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Convergence Properties of the Randomized Extended Gauss--Seidel and Kaczmarz Methods
The Kaczmarz and Gauss--Seidel methods both solve a linear system $\boldsymbol{X}{\boldsymbol{\beta}} = \boldsymbol{y}$ by iteratively refining the solution estimate. Recent interest in these methods has been sparked by a proof of Strohmer and Vershynin which shows the randomized Kaczmarz method converges linearly in expectation to the solution. Lewis and Leventhal …