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On eigenvector bounds
Publikationstyp
Journal Article
Date Issued
2003-12
Sprache
English
Author(s)
Institut
TORE-URI
Journal
Volume
43
Issue
4
Start Page
823
End Page
837
Citation
BIT Numerical Mathematics 43 (4): 823-837 (2003)
Publisher DOI
Scopus ID
We show under very general assumptions that error bounds for an individual eigenvector of a matrix can be computed if and only if the geometric multiplicity of the corresponding eigenvalue is one. Basically, this is true if not computing exactly like in computer algebra methods. We first show, under general assumptions, that nontrivial error bounds are not possible in case of geometric multiplicity greater than one. This result is also extended to symmetric, Hermitian and, more general, to normal matrices. Then we present an algorithm for the computation of error bounds for the (up to normalization) unique eigenvector in case of geometric multiplicity one. The effectiveness is demonstrated by numerical examples.
Subjects
Eigenvector inclusion
Multiple eigenvalue
Nonderogatory matrix
DDC Class
510: Mathematik