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An algorithm for the computation of the Jordan normal form of a complex square matrix is given. The definition of the Jordan normal form is modified in order to be applicable when working in finiteprecision arithmetic. It is then shown how an accurate and stable algorithm, which computes eigenvalue approximations and chains of principal vectors, can be constructed in this case. The algorithm is based on a sequence of similarity transformations and successive range-nullspace separations, following a suggestion by Kublanovskaya. It is shown how tolerance parameters in the algorithm should be chosen and how the results of the algorithm should be interpreted and evaluated. This is illustrated by a few numerical examples.
Kågström et al. (Mon,) studied this question.