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## 2006.256: The quadratic eigenvalue problem

2006.256: Françoise Tisseur and Karl Meerbergen (2001) The quadratic eigenvalue problem. SIAM Review, 43 (2). pp. 235-286. ISSN 1095-7200

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## Abstract

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.

Item Type: Article quadratic eigenvalue problem, gyroscopic system, linearization, backward error, pseudospectrum, condition number, Krylov methods, Arnoldi method, Lanczos method, Jacobi--Davidson method, eigenvalue, eigenvector, $\lambda$-matrix, matrix polynomial, second-order differential equation, vibration, Millennium footbridge, overdamped system MSC 2000 > 65 Numerical analysis 2006.256 Miss Louise Stait 09 August 2006