Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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 𝓗 in $L_{p}([0,1])$, 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 $𝓗^{d} = 𝓗 × ... × 𝓗$ in $L_{p}([0,1]^{d})$, 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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
199-223
Opis fizyczny
Daty
wydano
2004
Twórcy
autor
- Institute of Mathematics, Polish Academy of Sciences, Abrahama 18, 81-825 Sopot, Poland
autor
- Department of Mathematics, University of South Carolina, Columbia, SC 29208, U.S.A.
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm161-3-1