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March 2018 Tractability of $\mathbb{L}_2$-approximation in hybrid function spaces
Peter Kritzer, Helene Laimer, Friedrich Pillichshammer
Funct. Approx. Comment. Math. 58(1): 89-104 (March 2018). DOI: 10.7169/facm/1649

Abstract

We consider multivariate $\mathbb{L}_2$-approximation in reproducing kernel Hilbert spaces which are tensor products of weighted Walsh spaces and weighted Korobov spaces. We study the minimal worst-case error $e^{\mathbb{L}_2-\mathrm{app},\Lambda}(N,d)$ of all algorithms that use $N$ information evaluations from the class $\Lambda$ in the $d$-dimensional case. The two classes $\Lambda$ considered in this paper are the class $\Lambda^{{\rm all}}$ consisting of all linear functionals and the class $\Lambda^{{\rm std}}$ consisting only of function evaluations. The focus lies on the dependence of $e^{\mathbb{L}_2-\mathrm{app},\Lambda}(N,d)$ on the dimension $d$. The main results are conditions for weak, polynomial, and strong polynomial tractability.

Citation

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Peter Kritzer. Helene Laimer. Friedrich Pillichshammer. "Tractability of $\mathbb{L}_2$-approximation in hybrid function spaces." Funct. Approx. Comment. Math. 58 (1) 89 - 104, March 2018. https://doi.org/10.7169/facm/1649

Information

Published: March 2018
First available in Project Euclid: 5 May 2017

zbMATH: 06924918
MathSciNet: MR3780036
Digital Object Identifier: 10.7169/facm/1649

Subjects:
Primary: 41A25
Secondary: 41A63, 65D15, 65Y20

Rights: Copyright © 2018 Adam Mickiewicz University

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Vol.58 • No. 1 • March 2018
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