Average Best m-term Approximation

Greedy bases are best for m-term approximation

We study the approximation of a subset K in a Banach space X by choosing first basis B and then using n-term approximation. Into the competition for best bases we enter all unconditional bases for X. We show that if the subset K ⊂ X is well aligned with respect to a greedy basis B then, in certain sense, this basis is the best for this type of approximation. Our result extends the recent result...

Best m-term approximation and Lizorkin-Triebel spaces

We shall investigate the asymptotic behaviour of the widths of best mterm approximation with respect to Lizorkin-Triebel as well as Besov spaces. Our approach leads to final assertions in all possible situations. Furthermore, we shall also discuss embeddings into the approximation spaces Aq(Lp) with q < ∞. This leads to detailed information on the decay of wavelet coefficients for the elements ...

The best m-term approximation and greedy algorithms

Best Approximation in TVS

In this paper  we give newresults on the best approximation  in the Hausdorff topological vectorspace and  consider relationship  with orthogonality. Also we determined under  what conditions the map $P_{K,f}$ is upper semicontinous.

COMPRESSED SENSING AND BEST k-TERM APPROXIMATION

The typical paradigm for obtaining a compressed version of a discrete signal represented by a vector x ∈ R is to choose an appropriate basis, compute the coefficients of x in this basis, and then retain only the k largest of these with k < N . If we are interested in a bit stream representation, we also need in addition to quantize these k coefficients. Assuming, without loss of generality, tha...