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An efficient algorithm for the generalized centro-symmetric solution of matrix equation AXB=C. (English) Zbl 1129.65030
The authors construct an iterative algorithm for solving the linear matrix equation AXB=C for a generalized centro-symmetric matrix X and show that, in the absence of roundoff errors, a solution of the matrix equation can be obtained within finite iteration steps. Numerical examples are used to show that the proposed method is efficient.
MSC:
65F30Other matrix algorithms
15A24Matrix equations and identities
References:
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[7]Peng, Y.X., Hu, X.Y., Zhang, L.: An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation AXB = C. Appl. Math. Comput. 160, 763–777 (2005)
[8]Peng, Y.X., Hu, X.Y., Zhang, L.: An iteration method for symmetric solutions and optimal approximation solution of the system of matrix equations A 1 XB 1 = C 1, A 2 XB 2 = C 2. Appl. Math. Comput. 183, 1127–1137 (2006) · Zbl 1134.65032 · doi:10.1016/j.amc.2006.05.124
[9]Peng, Z.Y.: An iterative method for the least-squares symmetric solution of the linear matrix equation AXB = C. Appl. Math. Comput. 170, 711–723 (2005) · Zbl 1081.65039 · doi:10.1016/j.amc.2004.12.032
[10]Xie, D.X., Hu, X.Y., Sheng, Y.P.: The solvability conditions for the inverse eigenproblems of symmetric and generalized centro-symmetric matrices and their approximations. Linear Algebra Appl. 418, 142–152 (2006) · Zbl 1109.65034 · doi:10.1016/j.laa.2006.01.027