On the Construction of Jacobi Matrices from Mixed data
Alabama Journal of Mathematics
We show that a unique Jacobi matrix can be reconstructed from two types of mixed data: 1. its two eigenpairs, 2. its eigenvalues and the eigenvalues of its submatrix obtained by removing the first two rows and columns and its 1-1 entry. For the second case, the condition of existence is provided. In addition, we summarize the equivalent sets of parameters used to recover Jacobi matrices and show some direct connections.
Cao, Lei and Yang, Yilin, "On the Construction of Jacobi Matrices from Mixed data" (2015). Mathematics Faculty Articles. 268.