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- Title
Critical Points and Error Rank in Best H[sub2] Matrix Rational Approximation of Fixed McMillan Degree.
- Authors
Baratchart, L.; Olivi, M.
- 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[SUB2]-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.
- Subjects
APPROXIMATION theory; MATRICES (Mathematics)
- Publication
Constructive Approximation, 1998, Vol 14, Issue 2, p273
- ISSN
0176-4276
- Publication type
Article
- DOI
10.1007/s003659900075