Minimal norm least square Toeplitz solution of quaternion matrix equation(A1XB1,…,AkXBk)=(C1,…,Ck)
Based on the real representation of the quaternion matrix,combined with the matrix H-repre-sentation and semi-tensor product of matrices,an effective method for solving the minimal norm least square Toeplitz solution of the quaternion matrix equation(A1XB1,…,AkXBk)=(C1,…,Ck)is proposed in this paper.The necessary and sufficient condition for the existence of Toeplitz solution to the quaternion matrix equation are provided,and a general expression of solutions is also obtained.The numerical algo-rithm is given,and examples are given to verify the effectiveness of the method in terms of error and com-putation time.
quaternion matrix equationsemi-tensor product of matricesthe minimal norm least square Toeplitz solutionreal representationH-representation
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