Geodesic
Lower bounds for the rate of convergence of greedy algorithms
Izvestiya. Mathematics , Tome 73 (2009) no. 6, pp. 1197-1215

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We obtain a lower bound for the rate of convergence of a pure greedy algorithm in the spaces $\mathcal A_0(\mathcal D)$ and $\mathcal A_1(\mathcal D)$, and this bound turns out to be very close to the best known upper bound. We also obtain a precise lower bound for the rate of convergence of the orthogonal greedy algorithm in the space $\mathcal A_0(\mathcal D)$.
Keywords: pure greedy algorithm, best $n$-term approximation, rate of convergence.
Mots-clés : interpolation classes 
@article{IM2_2009_73_6_a5,
     author = {E. D. Livshits},
     title = {Lower bounds for the rate of convergence of greedy algorithms},
     journal = {Izvestiya. Mathematics },
     pages = {1197--1215},
     publisher = {mathdoc},
     volume = {73},
     number = {6},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2009_73_6_a5/}
}
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E. D. Livshits. Lower bounds for the rate of convergence of greedy algorithms. Izvestiya. Mathematics , Tome 73 (2009) no. 6, pp. 1197-1215. http://geodesic.mathdoc.fr/item/IM2_2009_73_6_a5/