Numerical methods for palindromic eigenvalue problems

We discuss numerical methods for the solution of the palindromic eigenvalue problem Ax=λ A^Tx, where A is a complex matrix. Such eigenvalue problems
occur, for example, in the vibration analysis of rail tracks.

The structure of palindromic eigenvalue problems leads to a symmetry in the spectrum: all eigenvalues occur in reciprocal pairs. The need for preservation of this
symmetry in finite precision arithmetic requires the use of structure-preserving numerical methods. In this talk, we explain how such methods can be derived.