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Zbl 1174.65382
Deng, Yuan-Bei; Bai, Zhong-Zhi; Gao, Yong-Hua
Iterative orthogonal direction methods for Hermitian minimum norm solutions of two consistent matrix equations. (English)
[J] Numer. Linear Algebra Appl. 13, No. 10, 801-823 (2006). ISSN 1070-5325; ISSN 1099-1506/e

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 2000:: *65F30 Other matrix algorithms
65F20 Overdetermined systems (numerical linear algebra)
15A24 Matrix equations

Keywords: linear matrix equation; Hermitian solutions; Moore-Penrose generalized inverse; iterative method; Hermitian minimum $F$-norm solutions; conjugate direction method; numerical results

Cited in: Zbl 1206.65145

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