**8. Chapter summary and conclusions**

In this chapter, two direct methods of solving inverse eigenvalue problems were presented and examples of the methods given. Both methods are not restricted in the type of matrices with which they can be employed. In both cases, *n*th order polynomial equations are obtained when working with *n*th order matrices, which must be solved for the inverse problem. Hence, good polynomial solvers, capable of producing the multiple solutions expected of both methods, are required. In using these inverse eigenvalue methods, careful care must be taken in setting up the forward modelling problem because the choice of modelling approach and chosen functions have a large effect on the order and solvability of the ensuing inverse problem.
