A Randomized Kaczmarz Algorithm with Exponential Convergence

@article{Strohmer2007ARK,
  title={A Randomized Kaczmarz Algorithm with Exponential Convergence},
  author={T. Strohmer and R. Vershynin},
  journal={Journal of Fourier Analysis and Applications},
  year={2007},
  volume={15},
  pages={262-278}
}
The Kaczmarz method for solving linear systems of equations is an iterative algorithm that has found many applications ranging from computer tomography to digital signal processing. Despite the popularity of this method, useful theoretical estimates for its rate of convergence are still scarce. We introduce a randomized version of the Kaczmarz method for consistent, overdetermined linear systems and we prove that it converges with expected exponential rate. Furthermore, this is the first solver… Expand

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