On Stable Eigendecompositions of Matrices
Rafikul Alam, Shreemayee Bora · SIAM Journal on Matrix Analysis and Applications · 2005
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.