| Autor: |
Lyons, Terry, McLeod, Andrew D. |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
|
| DOI: |
10.48550/arxiv.2205.07495 |
| Popis: |
In this paper we develop the Generalised Recombination Interpolation Method (GRIM) for finding sparse approximations of functions initially given as linear combinations of some (large) number of simpler functions. GRIM is a hybrid of dynamic growth-based interpolation techniques and thinning-based reduction techniques. We establish that the number of non-zero coefficients in the approximation returned by GRIM is controlled by the concentration of the data. In the case that the functions involved are Lip$(\gamma)$ for some $\gamma > 0$ in the sense of Stein, we obtain improved convergence properties for GRIM. In particular, we prove that the level of data concentration required to guarantee that GRIM finds a good sparse approximation is decreasing with respect to the regularity parameter $\gamma > 0$. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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