Centrohermitian and Skew-Centrohermitian Solutions to the Minimum Residual and Matrix Nearness Problems of the Quaternion Matrix Equation $${(AXB,DXE) = (C,F)}$$ ( A X B , D X E ) = ( C , F )

Abstract

It is established that the precise solutions on the minimum residual and matrix nearness problems of the quaternion matrix equation \({(AXB,DXE)=(C,F)}\) for centrohermitian and skew-centrohermitian matrices, where X is an unknown quaternion matrix and A, B, C, D, E, and F are known quaternion matrices of suitable sizes. Moreover, an algorithm to get the solutions of the problems considered is provided, and a numerical example is also given to exemplify the results.