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**Iterative solutions of a set of matrix equations by using the hierarchical identification principle.**
*(English)*
Zbl 1468.65038

Summary: This paper is concerned with iterative solution to a class of the real coupled matrix equations. By using the hierarchical identification principle, a gradient-based iterative algorithm is constructed to solve the real coupled matrix equations \(A_1 X B_1 + A_2 X B_2 = F_1\) and \(C_1 X D_1 + C_2 X D_2 = F_2\). The range of the convergence factor is derived to guarantee that the iterative algorithm is convergent for any initial value. The analysis indicates that if the coupled matrix equations have a unique solution, then the iterative solution converges fast to the exact one for any initial value under proper conditions. A numerical example is provided to illustrate the effectiveness of the proposed algorithm.

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\textit{H. Zhang}, Abstr. Appl. Anal. 2014, Article ID 649524, 10 p. (2014; Zbl 1468.65038)

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