An Inverse Eigenvalue Problem for Jacobi Matrices

Abstract

In this paper, we discuss an inverse eigenvalue problem for constructing a $2n\times 2n$ Jacobi matrix $T$ such that its $2n$ eigenvalues are given distinct real values and its leading principal submatrix of order $n$ is a given Jacobi matrix. A new sufficient and necessary condition for the solvability of the above problem is given in this paper. Furthermore, we present a new algorithm and give some numerical results.