Iterative solutions to the linear matrix equation AXB + CXTD = E
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Iterative solutions to the linear matrix equation AXB + CXTD = E

Authors: Yongxin Yuan, Jiashang Jiang


In this paper the gradient based iterative algorithm is presented to solve the linear matrix equation AXB +CXTD = E, where X is unknown matrix, A,B,C,D,E are the given constant matrices. It is proved that if the equation has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. Two numerical examples show that the introduced iterative algorithm is quite efficient.

Keywords: matrix equation, iterative algorithm, parameter estimation, minimum norm solution.

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