Critical Points and Error Rank in Best $H_2$ Matrix Rational Approximation of Fixed McMillan Degree

Abstract : This paper deals with best rational approximation of prescribed McMillan degree to matrix-valued functions in the real Hardy space of the complement of the unit disk endowed with the Frobenius $L_2$-norm. We describe the topological structure of the set of approximants in terms of inner--unstable factorizations. This allows us to establish a two--sided tangential interpolation equation for the critical points of the criterion, and to prove that the rank of the error $F-H$ is at most $k-n$ when $F$ is rational of degree $k$ and $H$ is critical of degree $n$. In the particular case where $k=n$, it follows that $H=F$ is the unique critical point, and this entails a local uniqueness result when approximating near--rational functions.
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Rapport
RR-2970, INRIA. 1996
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https://hal.inria.fr/inria-00073728
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Dernière modification le : samedi 27 janvier 2018 - 01:31:32
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Laurent Baratchart, Martine Olivi. Critical Points and Error Rank in Best $H_2$ Matrix Rational Approximation of Fixed McMillan Degree. RR-2970, INRIA. 1996. 〈inria-00073728〉

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