## Convergence of some greedy algorithms in Banach spaces

**A 2001 Preprint by
S. Dilworth,
D. Kutzarova, and
V. Temlyakov
**

- 2001:14
We consider some theoretical greedy algorithms for approximation in Banach spaces with respect to a general dictionary. We prove convergence of the algorithms for Banach spaces which satisfy certain smoothness assumptions. We compare the algorithms and their rates of convergence when the Banach space is $L _ p(T^d)$ ($1<p<\infty$) and the dictionary is the trigonometric system.