The Inverse Eigenvalue Problem for a Class of Sub-periodic Generalized Jacobi Matrices

Abstract The inverse eigenvalue problem of matrix has practical significance in engineering and scientific calculation. In this paper, the inverse eigenvalue problem of sub-periodic generalized Jacobi matrices is studied. Two eigenvalues and corresponding eigenvectors are used to construct generalized Jacobi matrices. The existence and uniqueness conditions of the solution are discussed, the solution algorithm for the inverse problem is given, and the effectiveness of the algorithm is verified by a numerical example.