A survey on inverse and generalized inverse eigenvalue problems for Jacobi matrices (Q2470135)

A survey of well-known ideas for constructing a specific tridiagonal matrix using prescribed data is presented. In particular, two well-known methods, namely \textit{m}-functions and the Lanczos algorithm, are considered. The first method is described for a generalized inverse eigenvalue problem and the second one for a classic inverse eigenvalue problem. The relation between both methods is discussed and their unique solvability is proven.