On computing condition numbers for the nonsymmetric eigenproblem

Zhaojun Bai, James Demmel, A. McKenney

Abstract: We review the theory of condition numbers for the nonsymmetric eigenproblem and give a tabular summary of bounds for eigenvalues, means of clusters of eigenvalues, eigenvectors, invariant subspaces, and related quantities. We describe the design of new algorithms for estimating these condition numbers. Fortran subroutines implementing these algorithms are in the LAPACK library [1].