Numerical Aspects of Recursive Realization Algorithms

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Abstract
The known recursive algorithms for the minimal realization problem are numerically unstable. The reasons for the numerical instability are explained for Rissanen’s algorithm. It is shown how the algorithm may be “stabilized”. Finally, a numerically stable algorithm is assessed with respect to efficiency, capability (i.e. which problems can be dealt with on the available computer) and with respect to suitability for finding approximate minimal realizations.

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