## Generalized reflexive and generalized antireflexive solutions to a system of matrix equations.(English)Zbl 1406.15016

Summary: Two efficient iterative algorithms are presented to solve a system of matrix equations $$A_1X_1B_1 + A_2X_2B_2=E$$, $$C_1X_1D_1 + C_2X_2D_2 =F$$ over generalized reflexive and generalized antireflexive matrices. By the algorithms, the least norm generalized reflexive (antireflexive) solutions and the unique optimal approximation generalized reflexive (antireflexive) solutions to the system can be obtained, too. For any initial value, it is proved that the iterative solutions obtained by the proposed algorithms converge to their true values. The given numerical examples demonstrate that the iterative algorithms are efficient.

### MSC:

 15A24 Matrix equations and identities 65F10 Iterative numerical methods for linear systems 65F30 Other matrix algorithms (MSC2010)
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