Uniform approximation of vectors using adaptive randomized information
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914897762189312 |
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| author | Kunsch, Robert J. Wnuk, Marcin |
| author_facet | Kunsch, Robert J. Wnuk, Marcin |
| contents | We study approximation of the embedding $\ell_p^m \rightarrow \ell_{\infty}^m$, $1 \leq p \leq 2$, based on randomized adaptive algorithms that use arbitrary linear functionals as information on a problem instance. We show upper bounds for which the complexity $n$ exhibits only a $(\log\log m)$-dependence. Our results for $p=1$ lead to an example of a gap of order $n$ (up to logarithmic factors) for the error between best adaptive and non-adaptive Monte Carlo methods. This is the largest possible gap for linear problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01098 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform approximation of vectors using adaptive randomized information Kunsch, Robert J. Wnuk, Marcin Numerical Analysis 65C, 65D, 46, 60 We study approximation of the embedding $\ell_p^m \rightarrow \ell_{\infty}^m$, $1 \leq p \leq 2$, based on randomized adaptive algorithms that use arbitrary linear functionals as information on a problem instance. We show upper bounds for which the complexity $n$ exhibits only a $(\log\log m)$-dependence. Our results for $p=1$ lead to an example of a gap of order $n$ (up to logarithmic factors) for the error between best adaptive and non-adaptive Monte Carlo methods. This is the largest possible gap for linear problems. |
| title | Uniform approximation of vectors using adaptive randomized information |
| topic | Numerical Analysis 65C, 65D, 46, 60 |
| url | https://arxiv.org/abs/2408.01098 |