Rate-optimal sparse approximation of compact break-of-scale embeddings

2022/03/18 by Byrenheid, Glenn, Hübner, Janina, Weimar, Markus
#41A25 #41A45 #41A46 #42C40 #46E35 #FOS: Mathematics #Functional Analysis (math.FA) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2203.10011

Abstract

The paper is concerned with the sparse approximation of functions having hybrid regularity borrowed from the theory of solutions to electronic Schrödinger 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.

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