Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the exponential convergence of the Kaczmarz algorithm   The Kaczmarz algorithm (KA) is a popular method for solving a system of
linear equations. In this note we derive a new exponential convergence result
for the KA. The key allowing us to establish the new result is to rewrite the
KA in such a way that its solution path can be interpreted as the output from a
particular dynamical system. The asymptotic stability results of the
corresponding dynamical system can then be leveraged to prove exponential
convergence of the KA. The new bound is also compared to existing bounds.

28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex