Algorithms for hyperbolic quadratic eigenvalue problems

@article{Guo2005AlgorithmsFH,
  title={Algorithms for hyperbolic quadratic eigenvalue problems},
  author={Chun-Hua Guo and Peter Lancaster},
  journal={Math. Comput.},
  year={2005},
  volume={74},
  pages={1777-1791}
}
We consider the quadratic eigenvalue problem (or the QEP) (λ2A + λB + C)x = 0, where A, B, and C are Hermitian with A positive definite. The QEP is called hyperbolic if (x∗Bx)2 > 4(x∗Ax)(x∗Cx) for all nonzero x ∈ Cn. We show that a relatively efficient test for hyperbolicity can be obtained by computing the eigenvalues of the QEP. A hyperbolic QEP is overdamped if B is positive definite and C is positive semidefinite. We show that a hyperbolic QEP (whose eigenvalues are necessarily real) is… CONTINUE READING

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