Vibration of fast trains, palindromic eigenvalue problems and structure-preserving doubling algorithms

The vibration of fast trains is governed by a quadratic palindromic eigenvalue problem (λ2A1T+λA0+A1)x=0, where A0,A1∈Cn×nA0,A1∈Cn×n and A0T=A0. Accurate and efficient solution can only be obtained using algorithms which preserve the structure of the eigenvalue problem. This paper reports on the successful application of the structure-preserving doubling algorithms.