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Author van der Sluis, A.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Subject Keyword Perturbation of eigenvalues ♦ Non-normal matrices ♦ Departure from normality ♦ Gershgorin circles
Abstract The problem considered is to give bounds for finite perturbations of simple and multiple eigenvalues λi of nonnormal matrices, where these bounds are in terms of the eigenvalues {λi}, the departure from normality &sgr;, and the Frobenius norm ‖ ΔA ‖ F of the perturbation matrix, but not in terms of the eigensystem. The bounds which are derived are shown to be almost attainable for any set of all matrices of given {λi} and &sgr;. One conclusion is that, very roughly speaking, a simple eigenvalue λ1 is perturbed by |Δλ1| ≲ ‖ ΔA ‖F · ∏ (&sgr;/&thgr;j) where &thgr;j is of the order of magnitude of |λ1 - λj|, the product being extended over all j where &thgr;j ≲ &sgr;.
Description Affiliation: Univ. of Utrecht, Utrecht, The Netherlands (van der Sluis, A.)
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2005-08-01
Publisher Place New York
Journal Communications of the ACM (CACM)
Volume Number 18
Issue Number 1
Page Count 7
Starting Page 30
Ending Page 36

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Source: ACM Digital Library