Quadratic eigenvalue problem: Difference between revisions

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In mathematics, the '''quadratic eigenvalue problem'''<ref>F. Tisseur and K. Meerbergen, The quadratic eigenvalue problem, SIAM

Rev., 43 (2001), pp. 235–286.</ref> (QEP) is to find scaler[[scalar]] eigenvalues[[eigenvalue]]s λ, left eigenvectors[[eigenvector]]s ''y'' and right eigenvectors ''x'' such that

:<math> Q(λ\lambda)x = 0\text{ and }y^*^\ast(λ\lambda) = 0,\, </math>

where ''Q''(λ) = λ²''A''₂&nbsp;+λA&nbsp;λ''A''₁&nbsp;+&nbsp;''A''₀, with matrix coefficients ''A''₂, ''A''₁ and ''A''₀ 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 λ²''M''&nbsp;+Cλ&nbsp;''C''λ&nbsp;+&nbsp;''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.

{{mathapplied-stub}}

==References==

<references/>