A survey of matrix inverse eigenvalue problems

The authors present a survey of some recent results regarding direct methods for solving certain symmetric inverse eigenvalue problems. The problems they discuss are those of generating a symmetric matrix either Jacobi, banded, or some variation thereof, given only some information on the eigenvalues of the matrix itself and some of its principal submatrices. Much of the motivation for the problems discussed came about from an interest in the inverse Sturm-Liouville problem.