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
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;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2015.2412253
