تقرير
Universal discretization and sparse sampling recovery
| العنوان: | Universal discretization and sparse sampling recovery |
|---|---|
| المؤلفون: | Dai, F., Temlyakov, V. |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, Computer Science - Information Theory, Mathematics - Classical Analysis and ODEs, Mathematics - Functional Analysis, Primary 65J05, Secondary 42A05, 65D30, 41A63 |
| الوصف: | 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 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2301.05962 |
| رقم الأكسشن: | edsarx.2301.05962 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |