Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast Matrix Rank Algorithms and Applications   We consider the problem of computing the rank of an m x n matrix A over a
field. We present a randomized algorithm to find a set of r = rank(A) linearly
independent columns in \~O(|A| + r^\omega) field operations, where |A| denotes
the number of nonzero entries in A and \omega < 2.38 is the matrix
multiplication exponent. Previously the best known algorithm to find a set of r
linearly independent columns is by Gaussian elimination, with running time
O(mnr^{\omega-2}). Our algorithm is faster when r < max(m,n), for instance when
the matrix is rectangular. We also consider the problem of computing the rank
of a matrix dynamically, supporting the operations of rank one updates and
additions and deletions of rows and columns. We present an algorithm that
updates the rank in \~O(mn) field operations. We show that these algorithms can
be used to obtain faster algorithms for various problems in numerical linear
algebra, combinatorial optimization and dynamic data structure.

17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an