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Ill-Conditioned Eigensystems and the Computation of the Jordan Canonical Form

G. H. Golub and J. H. Wilkinson
SIAM Review
Vol. 18, No. 4 (Oct., 1976), pp. 578-619
Stable URL: http://www.jstor.org/stable/2029711
Page Count: 42
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Ill-Conditioned Eigensystems and the Computation of the Jordan Canonical Form
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Abstract

The solution of the complete eigenvalue problem for a nonnormal matrix A presents severe practical difficulties when A is defective or close to a defective matrix. Moreover, 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.

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