Testing multidimensional integration routines
Proc. of international conference on Tools, methods and languages for scientific and engineering computation
Efficient and portable combined random number generators
Communications of the ACM
Random number generators: good ones are hard to find
Communications of the ACM
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Theory and application of Marsaglia's monkey test for pseudorandom number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
Remark on algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
One more experiment on estimating high-dimensional integrals by quasi-Monte Carlo methods
Mathematics and Computers in Simulation - Special issue: 3rd IMACS seminar on Monte Carlo methods - MCM 2001
Discrepancy behaviour in the non-asymptotic regime
Applied Numerical Mathematics
On a non-monotonicity effect of similarity measures
SIMBAD'11 Proceedings of the First international conference on Similarity-based pattern recognition
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In this paper, we show that the Sobol' and Richtmyer sequences can be effectively used for numerical integration of functions having up to 1000 variables. The results of integration obtained with the two sequences are compared and the parameters C and @a from the convergence model C/N^@a are estimated, where N is the number of points used. For all the tests done, the Sobol' sequence demonstrated somewhat better convergence, but for many practical values of N the relative error is higher than for Richtmyer sequences due to the large value of C. Constructing Sobol' sequences also takes considerably more time than constructing Richtmyer sequences.