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An Efficient Iterative Algorithm for a Quaternion Matrix Equation with I-conjugate of Unknown Matrix

We in this paper discuss the numerical method for a quaternion matrix equation with i-conjugate of unknown matrix. An iterative algorithm is proposed which can determine the solvability of the equation automatically. A solution can be obtained through the algorithm in finite iteration steps, when the equation is solvable. A numerical example illustrates the proposed algorithm is quite effective.