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Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems

✍ Scribed by Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Françoise


Book ID
118211790
Publisher
Society for Industrial and Applied Mathematics
Year
2009
Tongue
English
Weight
286 KB
Volume
30
Category
Article
ISSN
0895-4798

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Two important classes of quadratic eigenvalue problems are composed of elliptic and hyperbolic problems. In [Linear Algebra Appl., 351-352 (2002) 455], the distance to the nearest non-hyperbolic or non-elliptic quadratic eigenvalue problem is obtained using a global minimization problem. This paper

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We consider the quadratic eigenvalue problem with selfadjoint operators R, S and T in the Hilbert space 8. The operator S is supposed to be "large" with respect to the operators R and T. For simplicity we assume that R and T have bounded inverses. If, additionally, S is uniformly positive, then (1)