Corpus ID: 158047016

An algorithm for the complete solution of the quartic eigenvalue problem

@article{Drmavc2019AnAF,
  title={An algorithm for the complete solution of the quartic eigenvalue problem},
  author={Zlatko Drmavc and Ivana vSain Glibi'c},
  journal={arXiv: Numerical Analysis},
  year={2019}
}
Quartic eigenvalue problem $(\lambda^4 A + \lambda^3 B + \lambda^2C + \lambda D + E)x = \mathbf{0}$ naturally arises e.g. when solving the Orr-Sommerfeld equation in the analysis of the stability of the {Poiseuille} flow, in theoretical analysis and experimental design of locally resonant phononic plates, modeling a robot with electric motors in the joints, calibration of catadioptric vision system, or e.g. computation of the guided and leaky modes of a planar waveguide. This paper proposes a… Expand
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A new method for computing all eigenvalues and eigenvectors of quadratic matrix pencil Q(λ)=λ2 M + λ C + K so that careful preprocessing allows scaling invariant/component-wise backward error and thus a better condition number. Expand
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