Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Iterative methods for solving factorized linear systems   Stochastic iterative algorithms such as the Kaczmarz and Gauss-Seidel methods
have gained recent attention because of their speed, simplicity, and the
ability to approximately solve large-scale linear systems of equations without
needing to access the entire matrix. In this work, we consider the setting
where we wish to solve a linear system in a large matrix X that is stored in a
factorized form, X = UV; this setting either arises naturally in many
applications or may be imposed when working with large low-rank datasets for
reasons of space required for storage. We propose a variant of the randomized
Kaczmarz method for such systems that takes advantage of the factored form, and
avoids computing X. We prove an exponential convergence rate and supplement our
theoretical guarantees with experimental evidence demonstrating that the
factored variant yields significant acceleration in convergence.

8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol