Randomized Kaczmarz algorithms: Exact MSE analysis and optimal sampling probabilities

@article{Agaskar2014RandomizedKA,
  title={Randomized Kaczmarz algorithms: Exact MSE analysis and optimal sampling probabilities},
  author={Ameya Agaskar and Chuang Wang and Yue M. Lu},
  journal={2014 IEEE Global Conference on Signal and Information Processing (GlobalSIP)},
  year={2014},
  pages={389-393}
}
The Kaczmarz method, or the algebraic reconstruction technique (ART), is a popular method for solving large-scale overdetermined systems of equations. Recently, Strohmer et al. proposed the randomized Kaczmarz algorithm, an improvement that guarantees exponential convergence to the solution. This has spurred much interest in the algorithm and its extensions. We provide in this paper an exact formula for the mean squared error (MSE) in the value reconstructed by the algorithm. We also compute… CONTINUE READING
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