On greedy partially randomized extended Kaczmarz method for solving large sparse inconsistent linear systems

For solving large, sparse, and inconsistent linear systems, an effective method is the partially randomized extended Kaczmarz method. In this paper, we introduce a greedy probability criterion to select working rows in the partially randomized extended Kaczmarz method, and propose a greedy partially randomized extended Kaczmarz method. We derive upper bound for the expercted convergence rate of this method. Besides, numerical experiments verify the effectiveness of the greedy partially randomized extended Kaczmarz method.