## Iterative solutions to coupled Sylvester-conjugate matrix equations.(English)Zbl 1198.65083

Summary: This paper is concerned with iterative solutions to the coupled Sylvester-conjugate matrix equation with a unique solution. By applying a hierarchical identification principle, an iterative algorithm is established to solve this class of complex matrix equations. With a real representation of a complex matrix as a tool, a sufficient condition is given to guarantee that the iterative solutions given by the proposed algorithm converge to the exact solution for any initial matrices. In addition, a sufficient convergence condition that is easier to compute is also given by the original coefficient matrices. Finally, a numerical example is given to verify the effectiveness of the proposed algorithm.

### MSC:

 65F30 Other matrix algorithms (MSC2010) 15A24 Matrix equations and identities
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### References:

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