WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 13, 2014
Weak Greedy Algorithms for Nonlinear Approximation with Quasi-Greedy Bases
Authors: ,
Abstract: We study weak greedy approximation with respect to quasi-greedy bases. For a Hilbert space, we prove that the error of the m-th weak greedy approximation is bounded by the error of best m-term approximation mul- tiplied by an extra factor of order lnm. However we show weak greedy algorithm realizes the best expansional m-term approximation for individual element and best m-term approximation for some sparse classes. Further- more we establish sharp Lebesgue-type inequality for expansional m-term approximation with quasi-greedy bases in Banach spaces.