Equivalence of anchored and ANOVA spaces via interpolation

DOI10.1016/J.JCO.2015.11.002zbMath1353.46025arXiv1503.08933OpenAlexW1597545339MaRDI QIDQ5963458

Jan Schneider, Aicke Hinrichs

Publication date: 19 February 2016

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

Full work available at URL: https://arxiv.org/abs/1503.08933

zbMATH Keywords

ANOVA decompositionanchored decompositionnorm equivalences

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Multidimensional problems (41A63)

Related Items (13)

Stable splittings of Hilbert spaces of functions of infinitely many variables ⋮ Very low truncation dimension for high dimensional integration under modest error demand ⋮ A note on equivalence of anchored and ANOVA spaces; lower bounds ⋮ Equivalence of weighted anchored and ANOVA spaces of functions with mixed smoothness of order one in \(L_p\) ⋮ Equivalence between Sobolev spaces of first-order dominating mixed smoothness and unanchored ANOVA spaces on ℝ^{𝕕} ⋮ Embeddings of weighted Hilbert spaces and applications to multivariate and infinite-dimensional integration ⋮ On equivalence of weighted anchored and ANOVA spaces of functions with mixed smoothness of order one in \(L_1\) or \(L_\infty\) ⋮ Truncation Dimension for Function Approximation ⋮ Truncation dimension for linear problems on multivariate function spaces ⋮ Quasi-Monte Carlo and \(\varepsilon\)-truncation dimension in ANOVA spaces ⋮ Embeddings for infinite-dimensional integration and \(L_2\)-approximation with increasing smoothness ⋮ \( \varepsilon \)-superposition and truncation dimensions in average and probabilistic settings for \(\infty \)-variate linear problems ⋮ On quasi-Monte Carlo methods in weighted ANOVA spaces

Cites Work

• Unnamed Item
• Liberating the dimension
• When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
• On tractability of approximation in special function spaces
• On embeddings of weighted tensor product Hilbert spaces
• Tractability of approximation of \(\infty\)-variate functions with bounded mixed partial derivatives
• Good lattice rules in weighted Korobov spaces with general weights

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