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Rapport Année : 1996

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

Martine Olivi

Résumé

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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Dates et versions

inria-00073728 , version 1 (24-05-2006)

Identifiants

  • HAL Id : inria-00073728 , version 1

Citer

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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