Faster randomized block sparse Kaczmarz by averaging

Abstract The standard randomized sparse Kaczmarz (RSK) method is an algorithm to compute solutions of linear systems equations and uses sequential updates, thus, does not take advantage parallel computations. In this work, we introduce a (mini batch) version RSK based on averaging several steps. Naturally, allows for parallelization show that it can also leverage large overrelaxation. We prove expected convergence that, given computations be exploited, the provably provides faster than method. This viewed as variant linearized Bregman algorithm, dual block coordinate descent update, stochastic mirror or relaxed recover when batch size equal one. provide estimates inconsistent iterates converges error in order noise level. Finally, numerical examples illustrate benefits new algorithm.