The rate of convergence of the classical Thresholding Greedy Algorithm with respect to bases is studied in this paper. We bound the error of approximation by the product of both norms -- the norm of $f$ and the $A_1$-norm of $f$. We obtain some results for greedy bases, unconditional bases, and quasi-greedy bases. In particular, we prove that our bounds for the trigonometric basis and for the Haar basis are optimal.

翻译：本文研究了基于基的经典阈值贪婪算法的收敛速率。我们通过 $f$ 的范数与 $A_1$ 范数的乘积来限制逼近误差。针对贪婪基、无条件基和拟贪婪基，我们获得了一些结果。特别地，我们证明了三角基和哈尔基的误差界是最优的。