2018 Volume 10 Pages 17-20
In 2015, Gower and Richtárik presented a unifying framework for a variety of randomized iterative algorithms for consistent linear systems. The framework includes the randomized Kaczmarz method that exponentially converges in the mean square whenever the system is consistent. For noisy linear systems corresponding to inconsistent systems, the randomized Kaczmarz method computes an approximate solution within a fixed distance depending on the norm of the noise vector. We extend this error analysis to a general framework in inconsistent systems in a similar manner to Gower and Richtárik, and verify this theoretical analysis in numerical experiments.