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

A rational Even-IRA algorithm for the solution of T-even polynomial eigenvalue problems