Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructive subsampling of finite frames with applications in optimal
  function recovery   In this paper we present new constructive methods, random and deterministic,
for the efficient subsampling of finite frames in $\mathbb C^m$. Based on a
suitable random subsampling strategy, we are able to extract from any given
frame with bounds $0 < A \le B < \infty$ (and condition $B/A$) a similarly
conditioned reweighted subframe consisting of merely $\mathcal O(m \log m)$
elements. Further, utilizing a deterministic subsampling method based on
principles developed in [1, Sec. 3], we are able to reduce the number of
elements to $\mathcal O(m)$ (with a constant close to one). By controlling the
weights via a preconditioning step, we can, in addition, preserve the lower
frame bound in the unweighted case. This allows to derive new quasi-optimal
unweighted (left) Marcinkiewicz-Zygmund inequalities for $L_2(D, \nu)$ with
constructible node sets of size $\mathcal O(m)$ for $m$-dimensional subspaces
of bounded functions. Those can be applied e.g. for (plain) least-squares
sampling reconstruction of functions, where we obtain new quasi-optimal results
avoiding the Kadison-Singer theorem. Numerical experiments indicate the
applicability of our results.

12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th