Abstract:
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, interpolation classes, rate of convergence.
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