Finite Iterative Algorithm for Solving a Class of Complex Matrix Equation with Two Unknowns of General Form
Mohamed A. Ramadan · Applied and Computational Mathematics · 2014
This paper is concerned with an efficient iterative algorithm to solve general the Sylvester-conjugate matrix equation of the form ∑_(i= 1)^s▒〖A_i V B_i 〗+ ∑_(j=1)^t▒〖C_j W D_j 〗=∑_(l=1)^m▒〖E_1 V ̅ 〗 F_1+C The proposed algorithm is an extension to our proposed general Sylvester-conjugate equation of the form ∑_(i= 1)^s▒〖A_i V 〗+ ∑_(j=1)^t▒〖B_j W 〗=∑_(l=1)^m▒〖E_1 V ̅ 〗 F_1+C When a solution exists for this matrix equation, for any initial matrices, the solutions can be obtained 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. Finally, a numerical example is given to verify the effectiveness of the proposed algorithm.