Inverse Eigenvalue Problem for Quasi-tridiagonal Matrices

The inverse eigenvalue problem of quasi-tridiagonal matrices involves reconstruction of quasi-tridiagonal matrices with the given eigenvalues satisfying some properties. In particular, we first analyze the eigenvalue properties from two aspects. On this basis, we investigate the inverse eigenvalue problem of quasi-tridiagonal matrices from the theoretic issue on solvability and the practical issue on computability. Sufficient conditions of existence of solutions of the inverse eigenvalue problem of quasi-tridiagonal matrices concerning solvability are found, and algorithms concerning computability are given with the unitary matrix tool from which we construct matrices. Finally, examples are presented to illustrate the algorithms.