A search for extensible low-WAFOM point sets
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Shin Harase
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.
Funding source: Japan Society for the Promotion of Science
Award Identifier / Grant number: 26730015
Award Identifier / Grant number: 24.7985
Award Identifier / Grant number: 26310211
Award Identifier / Grant number: 15K13460
Funding statement: The author was partially supported by the Grants-in-Aid for Young Scientists (B) #26730015, for JSPS Fellows 247985, for Scientific Research (B) 26310211, and for Challenging Exploratory Research #15K13460 from the Japan Society for the Promotion of Scientific Research.
Acknowledgements
In an earlier version of this paper, Mr. Ryuichi Ohori checked the code in C written by the author, in particular for the correctness of the WAFOM values in Section 3, and gave the author invaluable comments to improve the presentation. The author thanks him for his help.
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© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Random walk on spheres method for solving drift-diffusion problems
- On the construction of boundary preserving numerical schemes
- Perfect and ε-perfect simulation methods for the one-dimensional Kac equation
- Approximation of Euler–Maruyama for one-dimensional stochastic differential equations involving the local times of the unknown process
- Improved Markov Chain Monte Carlo method for cryptanalysis substitution-transposition cipher
- The planar Couette flow with slip and jump boundary conditions in a microchannel
- A search for extensible low-WAFOM point sets
Artikel in diesem Heft
- Frontmatter
- Random walk on spheres method for solving drift-diffusion problems
- On the construction of boundary preserving numerical schemes
- Perfect and ε-perfect simulation methods for the one-dimensional Kac equation
- Approximation of Euler–Maruyama for one-dimensional stochastic differential equations involving the local times of the unknown process
- Improved Markov Chain Monte Carlo method for cryptanalysis substitution-transposition cipher
- The planar Couette flow with slip and jump boundary conditions in a microchannel
- A search for extensible low-WAFOM point sets
