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Structured Eigenvalue Condition Numbers

Please always quote using this URN:urn:nbn:de:0296-matheon-2451
  • This paper investigates the effect of structure-preserving perturbations on the eigenvalues of linearly and nonlinearly structured eigenvalue problems. Particular attention is paid to structures that form Jordan algebras, Lie algebras, and automorphism groups of a scalar product. Bounds and computable expressions for structured eigenvalue condition numbers are derived for these classes of matrices, which include complex symmetric, pseudo symmetric, persymmetric, skewsymmetric, Hamiltonian, symplectic, and orthogonal matrices. In particular we show that under mild assumptions on the scalar product, the structured and unstructured eigenvalue condition numbers are equal for structures in Jordan algebras. For Lie algebras, the effect on the condition number of incorporating structure varies greatly with the structure. We identify Lie algebras for which structure does not affect the eigenvalue condition number.

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Metadaten
Author:Michael Karow, Daniel Kressner, Francoise Tisseur
URN:urn:nbn:de:0296-matheon-2451
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2005/05/04
Release Date:2005/05/04
Preprint Number:234
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