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

Eric King Wah Chu; Tsung Min Hwang; Wen Wei Lin; Chin Tien Wu

doi:10.1016/j.cam.2007.07.016

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

Eric King Wah Chu, Tsung Min Hwang, Wen Wei Lin, Chin Tien Wu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

33 Citations (Scopus)

Abstract

The vibration of fast trains is governed by a quadratic palindromic eigenvalue problem (λ² A₁^T + λ A₀ + A₁) x = 0, where A₀, A₁ ∈ C^{n × n} and A₀^T = 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.

Original language	English
Pages (from-to)	237-252
Number of pages	16
Journal	Journal of Computational and Applied Mathematics
Volume	219
Issue number	1
DOIs	https://doi.org/10.1016/j.cam.2007.07.016
Publication status	Published - 2008 Sep 15

Keywords

Doubling algorithm
Nonlinear matrix equation
Palindromic eigenvalue problem
Structure-preserving

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2007.07.016

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abstract = "The vibration of fast trains is governed by a quadratic palindromic eigenvalue problem (λ2 A1T + λ A0 + A1) x = 0, where A0, 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.",

keywords = "Doubling algorithm, Nonlinear matrix equation, Palindromic eigenvalue problem, Structure-preserving",

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AU - Chu, Eric King Wah

AU - Hwang, Tsung Min

AU - Lin, Wen Wei

AU - Wu, Chin Tien

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AB - The vibration of fast trains is governed by a quadratic palindromic eigenvalue problem (λ2 A1T + λ A0 + A1) x = 0, where A0, 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.

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KW - Nonlinear matrix equation

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KW - Structure-preserving

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