Inverse Eigenvalue Problems Of Two Special Symmetric Matrices

Two types of inverse eigenvalue problems of symmetric matrices are described in this dissertation: the one is the inverse eigenvalue problem of symmetric claw matrix plus tridiagonal matrix,and the other is the generalized inverse eigenvalue problem of symmetric arrow matrix plus tridiagonal matrix.For the inverse eigenvalue problem of symmetric claw matrix plus tridiagonal matrix,the required matrix is constructed by applying the given eigenspectrum data and the recursive relationship of the eigenpolynomials of the principal submatrix of distinct order.The problem of the inverse eigenvalues of such matrices is solved with necessary and sufficient conditions,and numerical examples are used to verify the feasibility of the method.For the second type of special symmetric matrix,symmetric arrow matrix plus tridiagonal matrix,its generalized inverse eigenvalue problem is discussed in this dissertation.The required matrix is constructed from a given positive definite matrix and related partial spectral data.The necessary and sufficient conditions of the solution are obtained.And a proper algorithm and the corresponding numerical examples of the problem are given to verify the results.