Finite-order weights imply tractability of linear multivariate problems
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Publication:1881675
DOI10.1016/j.jat.2004.06.011zbMath1064.41025OpenAlexW2092905979MaRDI QIDQ1881675
Henryk Woźniakowski, Grzegorz W. Wasilkowski
Publication date: 14 October 2004
Published in: Journal of Approximation Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jat.2004.06.011
Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Multidimensional problems (41A63)
Related Items (13)
Tractability of multivariate approximation over a weighted unanchored Sobolev space ⋮ Exact cubature for a class of functions of maximum effective dimension ⋮ Tractability of quasilinear problems. I: General results ⋮ Generalized tractability for multivariate problems. I: Linear tensor product problems and linear information ⋮ Complexity of approximation of functions of few variables in high dimensions ⋮ A survey of average case complexity for linear multivariate problems ⋮ A note on the complexity and tractability of the heat equation ⋮ Quasi-polynomial tractability ⋮ On decompositions of multivariate functions ⋮ Polynomial-time algorithms for multivariate linear problems with finite-order weights: Average case setting ⋮ Tractability of the Helmholtz equation with non-homogeneous Neumann boundary conditions: the relation to the \(L_{2}\)-approximation ⋮ Tractability of quasilinear problems II: Second-order elliptic problems ⋮ Fast Discrete Fourier Transform on Generalized Sparse Grids
Cites Work
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- The effective dimension and quasi-Monte Carlo integration
- Finite-order weights imply tractability of multivariate integration
- Worst case complexity of multivariate Feynman--Kac path integration
- Weighted tensor product algorithms for linear multivariate problems
- Good lattice rules in weighted Korobov spaces with general weights
- Polynomial-time algorithms for multivariate linear problems with finite-order weights: worst case setting
- Why Are High-Dimensional Finance Problems Often of Low Effective Dimension?
- Theory of Reproducing Kernels
- Intractability results for integration and discrepancy
- On the power of standard information for weighted approximation
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