Gershgorin theory for the generalized eigenvalue problem $Ax=\lambda Bx$
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- by G. W. Stewart PDF
- Math. Comp. 29 (1975), 600-606 Request permission
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.References
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C. CARATHÈODORY, Theory of Functions of a Complex Variable. Vol. I, Translated by F. Steinhardt, Chelsea, New York, 1954. MR 15, 612.
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- G. W. Stewart, Error and perturbation bounds for subspaces associated with certain eigenvalue problems, SIAM Rev. 15 (1973), 727–764. MR 348988, DOI 10.1137/1015095
- J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422
Additional Information
- © Copyright 1975 American Mathematical Society
- 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