Quadratic eigenvalue problem

In mathematics, the quadratic eigenvalue problem^[1] (QEP) is to find scaler eigenvalues λ, left eigenvectors y and right eigenvectors x such that

Q(λ)x=0 and y^*(λ)=0,

where Q(λ)=λ²A₂+λA₁+A₀, with matrix coefficients A₂, A₁ and A₀ that are of dimension n-by-n.

Applications

A QEP can result in part of the dynamic analysis of structures discretized by the finite element method. In this case the quadratic, Q(λ) has the form λ²M+Cλ+K, where M is the mass matrix, C is the damping matrix and K is the stiffness matrix. Other applications include vibro-acoustics and fluid dymanics.

This applied mathematics–related article is a stub. You can help Wikipedia by expanding it.

References

^ F. Tisseur and K. Meerbergen, The quadratic eigenvalue problem, SIAM Rev., 43 (2001), pp. 235–286.

[1] F. Tisseur and K. Meerbergen, The quadratic eigenvalue problem, SIAM Rev., 43 (2001), pp. 235–286.

[1]