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

L-structure least squares solutions of reduced biquaternion matrix equations with applications