  In this paper, several Kaczmarz-type numerical methods for solving the matrix
equation $AX=B$ and $XA=C$ are proposed, where the coefficient matrix $A$ may
be full rank or rank deficient. These methods are iterative methods without
matrix multiplication. Theoretically, the convergence of these methods is
proved. The numerical results show that these methods are more efficient than
iterative methods involving matrix multiplication for high-dimensional
matrices.

Numerical Analysis;Numerical Analysis