Sampling recovery in $L_2$ and other norms
Numerical Analysis
2025-12-23 v5 Computational Complexity
Numerical Analysis
Abstract
We study the recovery of functions in various norms, including with , based on function evaluations. We obtain worst case error bounds for general classes of functions in terms of the best -approximation from a given nested sequence of subspaces and the Christoffel function of these subspaces. In the case , our results imply that linear sampling algorithms are optimal up to a constant factor for many reproducing kernel Hilbert spaces.
Keywords
Cite
@article{arxiv.2305.07539,
title = {Sampling recovery in $L_2$ and other norms},
author = {David Krieg and Kateryna Pozharska and Mario Ullrich and Tino Ullrich},
journal= {arXiv preprint arXiv:2305.07539},
year = {2025}
}