摘要
Consider ℓ <sub>q</sub> -hulls, 0 < q ≤ 1, from a dictionary of M functions in <sup>L p</sup> space for 1 ≤ p < ∞. Their precise metric entropy orders are derived. Sparse linear approximation bounds are obtained to characterize the number of terms needed to achieve accurate approximation of the best function in a ℓ <sub>q</sub> -hull that is closest to a target function. Furthermore, in the special case of p = 2, it is shown that a weak orthogonal greedy algorithm achieves the optimal approximation under an additional condition. © 2012 Elsevier Inc.