This is an announcement for the paper "Average best $m$-term approximation" by Jan Vybiral.

Abstract: We introduce the concept of average best $m$-term approximation widths with respect to a probability measure on the unit ball of $\ell_p^n$. We estimate these quantities for the embedding $id:\ell_p^n\to\ell_q^n$ with $0<p\le q\le \infty$ for the normalized cone and surface measure. Furthermore, we consider certain tensor product weights and show that a typical vector with respect to such a measure exhibits a strong compressible (i.e. nearly sparse) structure.

Archive classification: math.FA math.NA math.ST stat.TH

Mathematics Subject Classification: 41A46 (Primary) 46B20, 60B11 (Secondary)

Remarks: 2 figures

Submitted from: jan.vybiral@oeaw.ac.at

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1011.0943

or

http://arXiv.org/abs/1011.0943