Universal discretization and sparse sampling recovery

Autor:	Dai, F., Temlyakov, V.
Rok vydání:	2023
Předmět:	Mathematics - Numerical Analysis Computer Science - Information Theory Mathematics - Classical Analysis and ODEs Mathematics - Functional Analysis Primary 65J05 Secondary 42A05 65D30 41A63
Druh dokumentu:	Working Paper
Popis:	Recently, it was discovered that for a given function class $\mathbf{F}$ the error of best linear recovery in the square norm can be bounded above by the Kolmogorov width of $\mathbf{F}$ in the uniform norm. That analysis is based on deep results in discretization of the square norm of functions from finite dimensional subspaces. In this paper we show how very recent results on universal discretization of the square norm of functions from a collection of finite dimensional subspaces lead to an inequality between optimal sparse recovery in the square norm and best sparse approximations in the uniform norm with respect to appropriate dictionaries. Comment: 41 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2301.05962 Zobrazit plný text záznamu View this record from Arxiv