We study nonlinear m-term approximation in a Banach space with regard to a basis. It is known that in the case of a greedy basis (like the Haar basis in , 1 < p < ∞) a greedy type algorithm realizes nearly best m-term approximation for any individual function. In this paper we generalize this result in two directions. First, instead of a greedy algorithm we consider a weak greedy algorithm. Second, we study in detail unconditional nongreedy bases (like the multivariate Haar basis in , 1 < p < ∞, p ≠ 2). We prove some convergence results and also some results on convergence rate of weak type greedy algorithms. Our results are expressed in terms of properties of the basis with respect to a given weakness sequence.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm161-3-1,
author = {A. Kamont and V. N. Temlyakov},
title = {Greedy approximation and the multivariate Haar system},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {199-223},
zbl = {1071.41032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm161-3-1}
}
A. Kamont; V. N. Temlyakov. Greedy approximation and the multivariate Haar system. Studia Mathematica, Tome 162 (2004) pp. 199-223. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm161-3-1/