446 research outputs found
Lebesgue type inequalities for quasi-greedy bases
We show that for quasi-greedy bases in real or complex Banach spaces the
error of the thresholding greedy algorithm of order N is bounded by the best N-
term error of approximation times a function of N which depends on the
democracy functions and the quasi-greedy constant of the basis. If the basis is
democratic this function is bounded by C logN. We show with two examples that
this bound is attained for quasi-greedy democratic bases.Comment: 19 page
Chebushev Greedy Algorithm in convex optimization
Chebyshev Greedy Algorithm is a generalization of the well known Orthogonal
Matching Pursuit defined in a Hilbert space to the case of Banach spaces. We
apply this algorithm for constructing sparse approximate solutions (with
respect to a given dictionary) to convex optimization problems. Rate of
convergence results in a style of the Lebesgue-type inequalities are proved
- …