Gershgorin theory for the generalized eigenvalue problem 
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 | References | Similar Articles | Additional Information
Abstract: A generalization of Gershgorin's theorem is developed for the eigenvalue problem 
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.
- [1] C. CARATHÈODORY, Theory of Functions of a Complex Variable. Vol. I, Translated by F. Steinhardt, Chelsea, New York, 1954. MR 15, 612.
- [2] A. S. HOUSEHOLDER, The Theory of Matrices in Numerical Analysis, Blaisdell, New York, 1964. MR 30 #5475. MR 0175290 (30:5475)
- [3] G. W. STEWART, "Error and perturbation bounds for subspaces associated with certain eigenvalue problems," SIAM Rev., v. 15, 1973, pp. 727-764. MR 0348988 (50:1482)
- [4] J. H. WILKINSON, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965. MR 32 #1894. MR 0184422 (32:1894)
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Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1975-0379537-3
Keywords:
Eigenvalue,
generalized eigenvalue problem,
Gershgorin theorem,
condition numbers,
inclusion regions,
perturbation theory
Article copyright:
© Copyright 1975
American Mathematical Society
