On randomized partial block Kaczmarz method for solving huge linear algebraic systems

This paper investigates the numerical solution of huge linear algebraic systems, in which the number of rows or columns of the coefficient matrix A is greater than 100,000. Considering the idea of K -means algorithm and removing partial row vectors with small initial residuals, we propose a partitioning strategy and construct the randomized partial block Kaczmarz method. The working block of each iteration is randomly selected by using the uniform distribution, and the convergence property is also analyzed. Numerical examples illustrate the effectiveness of the proposed method.