Random points are optimal for the approximation of Sobolev functions
We show that independent and uniformly distributed sampling points are asymptotically as good as optimal sampling points for the approximation of functions from Sobolev spaces $W_p^s(\varOmega )$ on bounded convex domains $\varOmega \subset{\mathbb{R}}^d$ in the $L_q$-norm if $q
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| Veröffentlicht in: | IMA journal of numerical analysis 2024-06, Vol.44 (3), p.1346-1371 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We show that independent and uniformly distributed sampling points are asymptotically as good as optimal sampling points for the approximation of functions from Sobolev spaces $W_p^s(\varOmega )$ on bounded convex domains $\varOmega \subset{\mathbb{R}}^d$ in the $L_q$-norm if $q |
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| ISSN: | 0272-4979 1464-3642 |
| DOI: | 10.1093/imanum/drad014 |