Optimal sampling for approximation of functions
Event details
| Date | 14.12.2022 |
| Hour | 16:15 › 17:15 |
| Speaker | Matthieu Dolbeault (Laboratoire Jacques-Louis Lions, Sorbonne Université) |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
In this talk, we investigate the problem of approximating a function based on evaluations at some chosen points. A first approach, using weighted least-squares at i.i.d random points, provides a near-best approximation, however with a sampling budget larger than the dimension of the approximation space.
To reduce the gap between these two quantities, we use linear algebra for sums of rank-one matrices, and in particular the solution to the Kadison-Singer problem. This leads to sharp estimates, both in a randomized setting for L^2 functions, and in a deterministic setting for reproducing kernel Hilbert spaces.
Practical information
- General public
- Free
Organizer
- Fabio Nobile
Contact
- Fabio Nobile, Nicolas Boumal