A survey on inverse and generalized inverse eigenvalue problems for Jacobi matrices

In this paper, we give a survey of well-known works of constructing an specific tridiagonal matrix using prescribed data. Then we focus on two well-known methods namely, m-functions and Lanczos algorithm. We describe the first method for a generalized inverse eigenvalue problem and the second one for a classic inverse eigenvalue problem. We show that these two methods are linked together. In both method we prove that the solution is unique.