Abstract
Let H( z) be a given function in H 2 A classical problem in engineering analysis is to find a rational function G ( z) ϵ H 2 degree M say, which is closest to H( z) in 2-norm. This problem is typically approached using the cost function | H( z) − G( z)| 2, in which G( z) is allowed to vary over the set of Mth-order rational functions in H 2 and for which stationary points are sought. We show that each stationary point of degree M of this functional coincides with a weighted Hankel-norm approximant to H( z). The weighting function derives from the outer factor of the error function H( z) − G( z) stationary point of the rational H 2 approximation problem.
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