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A finite iterative method for solving a pair of linear matrix equations $(AXB,CXD)=(E,F)$. (English) Zbl 1133.65026
This paper deals with the system consisting of a pair of linear matrix equations. An iterative method is proposed. The iterative method automatically determines the solvability of the system. When the system is consistent, then, for any starting, a solution can be obtained within finite steps, and the least norm solution can be computed by specifically choosing the starting matrix. Theoretical analysis and numerical tests demonstrate that the iterative method is quite efficient.

65F30Other matrix algorithms
15A24Matrix equations and identities
Full Text: DOI
[1] Mitra, S. K.: A pair of the simultaneous linear matrix equations A1XB1=C1 and A2XB2=C2. Proc. Cambridge philos., soc. 74, 213-216 (1973)
[2] Mitra, S. K.: A pair of the simultaneous linear matrix equations and a matrix programming problem. Linear algebra appl. 131, 97-123 (1990) · Zbl 0712.15010
[3] J. Van der Would, Feedback decoupling and stabilization for linear system with multiple exogenous variables, Ph.D.Thesis, Technical University of Eindhoven, Netherlands, 1987.
[4] Van Der Would, J.: Almost noninteracting control by measurement feedback, systems. Control lett. 9, 7-16 (1987)
[5] Özgüler, A. B.; Akar, N.: Acommon solution to a pair of linear matrix equations over a principle domain. Linear algebra appl. 144, 85-99 (1991) · Zbl 0718.15006
[6] Navarra, A.; Odell, P. L.; Young, D. M.: A representation of the general common solution to the matrix equations A1XB1=C1 and A2XB2=C2 with applications. Comput. math. Appl. 41, 929-935 (2001) · Zbl 0983.15016
[7] Wang, Q. W.: The decomposition of pairwise matrices and matrix equations over an arbitrary skew field. Acta math. Sinica 39, No. 3, 396-403 (1996) · Zbl 0870.15007
[8] Wang, Q. W.: A system of matrix equations over arbitrary regular rings with identity. Linear algebra appl. 384, 44-53 (2004)
[9] Meng, T.: Experimental design and decision support. Expert system the technology of knowledge management and decision making for the 21st century 1 (2001)
[10] Peng, Zhen-Yun: An iterative method for the least squares symmetric solution of the linear matrix equation AXB=C. Appl. math. Comput 160, No. 3, 763-777 (2005) · Zbl 1081.65039
[11] Zhen-yun Peng, Ya-xin Peng. An efficient iterative method for solving the matrix equation AXB+CYD=E. Numer. Linear Algebra Appl., in press. · Zbl 1174.65389
[12] Ben-Israel, A.; Greville, T. N. E.: Generalized inverse: theory and applications [M]. (2003) · Zbl 1026.15004