On Stable Eigendecompositions of Matrices

Authors:
R. Alam;S. Bora
Affiliations:
-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2005

Citing 0
Cited 2

Note on structured indefinite perturbations to Hermitian matrices

Journal of Computational and Applied Mathematics
Structured pseudospectra and structured sensitivity of eigenvalues

Journal of Computational and Applied Mathematics

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Abstract

A general framework is presented for analyzing the continuous evolution of eigendecompositions of matrices. More specifically, for arbitrary operator norms, a general framework based on pseudospectra of matrices is developed for computing upper bounds on $\epsilon$ from the Schur or block Schur forms of a complex n-by-n matrix A that ensure stability of eigendecompositions of A when A varies in the ball ${ A' : \|A-A'\| \leq \epsilon}.$ For the 2-norm and the Frobenius norm, the new bounds presented compare well with the bounds obtained by Demmel and Wilkinson.