Optimal sampling for approximation of functions
|Hour||16:15 › 17:15|
|Speaker||Matthieu Dolbeault (Laboratoire Jacques-Louis Lions, Sorbonne Université)|
|Category||Conferences - Seminars|
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.