Complexity of weighted approximation over \(\mathbb{R}\)
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Publication:1976271
DOI10.1006/jath.1999.3435zbMath0977.41009OpenAlexW2010722609MaRDI QIDQ1976271
Henryk Woźniakowski, Grzegorz W. Wasilkowski
Publication date: 8 January 2002
Published in: Journal of Approximation Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jath.1999.3435
Analysis of algorithms and problem complexity (68Q25) Complexity and performance of numerical algorithms (65Y20) Approximation by other special function classes (41A30)
Related Items (19)
Complexity of weighted approximation over \(\mathbb{R}^d\) ⋮ Randomly shifted lattice rules for unbounded integrands ⋮ On the Choice of Weights in a Function Space for Quasi-Monte Carlo Methods for a Class of Generalised Response Models in Statistics ⋮ On alternative quantization for doubly weighted approximation and integration over unbounded domains ⋮ Optimal algorithms for doubly weighted approximation of univariate functions ⋮ Derandomization of the Euler scheme for scalar stochastic differential equations ⋮ On efficient weighted integration via a change of variables ⋮ Tractability of approximation of \(\infty\)-variate functions with bounded mixed partial derivatives ⋮ Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients ⋮ Fast CBC construction of randomly shifted lattice rules achieving \(\mathcal{O}(n^{- 1 + \delta})\) convergence for unbounded integrands over \(\mathbb{R}^s\) in weighted spaces with POD weights ⋮ Randomly shifted lattice rules with the optimal rate of convergence for unbounded integrands ⋮ Average case complexity of weighted approximation and integration over \(\mathbb R_{+}\) ⋮ Randomly shifted lattice rules on the unit cube for unbounded integrands in high dimensions ⋮ Liberating the dimension for function approximation: standard information ⋮ Liberating the dimension ⋮ New averaging technique for approximating weighted integrals ⋮ Worst case complexity of weighted approximation and integration over \(\mathbb{R}^d\) ⋮ On embeddings of weighted tensor product Hilbert spaces ⋮ Multilevel Quasi-Monte Carlo methods for lognormal diffusion problems
Cites Work
- Deterministic and stochastic error bounds in numerical analysis
- Asymptotically optimal weighted numerical integration
- Optimal integration of Lipschitz functions with a Gaussian weight
- Explicit cost bounds of algorithms for multivariate tensor product problems
- Weighted tensor product algorithms for linear multivariate problems
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