Existence of Higher Order Convergent Quasi-Monte Carlo Rules via Walsh Figure of Merit

DOI10.1007/978-3-642-41095-6_29zbMath1302.65015OpenAlexW2219620473MaRDI QIDQ2926239

Makoto Matsumoto, Takehito Yoshiki

Publication date: 31 October 2014

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-41095-6_29

zbMATH Keywords

quasi-Monte Carlo integrationWalsh figure of meritdigital net method

Mathematics Subject Classification ID

Monte Carlo methods (65C05)

Related Items (8)

Quasi-Monte Carlo point sets with small \(t\)-values and WAFOM ⋮ A search for extensible low-WAFOM point sets ⋮ Approximation of quasi-Monte Carlo worst case error in weighted spaces of infinitely times smooth functions ⋮ Walsh Figure of Merit for Digital Nets: An Easy Measure for Higher Order Convergent QMC ⋮ The Mean Square Quasi-Monte Carlo Error for Digitally Shifted Digital Nets ⋮ An explicit construction of point sets with large minimum Dick weight ⋮ A computable figure of merit for quasi-Monte Carlo point sets ⋮ Super-polynomial convergence and tractability of multivariate integration for infinitely times differentiable functions

Cites Work

• Low-discrepancy sequences and global function fields with many rational places
• An explicit construction of point sets with large minimum Dick weight
• On Quasi-Monte Carlo Rules Achieving Higher Order Convergence
• Duality theory and propagation rules for generalized digital nets
• Walsh Spaces Containing Smooth Functions and Quasi–Monte Carlo Rules of Arbitrary High Order
• A computable figure of merit for quasi-Monte Carlo point sets
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