Greedy algorithm in m-term approximation for periodic Besov class with mixed smoothness

Abstract

Nonlinear m-term approximation plays an important role in machine learning, signal processing and statistical estimating. In this paper by means of a nondecreasing dominated function, a greedy adaptive compression numerical algorithm in the best m-term approximation with regard to tensor product wavelet-type basis is proposed. The algorithm provides the asymptotically optimal approximation for the class of periodic functions with mixed Besov smoothness in the Lq 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.