On the Jacobi matrix inverse eigenvalue problem with mixed given data

In this paper, we discuss the problem of constructing a 2n × 2n Jacobi matrix J2n such that its eigenvalues are given distinct values λ1, λ2, . . . , λ2n and its leading n × n principal submatrix is a given n × n Jacobi matrix Jn. 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.