An Greedy-type Algorithm in m-term Approximation For Besov Class with Mixed Smoothness

We propose an greedy-type adaptive compression numerical algorithm in best m-term approximation. This algorithm provides the asymptotically optimal approximation by tensor product wavelet-type basis for functions from periodic Besov class with mixed smoothness in the L_q norm. Moreover it depends only on the expansion of function f by tensor product wavelet-type basis but neither on q nor on any special features of f.