Parallel High-Dimensional Integration: Quasi-Monte Carlo versus Adaptive Cubature Rules
نویسنده
چکیده
Parallel algorithms for the approximation of a multi-dimensional integral over an hyper-rectangular region are discussed. Algorithms based on quasi-Monte Carlo techniques are compared with adaptive algorithms, and scalable parallel versions of both algorithms are presented. Special care has been taken to point out the role of the cubature formulas the adaptive algorithms are based on, and different cubature formulas and their impact on the performance of the algorithm are evaluated. Tests are performed for the sequential and parallel algorithms using Genz’s test function package.
منابع مشابه
A comparison between (quasi-)Monte Carlo and cubature rule based methods for solving high-dimensional integration problems
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 dime...
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