Journal
SIAM REVIEW
Volume 43, Issue 2, Pages 235-286Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S0036144500381988
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
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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.
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