Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Fundamental Recovery Limit of Orthogonal Least Squares   Orthogonal least squares (OLS) is a classic algorithm for sparse recovery,
function approximation, and subset selection. In this paper, we analyze the
performance guarantee of the OLS algorithm. Specifically, we show that OLS
guarantees the exact reconstruction of any $K$-sparse vector in $K$ iterations,
provided that a sensing matrix has unit $\ell_{2}$-norm columns and satisfies
the restricted isometry property (RIP) of order $K+1$ with \begin{align*}
\delta_{K+1} &<C_{K} = \begin{cases} \frac{1}{\sqrt{K}}, & K=1, \\
\frac{1}{\sqrt{K+\frac{1}{4}}}, & K=2, \\ \frac{1}{\sqrt{K+\frac{1}{16}}}, &
K=3, \\ \frac{1}{\sqrt{K}}, & K \ge 4. \end{cases} \end{align*} Furthermore, we
show that the proposed guarantee is optimal in the sense that if $\delta_{K+1}
\ge C_{K}$, then there exists a counterexample for which OLS fails the
recovery.

15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph