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

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  • Schürer, Rudolf

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.

Suggested Citation

  • Schürer, Rudolf, 2003. "A comparison between (quasi-)Monte Carlo and cubature rule based methods for solving high-dimensional integration problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(3), pages 509-517.
    • Handle: RePEc:eee:matcom:v:62:y:2003:i:3:p:509-517
    DOI: 10.1016/S0378-4754(02)00250-1
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    Cited by:

    1. Joseph Francois & Julia Woerz, 0000. "Rags in the High Rent District: the Evolution of Quota Rents in Textiles and Clothing," Tinbergen Institute Discussion Papers 06-007/2, Tinbergen Institute.
    2. De Luigi Christophe & Maire Sylvain, 2010. "Adaptive integration and approximation over hyper-rectangular regions with applications to basket option pricing," Monte Carlo Methods and Applications, De Gruyter, vol. 16(3-4), pages 265-282, January.

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