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 pro-posed. The algorithm provides the asymptotically optimal approximation for the class of periodic functions with mixed Besov smoothness in the L q norm. Moreover, it depends only on the expansion of function f by tensor pro-duct wavelet-type basis, but neither on q nor on any special features of f.
Szász-type operators can be constructed by a Poisson process. The purpose of this paper is to derive the converse result in connection with Szász-type operators by Steckin-Marchaud-type inequalities and new Ditzian modulus of continuity. The degree of approximation on deterministic signals is also given.
