This study focuses on addressing the challenge of solving the reduced biquaternion equality constrained least squares (RBLSE) problem. We develop algebraic techniques to derive both complex and real solutions for the RBLSE problem by utilizing the complex and real forms of reduced biquaternion matrices. Additionally, we conduct a perturbation analysis for the RBLSE problem and establish an upper bound for the relative forward error of these solutions. Numerical examples are presented to illustrate the effectiveness of the proposed approaches and to verify the accuracy of the established upper bound for the relative forward errors.

翻译：本研究聚焦于解决约化双四元数等式约束最小二乘（RBLSE）问题的求解挑战。通过利用约化双四元数矩阵的复形式与实形式，我们发展了代数技术以推导RBLSE问题的复解与实解。此外，我们对RBLSE问题进行了扰动分析，并为这些解的相对前向误差建立了一个上界。数值算例被用于展示所提方法的有效性，并验证所建立的相对前向误差上界的准确性。