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

翻译：本文提出了简化双四元数混合最小二乘与总体最小二乘（RBMTLS）方法，用于求解简化双四元数代数中的超定系统$AX \approx B$。当矩阵$B$及矩阵$A$的若干列存在误差时，RBMTLS方法尤为适用。通过考察简化双四元数矩阵的实表示，我们研究了实RBMTLS解存在且唯一的条件，并推导出实RBMTLS解的显式表达式。所提出的方法涵盖两种特殊情况：简化双四元数总体最小二乘（RBTLS）方法与简化双四元数最小二乘（RBLS）方法。此外，该算法还可用于在复数域上寻找$AX \approx B$的最佳逼近解。最后，通过数值算例验证了我们的结论。