On convergence of a sketch-and-project method for the matrix equation $$AXB=C$$

In this paper, based on Lagrangian functions of the optimization problem we develop a sketch-and-project method for solving the linear matrix equation \(AXB = C\) by introducing three parameters. A thorough convergence analysis on the proposed method is explored in details. A lower bound on the convergence rate and some convergence conditions are derived. By varying three parameters in the new method and convergence theorems, an array of well-known algorithms and their convergence results are recovered. Finally, numerical experiments are given to illustrate the effectiveness of recovered methods.