Abstract
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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> 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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> .
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