Abstract
In this paper, an iterative algorithm is constructed for solving linear matrix equation AXB = C over generalized centro-symmetric matrix X. We show that, by this algorithm, a solution or the least-norm solution of the matrix equation AXB = C can be obtained within finite iteration steps in the absence of roundoff errors; we also obtain the optimal approximation solution to a given matrix X 0 in the solution set of which. In addition, given numerical examples show that the iterative method is efficient.
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Golub, G.H., Van Loan, C.F.: Matrix computations [M]. John Hopkins University Press, Baltimore, MD (1996)
Zhou, F.Z., Hu, X.Y., Zhang, L.: The solvability conditions for the inverse eigenvalue problems of centro-symmetric matrices. Linear Algebra Appl. 364, 147–160 (2003)
Dai, H.: On the symmetric solutions of linear matrix equations. Linear Algebra Appl. 131, 1–7 (1990)
Chu, K.E.: Symmetric solutions of linear matrix equations by matrix decompositions. Linear Algebra Appl. 119, 35–50 (1989)
Mitra, S.K.: Common solutions to a pair of linear matrix equations A 1 XB 1 = C 1, A 2 XB 2 = C 2. Proc. Camb. Philos. Soc. 74, 213–216 (1973)
Peng, X.Y., Hu, X.Y., Zhang, L.: The reflexive and anti-reflexive solutions of the matrix equation A * XB = C. J. Comput. Appl. Math. 200, 749–760 (2007)
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)
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)
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)
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)
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Liang, Ml., You, Ch. & Dai, Lf. An efficient algorithm for the generalized centro-symmetric solution of matrix equation A X B = C . Numer Algor 44, 173–184 (2007). https://doi.org/10.1007/s11075-007-9097-z
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DOI: https://doi.org/10.1007/s11075-007-9097-z