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

Authors:
Eric King-Wah Chu;Tsung-Min Hwang;Wen-Wei Lin;Chin-Tien Wu
Affiliations:
School of Mathematical Sciences, Monash University, Building 28, Vic. 3800, Australia;Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan;Department of Mathematics, National Tsinghua University, Hsinchu 300, Taiwan;Department of Computer Science and Engineering, National Taiwan Ocean University, Keelong 202-24, Taiwan
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

The vibration of fast trains is governed by a quadratic palindromic eigenvalue problem (@l^2A"1^T+@lA"0+A"1)x=0, where A"0,A"1@?C^n^x^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.