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