A search for extensible low-WAFOM point sets

Harase Shin ()
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Harase Shin: College of Science and Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga, 525-8577, Japan

Monte Carlo Methods and Applications, 2016, vol. 22, issue 4, 349-357

Abstract: Matsumoto, Saito and Matoba recently proposed the Walsh figure of merit (WAFOM), which is a computable criterion for quasi-Monte Carlo point sets using digital nets. Several algorithms have been proposed for finding low-WAFOM point sets. In the existing algorithms, the number of points is fixed in advance, but extensible point sets are preferred in some applications. In this paper, we propose a random search algorithm for extensible low-WAFOM point sets. For this, we introduce a method that uses lookup tables to compute WAFOM faster. Numerical results show that our extensible low-WAFOM point sets are comparable with Niederreiter–Xing sequences for some low-dimensional and smooth test functions.

Keywords: Quasi-Monte Carlo method; numerical integration; digital net; Walsh figure of merit (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1515/mcma-2016-0119

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