On the Jacobi Matrix Inverse Eigenvalue Problem with Mixed Given Data
Shufang Xu · SIAM Journal on Matrix Analysis and Applications · 1996
In this paper, we discuss the problem of constructing a $2n \times 2n$ Jacobi matrix $J_{2n} $ such that its eigenvalues are given distinct values $\lambda _1 ,\lambda _2 , \cdots ,\lambda _{2n} $ and its leading $n \times n$ principal submatrix is a given $n \times n$ Jacobi matrix $J_n $. We give some sufficient and necessary conditions for the solubility of the problem and propose a new fast algorithm for solving this problem. We also present some numerical results.