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The randomized extended Kaczmarz and Gauss-Seidel algorithms have attractedmuch attention because of their ability to treat all types of linear systems(consistent or inconsistent, full rank or rank-deficient). In this paper, weinterpret the randomized extended Kaczmarz and Gauss-Seidel algorithms asspecific combinations of the randomized Kaczmarz and Gauss-Seidel algorithmsand present refined upper bounds for their convergence.

Refined upper bounds for the convergence of the randomized extended Kaczmarz and Gauss-Seidel algorithms