King-Wah Eric Chu Exclusion theorems and the perturbation analysis of the generalized eigenvalue problem. (English) Zbl 0636.15009 SIAM J. Numer. Anal. 24, 1114-1125 (1987). 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 Cited in 9 Documents 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 Keywords:Bauer-Fike theorem; exclusion theorem; sensitivity; generalized eigenvalue problem; clusters of generalized eigenvalues; perturbation analysis; chordal metric PDFBibTeX XMLCite \textit{King-Wah Eric Chu}, SIAM J. Numer. Anal. 24, 1114--1125 (1987; Zbl 0636.15009) Full Text: DOI