Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Results on CGR/CUR Approximation of a Matrix   CUR and low-rank approximations are among most fundamental subjects of
numerical linear algebra, with a wide range of applications to a variety of
highly important areas of modern computing, which range from the machine
learning theory and neural networks to data mining and analysis. We first
dramatically accelerate computation of such approximations for the average
input matrix, then show some narrow classes of hard inputs for our algorithms,
and finally point out a tentative direction to narrowing such classes further
by means of pre-processing with quasi Gaussian structured multipliers. Our
extensive numerical tests with a variety of real world inputs for
regularization from Singular Matrix Database have consistently produced
reasonably close CUR approximations at a low computational cost. There is a
variety of efficient applications of our results and our techniques to
important subjects of matrix computations. Our study provides new insights and
enable design of faster algorithms for low-rank approximation by means of
sampling and oversampling, for Gaussian elimination with no pivoting and block
Gaussian elimination, and for the approximation of railing singular spaces
associated with the $\nu$ smallest singular values of a matrix having numerical
nullity. We conclude the paper with novel extensions of our acceleration to the
Fast Multipole Method and the Conjugate Gradient Algorithms. (This report is an
outline of our paper in arXiv:1611.01391.)

15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc