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30-04-2019 | Original Paper | Issue 2/2020

Detecting a hyperbolic quadratic eigenvalue problem by using a subspace algorithm

Journal:: Numerical Algorithms > Issue 2/2020

Author:: Marija Miloloža Pandur

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Abstract

We consider the quadratic eigenvalue problem (QEP) Q(λ)x := (λ²M + λD + K)x = 0. A Hermitian QEP is hyperbolic if M is positive definite and (x^HDx)² − 4(x^HMx)(x^HKx) > 0 for all nonzero vectors x. Although there exist many algorithms for detecting hyperbolicity, most of them are not suitable for large QEPs. Motivated by this, we propose a new basic subspace algorithm for detecting large hyperbolic QEPs. Furthermore, we propose a specialized algorithm and its preconditioned variant. Our algorithms can be easily adapted to detect a large overdamped QEP (a hyperbolic QEP with D positive definite and K positive semidefinite). Numerical experiments demonstrate the efficiency of our specialized algorithms.

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Title: Detecting a hyperbolic quadratic eigenvalue problem by using a subspace algorithm
Author:: Marija Miloloža Pandur
Publication date: 30-04-2019
DOI: https://doi.org/10.1007/s11075-019-00702-0
Publisher: Springer US
Journal: Numerical Algorithms
Issue 2/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265

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