On the power of adaption and randomization
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909800405663744 |
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| author | Krieg, David Novak, Erich Ullrich, Mario |
| author_facet | Krieg, David Novak, Erich Ullrich, Mario |
| contents | We present bounds on the maximal gain of adaptive and randomized algorithms over non-adaptive, deterministic ones for approximating linear operators on convex sets. If the sets are additionally symmetric, then our results are optimal. For non-symmetric sets, we unify some notions of $n$-widths and s-numbers, and show their connection to minimal errors. We also discuss extensions to non-linear widths and approximation based on function values, and conclude with a list of open problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07108 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the power of adaption and randomization Krieg, David Novak, Erich Ullrich, Mario Numerical Analysis Computational Complexity Functional Analysis We present bounds on the maximal gain of adaptive and randomized algorithms over non-adaptive, deterministic ones for approximating linear operators on convex sets. If the sets are additionally symmetric, then our results are optimal. For non-symmetric sets, we unify some notions of $n$-widths and s-numbers, and show their connection to minimal errors. We also discuss extensions to non-linear widths and approximation based on function values, and conclude with a list of open problems. |
| title | On the power of adaption and randomization |
| topic | Numerical Analysis Computational Complexity Functional Analysis |
| url | https://arxiv.org/abs/2406.07108 |