On weighted Hilbert spaces and integration of functions of infinitely many variables

DOI10.1016/j.jco.2013.05.004zbMath1286.65039OpenAlexW2069678416MaRDI QIDQ2442806

Sebastian Mayer, Michael Gnewuch, Klaus Ritter

Publication date: 1 April 2014

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

Full work available at URL: https://doi.org/10.1016/j.jco.2013.05.004

zbMATH Keywords

tensor productreproducing kernel Hilbert spaceintegration problemweighted superpositionfunctions of infinitely many variables

Mathematics Subject Classification ID

Multidimensional problems (41A63) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (14)

Stable splittings of Hilbert spaces of functions of infinitely many variables ⋮ MDFEM: Multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficients using higher-order QMC and FEM ⋮ Embeddings of weighted Hilbert spaces and applications to multivariate and infinite-dimensional integration ⋮ Some Results on the Complexity of Numerical Integration ⋮ On tractability of linear tensor product problems for \(\infty \)-variate classes of functions ⋮ Efficient algorithms for multivariate and \(\infty\)-variate integration with exponential weight ⋮ Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher-order convergence ⋮ Infinite-dimensional integration and the multivariate decomposition method ⋮ Optimal randomized changing dimension algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition ⋮ Embeddings for infinite-dimensional integration and \(L_2\)-approximation with increasing smoothness ⋮ Hyperbolic cross approximation in infinite dimensions ⋮ Explicit error bounds for randomized Smolyak algorithms and an application to infinite-dimensional integration ⋮ MDFEM: multivariate decomposition finite element method for elliptic PDEs with uniform random diffusion coefficients using higher-order QMC and FEM ⋮ On embeddings of weighted tensor product Hilbert spaces

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