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Exponential Convergence-(t, s)-Weak Tractability of Approximation in Weighted Hilbert Spaces
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Version 1
: Received: 17 May 2024 / Approved: 18 May 2024 / Online: 20 May 2024 (06:52:26 CEST)
How to cite: Chen, J.; Yan, H. Exponential Convergence-(t, s)-Weak Tractability of Approximation in Weighted Hilbert Spaces. Preprints 2024, 2024051207. https://doi.org/10.20944/preprints202405.1207.v1 Chen, J.; Yan, H. Exponential Convergence-(t, s)-Weak Tractability of Approximation in Weighted Hilbert Spaces. Preprints 2024, 2024051207. https://doi.org/10.20944/preprints202405.1207.v1
Abstract
We study L_2-approximation problems in the weighted Hilbert spaces in the worst case setting. Three interesting weighted Hilbert spaces appear in this paper, whose weights are equipped with two positive parameters $\ga_j$ and $\az_j$ for $j=1,\,2,\dots,\,d$. We consider the worst case error of algorithms that use finitely many arbitrary continuous linear functionals. We discuss the exponential convergence-(t,s)-weak tractability (EC-(t,s)-WT) of these L_2-approximation problems under the absolute or normalized error criterion. In particular, we obtain the sufficient and necessary conditions for EC-(1,1)-WT and EC-(t,1)-WT with t
Keywords
L_2-approximation; information complexity; tractability; weighted Hilbert spaces
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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