On the power of iid information for linear approximation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910289510793216 |
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| author | Sonnleitner, Mathias Ullrich, Mario |
| author_facet | Sonnleitner, Mathias Ullrich, Mario |
| contents | This survey is concerned with the power of random information for approximation in the (deterministic) worst-case setting, with special emphasis on information consisting of functionals selected independently and identically distributed (iid) at random on a class of admissible information functionals. We present a general result based on a weighted least squares method and derive consequences for special cases. Improvements are available if the information is ``Gaussian'' or if we consider iid function values for Sobolev spaces. We include open questions to guide future research on the power of random information in the context of information-based complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_12740 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the power of iid information for linear approximation Sonnleitner, Mathias Ullrich, Mario Numerical Analysis Computational Complexity Information Theory 65-02, 41A25, 47B06, 68Q25, 94A20 This survey is concerned with the power of random information for approximation in the (deterministic) worst-case setting, with special emphasis on information consisting of functionals selected independently and identically distributed (iid) at random on a class of admissible information functionals. We present a general result based on a weighted least squares method and derive consequences for special cases. Improvements are available if the information is ``Gaussian'' or if we consider iid function values for Sobolev spaces. We include open questions to guide future research on the power of random information in the context of information-based complexity. |
| title | On the power of iid information for linear approximation |
| topic | Numerical Analysis Computational Complexity Information Theory 65-02, 41A25, 47B06, 68Q25, 94A20 |
| url | https://arxiv.org/abs/2310.12740 |