Metric entropy and sparse linear approximation of \(\ell_q\)-hulls for \(0<q\leq 1\)
Given collections of functions defined on a measurable space, called dictionaries, sparse linear approximations from these to suitable target functions are studied in this paper, in particular, the smallest number of terms needed to pursue the approximation within an \(\ell_q\)-hull. This is considered, for instance, under the condition that the aforementioned elements of the dictionary have finite \(L_p\)-norms; for \(p=2\), a greedy algorithm is studied as a particular example.
scientific article; zbMATH DE number 6137306