Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved Bounds on the Restricted Isometry Constant for Orthogonal
  Matching Pursuit   In this letter, we first construct a counter example to show that for any
given positive integer $K\geq 2$ and for any $\frac{1}{\sqrt{K+1}}\leq t<1$,
there always exist a $K-$sparse $\x$ and a matrix $\A$ with the restricted
isometry constant $\delta_{K+1}=t$ such that the OMP algorithm fails in $K$
iterations. Secondly, we show that even when
$\delta_{K+1}=\frac{1}{\sqrt{K}+1}$, the OMP algorithm can also perfectly
recover every $K-$sparse vector $\x$ from $\y=\A\x$ in $K$ iteration. This
improves the best existing results which were independently given by Mo et al.
and Wang et al.

20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an