, March 2003, pages 49-57. Harald Niederreiter, Random Number Generation and quasi-Monte Carlo Methods, SIAM, 1992, ISBN13: 978-0-898712-95-7, LC: QA298.N54. William Press, Brian Flannery, Saul Teukolsky, William Vetterling, Numerical Recipes in FORTRAN: The Art of Scientific Computing, Second Edition, Cambridge University Press, 1992, ISBN: 0-521-43064-X, LC: QA297.N866. Ilya Sobol, Uniformly Distributed Sequences with an Additional Uniform Property, USSR Computational Mathematics and Mathematical Physics, Volume 16, 1977, pages 236-242. Ilya Sobol, YL Levitan, The Production of Points Uniformly Distributed in a Multidimensional Cube (in Russian), Preprint IPM Akademii Nauk SSSR, Number 40, Moscow 1976.

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A quasirandom or low discrepancy sequence, such as the Faure, Halton, Hammersley, Niederreiter or Sobol sequences

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