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• W2803398473 abstract "This paper describes an extension of Fourier approximation methods for multivariate functions defined on the torus $mathbb{T}^d$ to functions in a weighted Hilbert space $L_{2}(mathbb{R}^d, omega)$ via a multivariate change of variables $psi:left(-frac{1}{2},frac{1}{2}right)^dtomathbb{R}^d$. We establish sufficient conditions on $psi$ and $omega$ such that the composition of a function in such a weighted Hilbert space with $psi$ yields a function in the Sobolev space $H_{mathrm{mix}}^{m}(mathbb{T}^d)$ of functions on the torus with mixed smoothness of natural order $m in mathbb{N}_{0}$. In this approach we adapt algorithms for the evaluation and reconstruction of multivariate trigonometric polynomials on the torus $mathbb{T}^d$ based on single and multiple reconstructing rank-$1$ lattices. Since in applications it may be difficult to choose a related function space, we make use of dimension incremental construction methods for sparse frequency sets. Various numerical tests confirm obtained theoretical results for the transformed methods." @default.
• W2803398473 created "2018-06-01" @default.
• W2803398473 creator A5020926962 @default.
• W2803398473 creator A5048562301 @default.
• W2803398473 date "2018-05-23" @default.
• W2803398473 modified "2023-09-27" @default.
• W2803398473 title "Transformed rank-1 lattices for high-dimensional approximation" @default.
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