Diaphony, discrepancy, spectral test and worst-case error

DOI10.1016/j.matcom.2005.06.004zbMath1193.65003OpenAlexW2057844483MaRDI QIDQ2575900

Josef Dick, Friedrich Pillichshammer

Publication date: 7 December 2005

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

Full work available at URL: https://doi.org/10.1016/j.matcom.2005.06.004

zbMATH Keywords

weighted Sobolev spacesWalsh functionsHilbert spacesspectral testdiaphonydiaphony in base 2Owen scrambled point setroot mean square discrepancyweighted L2 discrepancyworst-case error of integration

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Probability distributions: general theory (60E05) Irregularities of distribution, discrepancy (11K38) General theory of distribution modulo (1) (11K06)

Related Items (7)

The \(p\)-adic diaphony of the Halton sequence ⋮ Statistical properties of $b$-adic diaphonies ⋮ Dyadic diaphony of digital sequences ⋮ On the existence of low‐diaphony sequences made of digital sequences and lattice point sets ⋮ The weighted \(b\)-adic diaphony ⋮ Diaphony, a measure of uniform distribution, and the Patterson function ⋮ Dyadic diaphony of digital nets over \(\mathbb Z_2\)

Cites Work

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• A class of generalized Walsh functions
• Dyadic diaphony
• A generalized discrepancy and quadrature error bound
• Digital (t,m,s)-nets and the spectral test
• Construction algorithms for polynomial lattice rules for multivariate integration

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