We first study the efficiency of the Weak Rescaled Pure Greedy Algorithm with respect to a dictionary in a Hilbert space. We obtain the sufficient and necessary condition for the convergence of WRPGA for any element and any dictionary. This condition is weaker than that of the Weak Pure Greedy Algorithm. Moreover, we estimate the error of WRPGA for general element. Then, we derive the corresponding results on some uniformly smooth Banach spaces.

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