Rate-optimal sparse approximation of compact break-of-scale embeddings
Numerical Analysis
2022-03-21 v1 Numerical Analysis
Functional Analysis
Abstract
The paper is concerned with the sparse approximation of functions having hybrid regularity borrowed from the theory of solutions to electronic Schr\"odinger equations due to Yserentant [43]. We use hyperbolic wavelets to introduce corresponding new spaces of Besov- and Triebel-Lizorkin-type to particularly cover the energy norm approximation of functions with dominating mixed smoothness. Explicit (non-)adaptive algorithms are derived that yield sharp dimension-independent rates of convergence.
Cite
@article{arxiv.2203.10011,
title = {Rate-optimal sparse approximation of compact break-of-scale embeddings},
author = {Glenn Byrenheid and Janina Hübner and Markus Weimar},
journal= {arXiv preprint arXiv:2203.10011},
year = {2022}
}
Comments
35 pages, 2 figures