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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Gershgorin theory for the generalized eigenvalue problem $ Ax=\lambda Bx$

Author: G. W. Stewart
Journal: Math. Comp. 29 (1975), 600-606
MSC: Primary 15A42; Secondary 65F15
MathSciNet review: 0379537
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Abstract: A generalization of Gershgorin's theorem is developed for the eigenvalue problem $ Ax = \lambda Bx$ and is applied to obtain perturbation bounds for multiple eigenvalues. The results are interpreted in terms of the chordal metric on the Riemann sphere, which is especially convenient for treating infinite eigenvalues.

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Keywords: Eigenvalue, generalized eigenvalue problem, Gershgorin theorem, condition numbers, inclusion regions, perturbation theory
Article copyright: © Copyright 1975 American Mathematical Society

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