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

2009 ◽  
Vol 30 (4) ◽  
pp. 1566-1592 ◽  
Author(s):  
Tsung-Ming Huang ◽  
Wen-Wei Lin ◽  
Jiang Qian
Keyword(s):  
Eigenvalue Problems ◽  
Structure Preserving ◽  
Quadratic Eigenvalue Problems ◽  
Quadratic Eigenvalue

Gyroscopically Stabilized Systems: A Class Of Quadratic Eigenvalue Problems With Real Spectrum

1991 ◽  
Vol 44 (1) ◽  
pp. 42-53 ◽  
Author(s):  
Lawrence Barkwell ◽  
Peter Lancaster ◽  
Alexander S. Markus
Keyword(s):  
Hilbert Space ◽  
Real Line ◽  
Spectral Properties ◽  
Eigenvalue Problems ◽  
Real Spectrum ◽  
Hyperbolic Operator ◽  
Quadratic Operator ◽  
Distribution Of Eigenvalues ◽  
Quadratic Eigenvalue Problems ◽  
Quadratic Eigenvalue

AbstractEigenvalue problems for selfadjoint quadratic operator polynomials L(λ) = Iλ2 + Bλ+ C on a Hilbert space H are considered where B, C∈ℒ(H), C >0, and |B| ≥ kI + k-l C for some k >0. It is shown that the spectrum of L(λ) is real. The distribution of eigenvalues on the real line and other spectral properties are also discussed. The arguments rely on the well-known theory of (weakly) hyperbolic operator polynomials.

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