Algorithms for hyperbolic quadratic eigenvalue problems

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Algorithms for hyperbolic quadratic eigenvalue problems

We consider the quadratic eigenvalue problem (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 ...

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ژورنال

عنوان ژورنال: Mathematics of Computation

سال: 2005

ISSN: 0025-5718

DOI: 10.1090/s0025-5718-05-01748-5