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arXiv · 1009.1751

Average best $m$-term approximation

Jan Vybíral
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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.

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Jan Vybíral. 2010-09-09. Average best $m$-term approximation. https://arxiv.org/abs/1009.1751

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