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 ( λ 2 A 1 T + λ A 0 + A 1 ) x = 0 , where A 0 , A 1 ∈ C n × n and A 0 T = A 0 . 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.