Bounds on the extreme generalized eigenvalues of Hermitian pencils
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Authors
Fargues, Monique P.
Subjects
Generalized eigenproblems
generalized Gershgorin theorem eigenvalue bounds
generalized Gershgorin theorem eigenvalue bounds
Advisors
Date of Issue
1990-12
Date
1990-12
Publisher
Monterey, CA; Naval Postgraduate School
Language
en_US
Abstract
We present easily computable bounds on the extreme generalized eigenvalues of Hermitian pencils (R,B) with finite eigenvalues and positive definite B matrices. The bounds are derived in terms of the generalized eigenvalues of the subpencil of maximum dimension contained in (R,B). Known results based on the generalization of the Gershgorin theorem and norm inequalities are presented and compared to the proposed bounds. It is shown that the new bounds compare favorably with these known results; they are easier to compute, require less restrictions on the properties of the pencils studied, and they are in an average sense tighter than those obtained with the norm inequality bounds
Type
Technical Report
Description
Series/Report No
Department
Electrical and Computer Engineering
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
NPS-62-90-016
Sponsors
Naval Postgraduate School, Monterey, CA
Funder
O&MN, Direct Funding
Format
21 p. : ill. ; 28 cm.
Citation
Distribution Statement
Approved for public release; distribution is unlimited.