Walsh Figure of Merit for Digital Nets: An Easy Measure for Higher Order Convergent QMC

DOI10.1007/978-3-319-33507-0_5zbMath1356.65013arXiv1412.0168OpenAlexW2964870604MaRDI QIDQ2957028

Makoto Matsumoto, Ryuichi Ohori

Publication date: 20 January 2017

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

Full work available at URL: https://arxiv.org/abs/1412.0168

zbMATH Keywords

numerical integrationnumerical examplesquasi-Monte Carlo integrationdigital netsWalsh figure of merit

Mathematics Subject Classification ID

Monte Carlo methods (65C05)

Related Items

Quasi-Monte Carlo point sets with small \(t\)-values and WAFOM ⋮ A search for extensible low-WAFOM point sets

Uses Software

• MersenneTwister
• TESTPACK
• Magic Point Shop
• sobol.cc

Cites Work

• Constructing Sobol Sequences with Better Two-Dimensional Projections
• A search for extensible low-WAFOM point sets
• Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules
• WAFOM over abelian groups for quasi-Monte Carlo point sets
• Low-discrepancy sequences and global function fields with many rational places
• Quasi-Monte Carlo point sets with small \(t\)-values and WAFOM
• A lower bound on WAFOM
• Bounds on Walsh coefficients by dyadic difference and a new Koksma-Hlawka type inequality for quasi-Monte Carlo integration
• An explicit construction of point sets with large minimum Dick weight
• On the existence of higher order polynomial lattices based on a generalized figure of merit
• High dimensional integration of smooth functions over cubes
• Duality for digital nets and its applications
• On the Fast Computation of the Weight Enumerator Polynomial and the $t$ Value of Digital Nets over Finite Abelian Groups
• Existence of Higher Order Convergent Quasi-Monte Carlo Rules via Walsh Figure of Merit
• The Mean Square Quasi-Monte Carlo Error for Digitally Shifted Digital Nets
• On Quasi-Monte Carlo Rules Achieving Higher Order Convergence
• Walsh Spaces Containing Smooth Functions and Quasi–Monte Carlo Rules of Arbitrary High Order
• THE DECAY OF THE WALSH COEFFICIENTS OF SMOOTH FUNCTIONS
• Mersenne twister
• A computable figure of merit for quasi-Monte Carlo point sets
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