Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators

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Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 12 , Issue 4 (December 1986) table of contents

Pages: 362 - 376

Year of Publication: 1986

ISSN:0098-3500

Author

Bennett L. Fox

Computer Science Department, University of Montreal, P.O. Box 6128, Station A, Montreal, Quebec, Canada H3C 3J7

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 11, Downloads (12 Months): 107, Citation Count: 11

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appendices and supplements references cited by index terms collaborative colleagues

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APPENDICES and SUPPLEMENTS

generation of sequences of quasirandom vectors with low discrepancy Such sequences may be used to reduce error bounds for multidimensional integration and global optimization. (647.gz) (7 KB)

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked 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.
	2	BRATLEY, P., AND Fox, B. L. Implementing ;Sobol's quasirandom sequence generator. Tech. Rep. Universite de Montreal, Montreal, Quebec, Canada.
	3	Paul Bratley , Bennett L Fox , Linus E Schrage, A guide to simulation (2nd ed.), Springer-Verlag New York, Inc., New York, NY, 1986
	4	DAVIS, P. J., AND RABINOWITZ, P. Methods of Numerical Integration. Academic Press, New York, 1984.
	5	FAURE, H. Discrepance de suites associees i un systeme de numeration (en dimension s). Acta Arithmetica XLZ (1982), 337-351.
	6	HALTON, J. H. On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numer. Math. 2 (1960), 84-90.
	7	J. H. Halton, Algorithm 247: Radical-inverse quasi-random point sequence, Communications of the ACM, v.7 n.12, p.701-702, Dec. 1964 [doi>10.1145/355588.365104]
	8	HLAWKA, E. Functionen von .beschranker Variation in der Theorie der Gleichverteilung. Ann. Math. Pura Appl. 54 (1961), 325-333.
	9	KAHANER, D. Sources of information on quadrature software. In Sources and Development of Mathematical Software (W. R. Cowell, Ed.). Prentice-Hall, Englewood Cliffs, N. J. 1984, pp. 134-164.
	10	NIEDERREITER, H. Quasi-Monte Carlo methods and pseudo-random numbers. Bull. Amer. Math. Sot. 84 (1978), 957-1041.
	11	NIEDERREITER, H. The serial test for pseudo-random numbers generated by the linear congruential method. Numer. Math. 46 (1985), 51-68.
	12	NIEDERREITER, H., AND MCCIJRLEY, K. Optimization of functions by quasi-random search methods. Computing 22 (1979), 119-123.
	13	John Rischard Rice, Numerical Methods, Software and Analysis, McGraw-Hill, Inc., New York, NY, 1983
	14	SOBOL', L. M. Pseudo-random numbers for constructing discrete Markov chains by the Monte Carlo method. USSR Comput. Math. Math. Phys. 14 (1974), 36-45.
	15	SOBOL', I. M. Uniformly distributed sequences with an additional uniform property. USSR Comput. Math. Math. Phys. 16 (1976), 236-242.
	16	SOBOL', I. M. On the systematic search in a hypercube. SIAM J. Numer. Anal. 16 (1979), 790-793.
	17	SOBOL', I. M. On an estimate of the accuracy of a simple multidimensional search. Sov. Math. Dokl. 26 (1982), 398-401.
	18	WICHMANN, B. A., AND HILL, I. D. An efficient and portable pseudo-random number generator. Appl. Stat. 31 (1982), 188-190.

CITED BY 11

	Paul Bratley , Bennett L. Fox , Harald Niederreiter, Implementation and tests of low-discrepancy sequences, ACM Transactions on Modeling and Computer Simulation (TOMACS), v.2 n.3, p.195-213, July 1992
	Paul Bratley , Bennett L. Fox, ALGORITHM 659: implementing Sobol's quasirandom sequence generator, ACM Transactions on Mathematical Software (TOMS), v.14 n.1, p.88-100, March 1988
	Christiane Lemieux , Pierre L'Ecuyer, Efficiency improvement by lattice rules for pricing Asian options, Proceedings of the 30th conference on Winter simulation, p.579-586, December 13-16, 1998, Washington, D.C., United States
	Ladislav Kocis , William J. Whiten, Computational investigations of low-discrepancy sequences, ACM Transactions on Mathematical Software (TOMS), v.23 n.2, p.266-294, June 1997
	Paul Bratley , Bennett L. Fox , Harald Niederreiter, Programs to generate Niederreiter's low-discrepancy sequences, ACM Transactions on Mathematical Software (TOMS), v.20 n.4, p.494-495, Dec. 1994
	Stephen Joe , Frances Y. Kuo, Remark on algorithm 659: Implementing Sobol's quasirandom sequence generator, ACM Transactions on Mathematical Software (TOMS), v.29 n.1, p.49-57, March 2003
	Jack Dongarra , Ian Foster , Geoffrey Fox , William Gropp , Ken Kennedy , Linda Torczon , Andy White, References, Sourcebook of parallel computing, Morgan Kaufmann Publishers Inc., San Francisco, CA, 2003
	Tim Langtry , Lindsay Botten , Ara Asatryan , Ross McPhedran, Monte Carlo modelling of imperfections in two-dimensional photonic crystals, Mathematics and Computers in Simulation, v.62 n.3-6, p.385-393, 3 March 2003
	Hongmei Chi , Edward L. Jones, Computational investigations of quasirandom sequences in generating test cases for specification-based tests, Proceedings of the 37th conference on Winter simulation, December 03-06, 2006, Monterey, California
	Hongmei Chi , Edward L. Jones, Research Note: Generating parallel quasirandom sequences via randomization, Journal of Parallel and Distributed Computing, v.67 n.7, p.876-881, July, 2007
	Javid Jaffari , Mohab Anis, On efficient Monte Carlo-based statistical static timing analysis of digital circuits, Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design, November 10-13, 2008, San Jose, California