Gradient based iterative solutions for general linear matrix equations

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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.

Keywords

Lyapunov matrix equations
Sylvester matrix equations
Iterations
Least-squares
Estimation

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This work was supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars (State Education Ministry).

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