An Accelerated Block Randomized Kaczmarz Method

The Kaczmarz method is a kind of row iterative method for solving large-scale linear equations. In this paper, we give a block accelerated randomized Kaczmarz method which is the block version of the accelerated randomized Kaczmarz method to deal with real linear systems. We analyze the upper bounds of the mean squared error and the estimate of the convergence rate of the algorithm. Moreover, we use the method to solve the real system of t-product tensor equations which has been paid a great deal of attention in recent years. Several numerical examples are presented to illustrate our methods.