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Computational error bounds for multiple or nearly multiple eigenvalues
Publikationstyp
Journal Article
Date Issued
2001-02-15
Sprache
English
Author(s)
Institut
TORE-URI
Volume
324
Issue
1-3
Start Page
209
End Page
226
Citation
Linear Algebra and Its Applications 1-3 (324): 209-226 (2001-02-15)
Publisher DOI
Scopus ID
Publisher
American Elsevier Publ.
In this paper bounds for clusters of eigenvalues of non-selfadjoint matrices are investigated. We describe a method for the computation of rigorous error bounds for multiple or nearly multiple eigenvalues, and for a basis of the corresponding invariant subspaces. The input matrix may be real or complex, dense or sparse. The method is based on a quadratically convergent Newton-like method; it includes the case of defective eigenvalues, uncertain input matrices and the generalized eigenvalue problem. Computational results show that verified bounds are still computed even if other eigenvalues or clusters are nearby the eigenvalues under consideration.
Subjects
15A18
65G10
Algebraiceigenvalueproblem
Defectiveeigenvalues
Multipleeigenvalues
Validatedbounds
DDC Class
004: Informatik
510: Mathematik