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Algorithm 659: Implementing Sobol's quasirandom sequence generator
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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“The Sobol sequence is a lowdiscrepancy sequence constructed using binary digits and designed so that the points are distributed evenly in the unit hypercube.”
From Doubly blocked variant of Genz’s method for multivariate normal integration (2026) · cites this paper as Bratley and Fox (1988)
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Cites
On the distribution of points in a cube and the approximate evaluation of integrals
Sobol', I. M. (1967) · USSR Computational Mathematics and Mathematical Physics · doi:10.1016/0041-5553(67)90144-9 · Cited by 2,975
Research works printed but not linked: 12
- ANTONOV I. A., 1979, An economic method of computing LP~-sequences, USSR Comput. Math. Math. Phys., 19, 252, 10.1016/0041-5553(79)90085-5 · DOI
- DAVIS P. J. AND RABINOWITZ P. Methods o{ Numerical Integration. Academic Press New York 1983. DAVIS P. J. AND RABINOWITZ P. Methods o{ Numerical Integration. Academic Press New York 1983. · doi:10.1016/b978-0-12-206360-2.50012-1
- FAURE H, 1982, Discr~pance de suites associ~es ~ un syst~me de numeration (en dimension s), Acta Arithmetica, 337, 10.4064/aa-41-4-337-351 · DOI
- 10.1145/22721.356187 · DOI · Paper page
- HALTON J.H, 1960, On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals, Numer. Math., 2, 84, 10.1007/BF01386213 · DOI · Paper page
- KNUTH D. E., 1981, Seminumerical Algorithms
- PETERSON W. W. AND WELDON E.J. Error-Correcting Codes. 2nd ed. MIT Press Cambridge Mass. 1972. PETERSON W. W. AND WELDON E.J. Error-Correcting Codes. 2nd ed. MIT Press Cambridge Mass. 1972.
- 10.1016/0021-9991(87)90045-3 · doi:10.1016/0021-9991(87)90045-3
- SOBOL' I.M, 1976, Uniformly distributed sequences with an additional uniform property, USSR Comput. Math. Math. Phys., 16, 236, 10.1016/0041-5553(76)90154-3 · DOI · Paper page
- SOBOL' I.M, 1979, On the systematic search in a hypercube, SIAM J. Numer. Anal., 16, 790, 10.1137/0716058 · DOI
- SOBOL' I. M., 1976, USSR Academy of Sciences
- AMERICAN NATIONAL STANDARDS INSTITUTES., 1978, American National Standards Institute
Cited by
Saltelli, A., Annoni, P., Azzini, I., Campolongo, F., Ratto, M., & Tarantola, S. (2010) · Computer Physics Communications · doi:10.1016/j.cpc.2009.09.018 · Cited by 3,623
Monte Carlo methods for security pricing
Boyle, P., Broadie, M., & Glasserman, P. (1997) · Journal of Economic Dynamics and Control · doi:10.1016/s0165-1889(97)00028-6 · Cited by 854
Berg, J., & Nyström, K. (2018) · Neurocomputing · doi:10.1016/j.neucom.2018.06.056 · Cited by 657
Analysis of variance designs for model output
Jansen, M. J. W. (1999) · Computer Physics Communications · doi:10.1016/s0010-4655(98)00154-4 · Cited by 650
High-dimensional integration: The quasi-Monte Carlo way
Dick, J., Kuo, F. Y., & Sloan, I. H. (2013) · Acta Numerica · doi:10.1017/s0962492913000044 · Cited by 615
Metadata
- Authors
- Bratley, P., & Fox, B. L.
- Venue
- ACM Transactions on Mathematical Software
- Published
- 1988-03
- Volume
- 14
- Issue
- 1
- Pages
- 88-100
- ISSN
- 0098-3500
- 1557-7295
- Cited by
- 754
- References
- 1
- Language
- en
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- Bratley, P., & Fox, B. L. (1988). Algorithm 659: Implementing Sobol's quasirandom sequence generator. ACM Transactions on Mathematical Software. https://doi.org/10.1145/42288.214372
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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