Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finding structure with randomness: Probabilistic algorithms for
  constructing approximate matrix decompositions   Low-rank matrix approximations, such as the truncated singular value
decomposition and the rank-revealing QR decomposition, play a central role in
data analysis and scientific computing. This work surveys and extends recent
research which demonstrates that randomization offers a powerful tool for
performing low-rank matrix approximation. These techniques exploit modern
computational architectures more fully than classical methods and open the
possibility of dealing with truly massive data sets.
  This paper presents a modular framework for constructing randomized
algorithms that compute partial matrix decompositions. These methods use random
sampling to identify a subspace that captures most of the action of a matrix.
The input matrix is then compressed---either explicitly or implicitly---to this
subspace, and the reduced matrix is manipulated deterministically to obtain the
desired low-rank factorization. In many cases, this approach beats its
classical competitors in terms of accuracy, speed, and robustness. These claims
are supported by extensive numerical experiments and a detailed error analysis.

9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph