Structure-Preserving Algorithms for Palindromic Quadratic Eigenvalue Problems Arising from Vibration of Fast Trains

In this paper, based on Patel’s algorithm (1993), we proposed a structure-preserving algorithm for solving palindromic quadratic eigenvalue problems (QEPs). We also show the relationship between the structure-preserving algorithm and the URV-based structure-preserving algorithm by Schröder (2007). For large sparse palindromic QEPs, we develop a generalized >skew-Hamiltonian implicity-restarted shift-and-invert Arnoldi algorithm (G>SHIRA) for solving the resulting >-skew-Hamiltonian pencils. Numerical experiments show that our proposed structurepreserving algorithms perform well on the palindromic QEP arising from a finite element model of high-speed trains and rails.