Gershgorin theory for the generalized eigenvalue problem 𝐴𝑥=𝜆𝐵𝑥

Stewart, G. W.

doi:10.1090/S0025-5718-1975-0379537-3

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
DOI: https://doi.org/10.1090/S0025-5718-1975-0379537-3
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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