Construction of good polynomial lattice rules in weighted Walsh spaces by an alternative component-by-component construction

DOI10.1016/j.matcom.2021.09.007OpenAlexW3199384618MaRDI QIDQ2666535

Peter Kritzer, Onyekachi Osisiogu, Adrian Ebert, Tetiana A. Stepaniuk

Publication date: 22 November 2021

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.12586

zbMATH Keywords

numerical integrationweighted function spacesquasi-Monte Carlo methodscomponent-by-component constructionfast implementationpolynomial lattice points

Mathematics Subject Classification ID

Numerical analysis (65-XX) Computer science (68-XX)

Cites Work

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• Point sets and sequences with small discrepancy
• Zur angenäherten Berechnung mehrfacher Integrale
• 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
• Digit-by-digit and component-by-component constructions of lattice rules for periodic functions with unknown smoothness
• Stability of lattice rules and polynomial lattice rules constructed by the component-by-component algorithm
• Component-by-component construction of good lattice rules
• Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces
• Low-discrepancy point sets obtained by digital constructions over finite fields
• Construction algorithms for polynomial lattice rules for multivariate integration
• High-dimensional integration: The quasi-Monte Carlo way