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Algorithm 659: Implementing Sobol's quasirandom sequence generator

Editor: John R. Rice Authors:

Paul Bratley,

Bennett L. FoxAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 14, Issue 1

Pages 88 - 100

https://doi.org/10.1145/42288.214372

Published: 01 March 1988 Publication History

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Abstract

We compare empirically accuracy and speed of low-discrepancy sequence generators of Sobol' and Faure. These generators are useful for multidimensional integration and global optimization. We discuss our implementation of the Sobol' generator.

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Sobol's quasirandom sequence generator for multivariate quadrature and optimization Gams: G2i,H2c

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References

[1]

ANTONOV, I. A., AND SALEEV, V.M. An economic method of computing LP~-sequences. USSR Comput. Math. Math. Phys. 19 (1979), 252-256.

Google Scholar

[2]

DAVIS, P. J., AND RABINOWITZ, P. Methods o{ Numerical Integration. Academic Press, New York, 1983.

Google Scholar

[3]

FAURE, H. Discr~pance de suites associ~es ~ un syst~me de numeration (en dimension s). Acta Arithmetica XLI (1982), 337-351.

Google Scholar

[4]

FOX, B. L. ACM Algorithm 647. Implementation and relative efficiency of quasirandom sequence generators. ACM Trans. Math. Softw. 12 (1986), 362-376.

Crossref

Google Scholar

[5]

HALTON, J.H. On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numer. Math. 2 (1960), 84-90.

Google Scholar

[6]

KNUTH, D. E. The Art of Computer Programming, vol. 2: Seminumerical Algorithms. 2nd ed., Addison-Wesley, Reading, Mass., 1981.

Crossref

Google Scholar

[7]

PETERSON, W. W., AND WELDON, E.J. Error-Correcting Codes. 2nd ed. MIT Press, Cambridge, Mass., 1972.

Google Scholar

[8]

NIEDERREITER, H. Point sets and sequences with small discrepancy. Monatsh. Math. (to appear).

Google Scholar

[9]

SARKAR, P. K., AND PRASAD, M.A. A comparative study of pseudo and quasirandom sequences for the solution of integral equations. J. Comput. Phys. 68 (1987), 66-88.

Crossref

Google Scholar

[10]

SOBOL', I. M. On the distribution of points in a cube and the approximate evaluation of integrals. USSR Comput. Math. Math. Phys. 7 (1967), 86-112.

Google Scholar

[11]

SOBOL', I.M. Uniformly distributed sequences with an additional uniform property. USSR Comput. Math. Math. Phys. 16 (1976), 236-242.

Google Scholar

[12]

SOBOL', I.M. On the systematic search in a hypercube. SIAM J. Numer. Anal. 16 (1979), 790-793.

Google Scholar

[13]

SOBOL', I. M. Points which uniformly fill a multidimensional cube. Math. Cybern. 2 (1985) Znanie, Moscow (in Russian).

Google Scholar

[14]

SOBOL', I. M., AND LEVITAN, Yu.L. The production of points uniformly distributed in a multidimensional cube. Preprint 40, Institute of Applied Mathematics, USSR Academy of Sciences, 1976 (in Russian).

Google Scholar

[15]

AMERICAN NATIONAL STANDARDS INSTITUTES. American National Standard Programming Language FORTRAN. Standard X3.9-1978, American National Standards Institute, New York, 1978.

Google Scholar

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Index Terms

Algorithm 659: Implementing Sobol's quasirandom sequence generator
1. Computing methodologies
  1. Modeling and simulation
    1. Model development and analysis
      1. Model verification and validation
2. Mathematics of computing
  1. Mathematical analysis
  2. Mathematical software

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Implementation and tests of low-discrepancy sequences

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Computational investigations of low-discrepancy sequences

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An algorithm to generate Sobol' sequences to approximate integrals in up to 40 dimensions has been previously given by Bratley and Fox in Algorithm 659. Here, we provide more primitive polynomials and "direction numbers" so as to allow the generation of ...

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 14, Issue 1

March 1988

111 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/42288

Editor:
John R. Rice

Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 March 1988

Published in TOMS Volume 14, Issue 1

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Abstract

Supplementary Material

References

Cited By

Index Terms

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Implementation and tests of low-discrepancy sequences

Computational investigations of low-discrepancy sequences

Remark on algorithm 659: Implementing Sobol's quasirandom sequence generator

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