Construction algorithms for higher order polynomial lattice rules

DOI10.1016/j.jco.2010.06.002zbMath1218.65003OpenAlexW1980498334MaRDI QIDQ544121

Jan Baldeaux, Julia Greslehner, Friedrich Pillichshammer, Josef Dick

Publication date: 14 June 2011

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2010.06.002

zbMATH Keywords

algorithmconvergencenumerical integrationquasi-Monte Carlopolynomial lattice ruleshigher order digital nets

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Numerical integration (65D30) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items (13)

Embeddings of weighted Hilbert spaces and applications to multivariate and infinite-dimensional integration ⋮ Construction of interlaced scrambled polynomial lattice rules of arbitrary high order ⋮ A Tool for Custom Construction of QMC and RQMC Point Sets ⋮ Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules ⋮ Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher-order convergence ⋮ A computable figure of merit for quasi-Monte Carlo point sets ⋮ Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients: a survey of analysis and implementation ⋮ Richardson Extrapolation of Polynomial Lattice Rules ⋮ Constructing good higher order polynomial lattice rules with modulus of reduced degree ⋮ The \(b\)-adic tent transformation for quasi-Monte Carlo integration using digital nets ⋮ Good interlaced polynomial lattice rules for numerical integration in weighted Walsh spaces ⋮ Discrepancy Theory and Quasi-Monte Carlo Integration ⋮ Fast construction of higher order digital nets for numerical integration in weighted Sobolev spaces

Cites Work

• Point sets and sequences with small discrepancy
• Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules
• When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
• Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces
• Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules
• On the existence of higher order polynomial lattices based on a generalized figure of merit
• A class of generalized Walsh functions
• Component-by-component construction of good lattice rules
• The construction of good extensible rank-1 lattices
• Explicit Constructions of Quasi-Monte Carlo Rules for the Numerical Integration of High-Dimensional Periodic Functions
• The construction of extensible polynomial lattice rules with small weighted star discrepancy
• Walsh Spaces Containing Smooth Functions and Quasi–Monte Carlo Rules of Arbitrary High Order
• THE DECAY OF THE WALSH COEFFICIENTS OF SMOOTH FUNCTIONS
• Low-discrepancy point sets obtained by digital constructions over finite fields
• Construction algorithms for polynomial lattice rules for multivariate integration
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