English

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.

Keywords

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

R2 v1 2026-06-24T10:18:32.017Z