Least Squares Symmetrizable Solutions for a Class of Matrix Equations

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References

[1] A. Dajic and J. J. Koliha, “Equations ax = c and xb = b in Rings and Rings with Involution with Applications to Hilbert Space Operators,” Linear Algebra and Its Applications, Vol. 429, No. 7, 2008, pp. 1779-1809.
doi:10.1016/j.laa.2008.05.012

[2] S. K. Mitra, “The Matrix Equations AX = C, XB = D,” Linear Algebra and Its Applications, Vol. 59, 1984, pp. 171-181. doi:10.1016/0024-3795(84)90166-6

[3] K. W. E. Chu, “Singular Value and Generalized Singular Value Decomposition and the Solution of Linear Matrix Equations,” Linear Algebra and Its Applications, Vol. 88-89, 1987, pp. 83-98.
doi:10.1016/0024-3795(87)90104-2

[4] S. K. Mitra, “A Pair of Simultaneous Linear Matrix Equations A1XB1 = C1, A2XB2 = C2 and a Matrix Programming Problem,” Linear Algebra and Its Applications, Vol. 131, 1990, pp. 107-123. doi:10.1016/0024-3795(90)90377-O

[5] A. Dajic and J. J. Koliha, “Positive Solutions to the Equations AX = C, and XB = D for Hilbert Space Operators,” Journal of Mathematical Analysis and Applications, Vol. 333, No. 2, 2007, pp. 567-576.
doi:10.1016/j.jmaa.2006.11.016

[6] Q. X. Xu, “Common Hermitian and Positive Solutions to the Adjointable Operator Equations AX = C, XB = D,” Linear Algebra and Its Applications, Vol. 429, No. 1, 2008, pp. 1-11. doi:10.1016/j.laa.2008.01.030

[7] Q. W. Wang, “Bisymmetric and Centrosymmetric Solutions to Systems of Real Quaternion Matrix Equations,” Computers and Mathematics with Applications, Vol. 49, No. 5-6, 2005, pp. 641-650.
doi:10.1016/j.camwa.2005.01.014

[8] Y. Qiu and A. Wang, “Least Squares Solutions to the Equations AX = B, XC = D with Some Constraints,” Applied Mathematics and Computation, Vol. 204, No. 2, 2008, pp. 872-880. doi:10.1016/j.amc.2008.07.035

[9] F. L. Li, X. Y. Hu and L. Zhang, “The Generalized Reflexive Solution for a Class of Matrix Equations (AX = B, XC = D),” Acta Mathematica Scientia Series B, Vol. 1, No. 28, 2008, pp. 185-193.

[10] F. L. Li, X. Y. Hu and L. Zhang, “The Generalized Anti-Reflexive Solution for a Class of Matrix Equations (BX = C, XD = E),” Computational & Applied Mathematics, Vol. 1, No. 27, 2008, pp. 31-46.

[11] O. Taussky, “The Role of Symmetric Matrices in the Study of General Matrices,” Linear Algebra and Its Applications, Vol. 51, 1972, pp. 13-18.

[12] S. J. Chang, “On Positive Symmetrizable Matrices and Pre-Symmetry Iteration Algorithms,” Mathematica Numerica Sinica, Vol. 3, No. 22, 2000, pp. 379-384.

[13] Z. Y. Peng, “The Least-Squares Solution of Inverse Problem for One Kind of Symmetrizable Matrices,” Chinese Journal of Numerical Mathematics and Applications, No. 3, 2004, pp. 219-224.

[14] D. W. Fausett and C. T. Fulton, “Large Least Squares Problems Involving Kronecker Products,” SIAM Journal on Matrix Analysis and Applications, Vol. 15, No. 1, 1994, pp. 219-227. doi:10.1137/S0895479891222106