Sampling recovery in $L_2$ and other norms
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866915688822603776 |
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| author | Krieg, David Pozharska, Kateryna Ullrich, Mario Ullrich, Tino |
| author_facet | Krieg, David Pozharska, Kateryna Ullrich, Mario Ullrich, Tino |
| contents | We study the recovery of functions in various norms, including $L_p$ with $1\le p\le\infty$, based on function evaluations. We obtain worst case error bounds for general classes of functions in terms of the best $L_2$-approximation from a given nested sequence of subspaces and the Christoffel function of these subspaces. In the case $p=\infty$, our results imply that linear sampling algorithms are optimal up to a constant factor for many reproducing kernel Hilbert spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_07539 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sampling recovery in $L_2$ and other norms Krieg, David Pozharska, Kateryna Ullrich, Mario Ullrich, Tino Numerical Analysis Computational Complexity 68Q25, 41A50, 46B09, 41A63, 47B06 We study the recovery of functions in various norms, including $L_p$ with $1\le p\le\infty$, based on function evaluations. We obtain worst case error bounds for general classes of functions in terms of the best $L_2$-approximation from a given nested sequence of subspaces and the Christoffel function of these subspaces. In the case $p=\infty$, our results imply that linear sampling algorithms are optimal up to a constant factor for many reproducing kernel Hilbert spaces. |
| title | Sampling recovery in $L_2$ and other norms |
| topic | Numerical Analysis Computational Complexity 68Q25, 41A50, 46B09, 41A63, 47B06 |
| url | https://arxiv.org/abs/2305.07539 |