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Exclusion theorems and the perturbation analysis of the generalized eigenvalue problem. (English) Zbl 0636.15009

A Bauer-Fike type theorem is proved for the generalized eigenvalue problem and extended for clusters of generalized eigenvalues. A perturbation analysis is given for generalized eigenvalues using a chordal metric.
Reviewer: V.Mehrmann

MSC:

15A42 Inequalities involving eigenvalues and eigenvectors
15A18 Eigenvalues, singular values, and eigenvectors
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F35 Numerical computation of matrix norms, conditioning, scaling
93B55 Pole and zero placement problems
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