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

Rudolf Schürer

Mathematics and Computers in Simulation (MATCOM), 2003, vol. 62, issue 3, 509-517

Abstract: 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 non-adaptive 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.

Keywords: Numerical integration; Monte Carlo; Quasi-Monte Carlo; Cubature rule (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:62:y:2003:i:3:p:509-517

DOI: 10.1016/S0378-4754(02)00250-1

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