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Institute of Electrical and Electronics Engineers, IEEE Signal Processing Letters, 10(22), p. 1571-1574, 2015

DOI: 10.1109/lsp.2015.2412253

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On the exponential convergence of the Kaczmarz algorithm

Journal article published in 2014 by Liang Dai, Thomas B. Schön ORCID
This paper is available in a repository.
This paper is available in a repository.

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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.