Greedy algorithm and m-term trigonometric approximation

We study the following nonlinear method of approximation by trigonometric polynomials in this paper. For a periodic function f we take as an approximant a trigonometric polynomial of the form G(m) (f) := Sigma(k epsilon Lambda) (f) over cap(k)e(i(k,x)), where Lambda subset of Z(d) is a set of cardinality m containing the indices of the nl biggest (in absolute value) Fourier coefficients (f) over cap(k) of function f. We compare the efficiency of this method with the best m-term trigonometric approximation both for individual functions and for some function classes. It turns out that the operator G(m) provides the optimal (in the sense of order) error of m-term trigonometric approximation in the L-p-norm for many classes.