Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Low-Rank Matrix Approximation in the Infinity Norm   The low-rank matrix approximation problem with respect to the entry-wise
$\ell_{\infty}$-norm is the following: given a matrix $M$ and a factorization
rank $r$, find a matrix $X$ whose rank is at most $r$ and that minimizes
$\max_{i,j} |M_{ij} - X_{ij}|$. In this paper, we prove that the decision
variant of this problem for $r=1$ is NP-complete using a reduction from the
problem `not all equal 3SAT'. We also analyze several cases when the problem
can be solved in polynomial time, and propose a simple practical heuristic
algorithm which we apply on the problem of the recovery of a quantized low-rank
matrix.

28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph