Constructing Jacobi matrices with prescribed ordered defective eigenpairs and a principal submatrix

This paper considers the problem of constructing a Jacobi matrix from prescribed ordered defective eigenpairs and the leading principal submatrix. According to the relationship between the eigenvalue ordered and the number of variations in signs of the corresponding eigenvector, the necessary and sufficient conditions for the solvability of the problem are derived, and the numerical algorithm is developed. Numerical examples show that the algorithm is quite efficient.