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  4. Eigenvalues, pseudospectrum and structured perturbations
 
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Eigenvalues, pseudospectrum and structured perturbations

Publikationstyp
Journal Article
Date Issued
2006
Sprache
English
Author(s)
Rump, Siegfried M.  orcid-logo
Institut
Zuverlässiges Rechnen E-19  
TORE-URI
http://hdl.handle.net/11420/8878
Journal
Linear algebra and its applications  
Volume
413
Issue
2-3 SPEC. ISS.
Start Page
567
End Page
593
Citation
Linear Algebra and Its Applications 413 (2-3 SPEC. ISS.): 567-593 (2006)
Publisher DOI
10.1016/j.laa.2005.06.009
Scopus ID
2-s2.0-31544478845
Publisher
American Elsevier Publ.
We investigate the behavior of eigenvalues under structured perturbations. We show that for many common structures such as (complex) symmetric, Toeplitz, symmetric Toeplitz, circulant and others the structured condition number is equal to the unstructured condition number for normwise perturbations, and prove similar results for real perturbations. An exception are complex skewsymmetric matrices. We also investigate componentwise complex and real perturbations. Here Hermitian and skew-Hermitian matrices are exceptional for real perturbations. Furthermore we characterize the structured (complex and real) pseudospectrum for a number of structures and show that often there is little or no significant difference to the usual, unstructured pseudospectrum.
Subjects
Componentwise
Condition number
Eigenvalues
Normwise
Pseudospectrum
Structured perturbations
DDC Class
510: Mathematik
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