计算与应用讨论班——Efficiency of the Weak Rescaled Pure Greedy Algorithm

Abstract:

We study the efficiency of the Weak Rescaled Pure Greedy Algorithm(WRPGA) with respect to a dictionary in a Hilbert space. We obtain the sufficient and necessary conditions for the convergence of WRPGA for any element and any dictionary. This condition is weaker than the sufficient conditions for convergence of the Weak Pure Greedy Algorithm (WPGA).Moreover we derive the error estimate of WRPGA for general element and show the results can be generalized to some Banach paces. Finally, we consider the application of the RPGA to kernel-based regression.