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Parameter-dependent rank-one perturbations of singular Hermitian or symmetric pencils

Please always quote using this URN:urn:nbn:de:0296-matheon-13714
  • Structure-preserving generic low-rank perturbations are studied for classes of structured matrix pencils, including real symmetric, complex symmetric, and complex Hermitian pencils. For singular pencils it is analyzed which characteristic quantities stay invariant in the perturbed canonical form, and it is shown that the regular part of a structured matrix pencil is not affected by generic perturbations of rank one. When the rank one perturbations involve a scaling parameter, the behavior of the canonical forms in dependence of this parameter is analyzed as well.

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Metadaten
Author:Christian Mehl, Volker Mehrmann, Michal Wojtylak
URN:urn:nbn:de:0296-matheon-13714
Referee:Caren Tischendorf
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2016/02/06
Release Date:2016/02/06
Tag:Hermitian pencils; generic low-rank perturbations; singular pencils; structured Kronecker canonical form; symmetric pencils
Institute:Technische Universität Berlin
Project:C Energy and Materials (Production) / C-SE3 Stability analysis of power networks and power network models
MSC-Classification:15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A22 Matrix pencils [See also 47A56]
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
Preprint Number:1101
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