Testing multidimensional integration routines
Proc. of international conference on Tools, methods and languages for scientific and engineering computation
Programs to generate Niederreiter's low-discrepancy sequences
ACM Transactions on Mathematical Software (TOMS)
Algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
Computational investigations of low-discrepancy sequences
ACM Transactions on Mathematical Software (TOMS)
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Parallel High-Dimensional Integration: Quasi-Monte Carlo versus Adaptive Cubature Rules
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
An adaptive Monte Carlo integration algorithm with general division approach
Mathematics and Computers in Simulation
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Algorithms for estimating the integral over hyper-rectangular regions are discussed. Solving this problem in high dimensions is usually considered a domain of Monte Carlo and quasi-Monte Carlo methods, because their power degrades little with increasing dimension. These algorithms are compared to integration routines based on interpolatory cubature rules, which are usually only used in low dimensions. Adaptive as well as nonadaptive algorithms based on a variety of rules result in a wide range of different integration routines. Empirical tests performed with Genz's test function package show that cubature rule based algorithms can provide more accurate results than quasi-Monte Carlo routines for dimensions up to s = 100.