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

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.

Authors:

• Yongxin Yuan
• Jiashang Jiang

Keywords:

• matrix equation
• iterative algorithm
• parameter estimation
• minimum norm solution.

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