Before revision: We present analytical solutions to two classes of generalized matrix eigenvalue problems ( GMEVPs) which naturally cover the matrix eigenvalue problems (MEVPs) with matrices such as the tridiagonal and pentadiagonal matrices. We refer to the matrices in the two classes as Toeplitz-regularized and  corner-overlapped block-diagonal matrices.
After revision: We present analytical solutions to two classes of generalized matrix eigenvalue problems ( GEVPs) A x= \lambda Bx which arise from the finite element method (FEM) and corner-overlapped block-diagonal matrices.