## 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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