# 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} }

- Published 2005 in Math. Comput.
DOI:10.1090/S0025-5718-05-01748-5

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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