# The quadratic eigenvalue problem

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

 PDF 38198.pdf Download (1MB)

## 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 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis Ms Lucy van Russelt 09 Aug 2006 20 Oct 2017 14:12 http://eprints.maths.manchester.ac.uk/id/eprint/466

### Actions (login required)

 View Item