Ill-conditioned eigensystems and the computation of the Jordan canonical form

@inproceedings{Golub2007IllconditionedEA,
  title={Ill-conditioned eigensystems and the computation of the Jordan canonical form},
  author={G. Golub and J. H. Wilkinson},
  booktitle={Milestones in Matrix Computation},
  year={2007}
}
The solution of the complete eigenvalue problem for a non-normal matrix A presents severe practical difficulties when A is defective or close to a defective matrix. However in the presence of rounding errors one cannot even determine whether or not a matrix is defective. Several of the more stable methods for computing the Jordan canonical form are discussed together with the alternative approach of computing well-defined bases (usually orthogonal) of the relevant invariant subspaces. 
106 Citations
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