AJGI iterative algorithm for solving coupled Sylvester matrix equations with one side

Wenli Wang, Caiqin Song

Abstract


This paper consider the coupled Sylvester matrix equations with one side, which have many important applications in control theory and system theory. Based on the Jacobi iterative algorithm and the hierarchical identification principle, the present work provides two new iterative algorithms for solving the coupled Sylvester matrix equations, which are the Jacobi-gradient based iterative algorithm and the accelerated Jacobi-gradient based iterative algorithm. It is theoretically proved that the proposed iterative algorithms are convergent for any initial matrix under appropriate conditions, and a numerical example is given to show that the presented algorithms are faster than three existing iterative algorithms, which are presented by Ding et al. (2006), Sheng (2018) and Bayoumi et al. (2018). In addition, the application of the accelerated Jacobi-gradient based iterative algorithm in dynamical systems is presented.

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