Entropy-based convergence rates of greedy algorithms (Q6551364)

This paper studies the so-called greedy methods that compute optimal solutions when only using the previous steps in the computations and searching each time the current best solution before proceeding. The purpose of the article are two convergence proofs. In fact, two different algorithms are considered, and the convergence proofs are in terms of the entropy numbers of the undelying defining, compact sets. Convergence results in approximation theory normally use the so-called Kolmogorov widths as upper bounds in the estimates, but in this approach the authors use the entropy of the solution manifold in Banach space in order to have a convergence result. Among other aspects, this approach has the advantage of the estimates being the best possible.