This paper presents a framework for computing the structure-constrained least squares solutions to the generalized reduced biquaternion matrix equations (RBMEs). The investigation focuses on three different matrix equations: a linear matrix equation with multiple unknown L-structures, a linear matrix equation with one unknown L-structure, and the general coupled linear matrix equations with one unknown L-structure. Our approach leverages the complex representation of reduced biquaternion matrices. To showcase the versatility of the developed framework, we utilize it to find structure-constrained solutions for complex and real matrix equations, broadening its applicability to various inverse problems. Specifically, we explore its utility in addressing partially described inverse eigenvalue problems (PDIEPs) and generalized PDIEPs. Our study concludes with numerical examples.

翻译：本文提出了一个框架，用于计算广义简化双四元数矩阵方程的结构约束最小二乘解。研究聚焦于三种不同的矩阵方程：涉及多个未知L-结构的线性矩阵方程、一个未知L-结构的线性矩阵方程，以及一个未知L-结构的广义耦合线性矩阵方程。我们的方法利用了简化双四元数矩阵的复数表示。为展示所提框架的通用性，我们将其用于寻找复矩阵方程和实矩阵方程的结构约束解，从而扩展其在各类反问题中的适用性。具体而言，我们探讨了其在部分描述逆特征值问题及广义部分描述逆特征值问题中的应用。研究最后通过数值算例进行验证。