Parallel High-Dimensional Integration: Quasi-Monte Carlo versus Adaptive Cubature Rules

Authors:
Rudolf Schürer
Affiliations:
-
Venue:
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
Year:
2001

Citing 3
Cited 1

Testing multidimensional integration routines

Proc. of international conference on Tools, methods and languages for scientific and engineering computation
Adaptive quadrature on a message-passing multiprocessor

Journal of Parallel and Distributed Computing
Scalability and load balancing in adaptive algorithms for multidimensional integration

Parallel Computing

A comparison between (quasi-)Monte Carlo and cubature rule based methods for solving high-dimensional integration problems

Mathematics and Computers in Simulation - Special issue: 3rd IMACS seminar on Monte Carlo methods - MCM 2001

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Abstract

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.