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Elliptic and hyperbolic quadratic eigenvalue problems and associated distance problems

✍ Scribed by Y. Hachez; P. Van Dooren

Book ID
104155547
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
156 KB
Volume
371
Category
Article
ISSN
0024-3795

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✦ Synopsis

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 proposes explicit formulas to compute these distances and the optimal perturbations. The problem of computing the nearest elliptic or hyperbolic quadratic eigenvalue problem is also solved. Numerical results are given to illustrate the theory.

πŸ“œ SIMILAR VOLUMES

Quadratic Eigenvalue Problems
Quadratic Eigenvalue Problems
πŸ“‚ Article πŸ“… 1995 πŸ› John Wiley and Sons 🌐 English βš– 517 KB

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)