Function values are enough for $L_2$-approximation: Part II
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866912070230867968 |
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| author | Krieg, David Ullrich, Mario |
| author_facet | Krieg, David Ullrich, Mario |
| contents | In the first part we have shown that, for $L_2$-approximation of functions from a separable Hilbert space in the worst-case setting, linear algorithms based on function values are almost as powerful as arbitrary linear algorithms if the approximation numbers are square-summable. That is, they achieve the same polynomial rate of convergence. In this sequel, we prove a similar result for separable Banach spaces and other classes of functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2011_01779 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Function values are enough for $L_2$-approximation: Part II Krieg, David Ullrich, Mario Numerical Analysis Probability 41A25, 41A45, 41A65, 60B20, 41A63 In the first part we have shown that, for $L_2$-approximation of functions from a separable Hilbert space in the worst-case setting, linear algorithms based on function values are almost as powerful as arbitrary linear algorithms if the approximation numbers are square-summable. That is, they achieve the same polynomial rate of convergence. In this sequel, we prove a similar result for separable Banach spaces and other classes of functions. |
| title | Function values are enough for $L_2$-approximation: Part II |
| topic | Numerical Analysis Probability 41A25, 41A45, 41A65, 60B20, 41A63 |
| url | https://arxiv.org/abs/2011.01779 |