Adaptive quasi-Monte-Carlo integration based on MISER and VEGAS. (English) Zbl 1042.65009
Niederreiter, Harald (ed.), Monte Carlo and quasi-Monte Carlo methods 2002. Proceedings of a conference, National University of Singapore, Republic of Singapore, November 25--28, 2002. Berlin: Springer (ISBN 3-540-20466-0/pbk). 393-406 (2004).
Summary: Quasi-Monte Carlo (QMC) routines are one of the most common techniques for solving integration problems in high dimensions. However, their efficiency degrades if the variation of the integrand is concentrated in small areas of the integration domain. Adaptive algorithms cope with this situation by adjusting the flow of computation based on previous integrand evaluations.
We explore ways to modify the Monte Carlo based adaptive algorithms MISER and VEGAS such that low-discrepancy point sets are used instead of random samples. Experimental results show that the proposed algorithms outperform plain QMC as well as the original adaptive integration routine for certain classes of test cases. For the entire collection see [Zbl 1029.00038