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Iterative orthogonal direction methods for Hermitian minimum norm solutions of two consistent matrix equations. (English) Zbl 1174.65382
Summary: The consistency conditions and the general expressions about the Hermitian solutions of the linear matrix equations \(AXB=C\) and \((AX,XB)=(C,D)\) are studied, where \(A\), \(B\), \(C\), and \(D\) are given matrices of suitable sizes. The Hermitian minimum \(F\)-norm solutions are obtained for these matrix equations using the Moore-Penrose generalized inverses, respectively. For both matrix equations, we design iterative methods according to the fundamental idea of the classical conjugate direction method for a standard system of linear equations. Numerical results show that these iterative methods are feasible and effective in actual computations of the solutions of the above-mentioned matrix equations.

MSC:
65F30 Other matrix algorithms (MSC2010)
65F20 Numerical solutions to overdetermined systems, pseudoinverses
15A24 Matrix equations and identities
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