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The quadratic eigenvalue problem
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DOI：10.1137/S0036144500381988.png)
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Abstract
En 中文
We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse. real, complex, Hermitian, skew-Hermitian) and the spectral properties of the problem. We classify numerical methods and catalogue available software.
Keywords:
quadratic eigenvalue problem
eigenvalue
eigenvector
lambda-matrix
matrix polynomial
second-order differential equation
vibration
Millennium footbridge
overdamped system
gyroscopic system
linearization
backward error
pseudospectrum
condition number
Krylov methods
Arnoldi method
Lanczos method
Jacobi-Davidson method