Algorithm 659: Implementing Sobol's Quasirandom Sequence Generator

ACM Transactions on Mathematical Software (TOMS)

Volumn 14, Issue 1, 1988, Pages 88-100

  Bratley, Paul ^a   Fox, Bennett L ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

computational complexity; discrepancy; generators; global optimization; multidimensional integration; quasirandom sequences

Indexed keywords

MATHEMATICAL STATISTICS - RANDOM NUMBER GENERATION; OPTIMIZATION;

COMPUTATIONAL COMPLEXITY; GLOBAL OPTIMIZATION; MATHEMATICAL SOFTWARE; MULTIDIMENSIONAL INTEGRATION; QUASIRANDOM SEQUENCE GENERATOR;

COMPUTER PROGRAMMING;

EID: 0023979638     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/42288.214372     Document Type: Article

References (15)

1. Antonov, I. A., and Saleev, V. M. An economic method of computing LP τ-sequences. USSR Comput. Math. Math. Phys. 19 (1979), 252–256.
2. Davis, P. J., and Rabinowitz, P. Methods of Numerical Integration. Academic Press, New York, 1983.
3. Faure, H. Discrépance de suites associées à un système de numération (en dimension s). Acta Arithmetica XLI (1982), 337–351.
4. Fox, B. L. ACM Algorithm 647. Implementation and relative efficiency of quasirandom sequence generators. ACM Trans. Math. Softw. 12 (1986), 362–376.
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.
6. Knuth, D. E. The Art of Computer Programming, vol. 2: Seminumerieal Algorithms. 2nd ed., Addison-Wesley, Reading, Mass., 1981.
7. Peterson, W. W., and Weldon, E. J. Error-Correcting Codes. 2nd ed. MIT Press, Cambridge, Mass., 1972.
8. Niederreiter, H. Point sets and sequences with small discrepancy. Monatsh. Math, (to appear).
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.
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.
11. Sobol’, I. M. Uniformly distributed sequences with an additional uniform property. USSR Comput. Math. Math. Phys. 16 (1976), 236–242.
12. Sobol’, I. M. On the systematic search in a hypercube. SIAM J. Numer. Anal. 16 (1979), 790–793.
13. Sobol’, I. M. Points which uniformly fill a multidimensional cube. Math. Cybern. 2 (1985) Znanie, Moscow (in Russian).
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).
15. American National Standards Institutes. American National Standard Programming Language FORTRAN. Standard X3.9-1978, American National Standards Institute, New York, 1978.