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This paper presents the reduced biquaternion mixed least squares and totalleast squares (RBMTLS) method for solving an overdetermined system $AX \approxB$ in the reduced biquaternion algebra. The RBMTLS method is suitable whenmatrix $B$ and a few columns of matrix $A$ contain errors. By examining realrepresentations of reduced biquaternion matrices, we investigate the conditionsfor the existence and uniqueness of the real RBMTLS solution and derive anexplicit expression for the real RBMTLS solution. The proposed technique coverstwo special cases: the reduced biquaternion total least squares (RBTLS) methodand the reduced biquaternion least squares (RBLS) method. Furthermore, thedeveloped method is also used to find the best approximate solution to $AX\approx B$ over a complex field. Lastly, a numerical example is presented tosupport our findings.

Algebraic technique for mixed least squares and total least squares problem in the reduced biquaternion algebra