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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
has been cited by the following article:
TITLE: Least Squares Symmetrizable Solutions for a Class of Matrix Equations
AUTHORS: Fanliang Li
KEYWORDS: Matrix Equations; Matrix Row Stacking; Topological Isomorphism; Least Squares Solution; Optimal Approximation
JOURNAL NAME: Applied Mathematics, Vol.4 No.5, May 13, 2013
ABSTRACT: In this paper, we discuss least squares symmetrizable solutions of matrix equations (AX = B, XC = D) and its optimal approximation solution. With the matrix row stacking, Kronecker product and special relations between two linear subspaces are topological isomorphism, and we derive the general solutions of least squares problem. With the invariance of the Frobenius norm under orthogonal transformations, we obtain the unique solution of optimal approximation problem. In addition, we present an algorithm and numerical experiment to obtain the optimal approximation solution.
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