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In this paper, by regarding the two-subspace Kaczmarz method [20] as analternated inertial randomized Kaczmarz algorithm we present a new convergencerate estimate which is shown to be better than that in [20] under a mildcondition. Furthermore, we accelerate the alternated inertial randomizedKaczmarz algorithm and introduce a multi-step inertial randomized Kaczmarzalgorithm which is proved to have a faster convergence rate. Numericalexperiments support the theory results and illustrate that the multi-inertialrandomized Kaczmarz algorithm significantly outperform the two-subspaceKaczmarz method in solving coherent linear systems.

Inertial randomized Kaczmarz algorithms for solving coherent linear systems