On Lebesgue-type inequalities for greedy approximation (Q2643860)

Lebesgue proved an inequality that relates the error of a particular method of approximation by the trigonometric polynomials of order n to the best possible error of approximation by the trigonometric polynomials of order n. In the case of approximation with regard to bases, the Lebesgue-type inequalities are known both in linear and in nonlinear settings. In this paper, the authors describe a pure greedy algorithm for a general dictionary. A general Lebesgue-type inequality for the pure greedy algorithm with regard to a m-coherent dictionary is proved, and an analogous inequality is established for the orthogonal greedy algorithm.