Unified error estimate for weak biorthogonal Greedy algorithms

Abstract

In this paper, we obtain the unified error estimate for some weak biorthogonal greedy algorithms with respect to dictionaries in Banach spaces by using some kind of [Formula: see text]-functional. From this estimate, we derive the sufficient conditions for the convergence and the convergence rates on sparse classes induced by the [Formula: see text]-functional. The results on convergence and the convergence rates are sharp.