Average Best m-term Approximation

作者：Vybiral Jan^*

来源：Constructive Approximation, 2012, 36(1): 83-115.

DOI：10.1007/s00365-012-9163-1

• Nonlinear approximation
• Best m-term approximation
• Average widths
• Random sparse vectors
• Cone measure
• Surface measure

We introduce the concept of average best m-term approximation widths with respect to a probability measure on the unit ball or the unit sphere of . We estimate these quantities for the embedding with 0 < pa parts per thousand currency signqa parts per thousand currency signa 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. This measure may therefore be used as a random model for sparse signals.

• 出版日期2012-8