A search for extensible low-WAFOM point sets

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.

12 pages

References in corpus (7)

• Walsh spaces containing smooth functions and quasi-Monte Carlo rules of arbitrary high order
• Explicit constructions of quasi-Monte Carlo rules for the numerical integration of high dimensional periodic functions
• Super-polynomial convergence and tractability of multivariate integration for infinitely times differentiable functions
• WAFOM on abelian groups for quasi-Monte Carlo point sets
• Quasi-Monte Carlo point sets with small $t$-values and WAFOM
• The Mean Square Quasi-Monte Carlo Error for Digitally Shifted Digital Nets
• Walsh Figure of Merit for Digital Nets: An Easy Measure for Higher Order Convergent QMC

Cited by in corpus (4)

• Super-polynomial convergence and tractability of multivariate integration for infinitely times differentiable functions
• Quasi-Monte Carlo point sets with small $t$-values and WAFOM
• The Mean Square Quasi-Monte Carlo Error for Digitally Shifted Digital Nets
• Walsh Figure of Merit for Digital Nets: An Easy Measure for Higher Order Convergent QMC