STRUCTURE-PRESERVING ALGORITHMS FOR PALINDROMIC QUADRATIC EIGENVALUE PROBLEMS ARISING FROM VIBRATION OF FAST TRAINS

Abstract

In this paper, based on Patel's algorithm (1993), we propose 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 Schroder (2007). For large sparse palindromic QEPs, we develop a generalized T-skew-Hamiltonian implicitly restarted shift-and-invert Arnoldi algorithm for solving the resulting T-skew-Hamiltonian pencils. Numerical experiments show that our proposed structure-preserving algorithms perform well on the palindromic QEP arising from a finite element model of high-speed trains and rails.