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2024 | OriginalPaper | Chapter

Generator Matrices by Solving Integer Linear Programs

Authors : Loïs Paulin, David Coeurjolly, Nicolas Bonneel, Jean-Claude Iehl, Victor Ostromoukhov, Alexander Keller

Published in: Monte Carlo and Quasi-Monte Carlo Methods

Publisher: Springer International Publishing

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Abstract

In quasi-Monte Carlo methods, generating high-dimensional low discrepancy sequences by generator matrices is a popular and efficient approach. Historically, constructing or finding such generator matrices has been a hard problem. In particular, it is challenging to take advantage of the intrinsic structure of a given numerical problem to design samplers of low discrepancy in certain subsets of dimensions. To address this issue, we devise a greedy algorithm allowing us to translate desired net properties into linear constraints on the generator matrix entries. Solving the resulting integer linear program yields generator matrices that satisfy the desired net properties. We demonstrate that our method finds generator matrices in challenging settings, offering low discrepancy sequences beyond the limitations of classic constructions.

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previous chapter A Randomised Lattice Rule Algorithm with Pre-determined Generating Vector and Random Number of Points for Korobov Spaces with 
next chapter Multi-fidelity No-U-Turn Sampling
Literature
1.
Hong, H.S.: Digital Nets and Sequences for Quasi-Monte Carlo Methods. Ph.D. thesis, Hong Kong Baptist University, China (2002)
2.
3.
Joe, S., Kuo, F.: Constructing Sobol’ sequences with better two-dimensional projections. SIAM J. Sci. Comput. 30(5), 2635–2654 (2008)MathSciNetCrossRef
4.
Keller, A.: Stratification by rank-1 lattices. In: Niederreiter, H. (ed.) Monte Carlo and Quasi-Monte Carlo Methods 2002, pp. 299–313. Springer (2004)
5.
6.
L’Ecuyer, P., Marion, P., Godin, M., Puchhammer, F.: A tool for custom construction of QMC and RQMC point sets. In: International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, pp. 51–70. Springer (2022)
7.
Niederreiter, H.: Random Number Generation and quasi-Monte Carlo Methods. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, USA (1992)CrossRef
8.
9.
Sobol’, I.M.: On the distribution of points in a cube and the approximate evaluation of integrals. Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki 7(4), 784–802 (1967)MathSciNet
Metadata
Title
Generator Matrices by Solving Integer Linear Programs
Authors
Loïs Paulin
David Coeurjolly
Nicolas Bonneel
Jean-Claude Iehl
Victor Ostromoukhov
Alexander Keller
Copyright Year
2024
Book
Monte Carlo and Quasi-Monte Carlo Methods

Print ISBN: 978-3-031-59761-9

Electronic ISBN: 978-3-031-59762-6

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-59762-6_26

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