Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rapid factorization of structured matrices via randomized sampling   Randomized sampling has recently been demonstrated to be an efficient
technique for computing approximate low-rank factorizations of matrices for
which fast methods for computing matrix vector products are available. This
paper describes an extension of such techniques to a wider class of matrices
that are not themselves rank-deficient, but have off-diagonal blocks that are.
Such matrices arise frequently in numerical analysis and signal processing, and
there exist several methods for rapidly performing algebraic operations
(matrix-vector multiplications, matrix factorizations, matrix inversion,
\textit{etc}) on them once low-rank approximations to all off-diagonal blocks
have been constructed. The paper demonstrates that if such a matrix can be
applied to a vector in O(N) time, where the matrix is of size $N\times N$, and
if individual entries of the matrix can be computed rapidly, then in many
cases, the task of constructing approximate low-rank factorizations for all
off-diagonal blocks can be performed in $O(N k^{2})$ time, where $k$ is an
upper bound for the numerical rank of the off-diagonal blocks.

22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas