  The randomized Kaczmarz algorithm is one of the most popular approaches for
solving large-scale linear systems due to its simplicity and efficiency. In
this paper, we propose two classes of global randomized Kaczmarz methods for
solving large-scale linear matrix equations $AXB=C$, the global randomized
block Kaczmarz algorithm and global randomized average block Kaczmarz
algorithm. The feature of global randomized block Kaczmarz algorithm is the
fact that the current iterate is projected onto the solution space of the
sketched matrix equation at each iteration, while the global randomized average
block Kaczmarz approach is pseudoinverse-free and therefore can be deployed on
parallel computing units to achieve significant improvements in the
computational time. We prove that these two methods linearly converge in the
mean square to the minimum norm solution $X_*=A^\dag CB^\dag$ of a given linear
matrix equation. The convergence rates depend on the geometric properties of
the data matrices and their submatrices and on the size of the blocks.
Numerical results reveal that our proposed algorithms are efficient and
effective for solving large-scale matrix equations. In particular, they can
also achieve satisfying performance when applied to image deblurring problems.
