论文信息 - Real iterative algorithms for a common solution to the complex conjugate matrix equation system

Real iterative algorithms for a common solution to the complex conjugate matrix equation system

In this paper, we propose a new algorithm for the computation of the common solution to the complex conjugate matrix equation system A i X B i + C i X ? D i = E i , i = 1 , 2 , ? , N . The algorithms only need finite iteration steps, requiring only real computation. Furthermore, the algorithm can be extended to solve a more general complex matrix equation system. Two numerical examples are given to illustrate the effectiveness of the proposed algorithm.

Xue Peng | Xiao-Xia Guo

[1] Guoliang Chen,et al. A finite iterative method for solving a pair of linear matrix equations (AXB, CXD)=(E, F) , 2007, Appl. Math. Comput..

[2] Ai-Guo Wu,et al. Finite iterative algorithms for extended Sylvester-conjugate matrix equations , 2011, Math. Comput. Model..

[3] Sujit Kumar Mitra,et al. A pair of simultaneous linear matrix equations A1XB1 = C1, A2XB2 = C2 and a matrix programming problem , 1990 .

[5] Ai-Guo Wu,et al. Finite iterative algorithms for a common solution to a group of complex matrix equations , 2011, Appl. Math. Comput..

[6] Ai-Guo Wu,et al. On solutions of the matrix equations XF , 2006, Appl. Math. Comput..

[7] K. Chu,et al. Singular value and generalized singular value decompositions and the solution of linear matrix equations , 1987 .

[8] Robert E. Skelton,et al. Assigning controllability and observability Gramians in feedback control , 1991 .

[9] M. Ramadan,et al. Finite iterative algorithm for solving the generalized coupled Sylvester – conjugate matrix equations , 2013 .

[10] Tatjana Stykel,et al. Stability and inertia theorems for generalized Lyapunov equations , 2002 .

[11] Musheng Wei,et al. On solutions of the matrix equations X−AXB=C and X−AXB=C , 2003 .

[12] Dean M. Young,et al. A representation of the general common solution to the matrix equations A1XB1 = C1 and A2XB2 = C2 with applications , 2001 .