  In this work we present a rational Krylov subspace method for solving real
large-scale polynomial eigenvalue problems with T-even (that is,
symmetric/skew-symmetric) structure. Our method is based on the Even-IRA
algorithm. To preserve the structure, a sparse T-even linearization from the
class of block minimal bases pencils is applied. Due to this linearization, the
Krylov basis vectors can be computed in a cheap way. A rational decomposition
is derived so that our method explicitly allows for changes of the shift during
the iteration. This leads to a method that is able to compute parts of the
spectrum of a T-even matrix polynomial in a fast and reliable way.
