Randomized Smolyak algorithms based on digital sequences for multivariate integration

DOI10.1093/imanum/drm002zbMath1134.65006OpenAlexW2074085069MaRDI QIDQ5436484

Josef Dick, Gunther Leobacher, Friedrich Pillichshammer

Publication date: 16 January 2008

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1093/imanum/drm002

zbMATH Keywords

numerical experimentsWalsh functionsrandomized algorithmworst-case errordeterministic algorithmSmolyak algorithmdigital nets and sequencesreproducing kernel Sobolev spaces\(l\)-fold sparse gridsQuasi-Monte Carlo algorithmroot-means-square worst-case error

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Random number generation in numerical analysis (65C10) Well-distributed sequences and other variations (11K36) Pseudo-random numbers; Monte Carlo methods (11K45)

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Explicit error bounds for randomized Smolyak algorithms and an application to infinite-dimensional integration

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