Constructive sparse trigonometric approximations for the functions with generalized mixed smoothness

摘要

The order bounds (in the case of uniform metrics) and exact order bounds (in the case of integral metrics) for the best m-term trigonometric approximation of periodic functions with generalized mixed smoothness from classes close to the Nikol'skii-Besov-type ones are obtained. Every of the upper bounds is realized by a constructive method based on greedy algorithms.