Gradient based iterative solutions for general linear matrix equations

Authors:
Li Xie;Jie Ding;Feng Ding
Affiliations:
School of Communication and Control Engineering, Jiangnan University, Wuxi 214122, PR China;School of Communication and Control Engineering, Jiangnan University, Wuxi 214122, PR China;School of Communication and Control Engineering, Jiangnan University, Wuxi 214122, PR China
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

In this paper, we present a gradient based iterative algorithm for solving general linear matrix equations by extending the Jacobi iteration and by applying the hierarchical identification principle. Convergence analysis indicates that the iterative solutions always converge fast to the exact solutions for any initial values and small condition numbers of the associated matrices. Two numerical examples are provided to show that the proposed algorithm is effective.