DocumentCode
1761995
Title
On the Exponential Convergence of the Kaczmarz Algorithm
Author
Liang Dai ; Schon, Thomas B.
Author_Institution
Dept. of Inf. Technol., Uppsala Univ., Uppsala, Sweden
Volume
22
Issue
10
fYear
2015
fDate
Oct. 2015
Firstpage
1571
Lastpage
1574
Abstract
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.
Keywords
asymptotic stability; convergence of numerical methods; iterative methods; KA; Kaczmarz algorithm; asymptotic stability; dynamical system; exponential convergence; linear equations; Algorithm design and analysis; Approximation methods; Convergence; Equations; Heuristic algorithms; Mathematical model; Signal processing algorithms; Cyclic algorithm; Kaczmarz algorithm; stability analysis;
fLanguage
English
Journal_Title
Signal Processing Letters, IEEE
Publisher
ieee
ISSN
1070-9908
Type
jour
DOI
10.1109/LSP.2015.2412253
Filename
7058437
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