A shift-splitting hierarchical identification iterative algorithm for solving the matrix equation $AX - \overline{X} B=C$

Based on the Hermitian and skew Hermitian splitting of the coefficient matrices, we demonstrate a shift-splitting hierarchical identification (SSHI) iterative algorithm to solve the matrix equation $AX - \overline{X} B=C$ . For any initial value, the suggested method converges to the exact solution under certain conditions. Three numerical examples are presented to demonstrate the effectiveness of the shift-splitting hierarchical identification (SSHI) iterative method and to compare it to the Jacobi-gradient iterative algorithm (JGI) (Bayoumi in Appl. Math. Inf. Sci. (2021)) and the gradient iterative algorithm (GI).