An almost-maximal residual tensor block Kaczmarz method for large tensor linear systems

Abstract

This paper presents an almost-maximal residual tensor block Kaczmarz (TBEM) method for solving a tensor linear system of equations under the t-product between tensors. The TBEM method collects all indices of the larger entries of the residual vector as the block index set for the current iteration. The convergence of the TBEM method is considered. Several numerical examples are given to illustrate the effectiveness and efficiency of the TBEM method compared with the tensor randomized Kaczmarz (TRK) and tensor randomized average Kaczmarz algorithm with random sampling (TRAKS) methods.