Finite iterative algorithm for solving a complex of conjugate and transpose matrix equation (Q2249920)

Summary: We consider an iterative algorithm for solving a complex matrix equation with conjugate and transpose of two unknowns of the form: \(A_1VB_1 + C_1WD_1+A_2\overline{V}B_2+C_2\overline{W}D_2+A_3V^HB_3+C_3W^HD_3+A_4V^TB_4+ C_4W^TD_4=E\). With the iterative algorithm, the existence of a solution of this matrix equation can be determined automatically. When this matrix equation is consistent, for any initial matrices \(V_1, W_1\) the solutions can be obtained by iterative algorithm within finite iterative steps in the absence of round-off errors. Some lemmas and theorems are stated and proved where the iterative solutions are obtained. A numerical example is given to illustrate the effectiveness of the proposed method and to support the theoretical results of this paper.