Strong unicity of best approximations : a numerical aspect

Nürnberger, Günther

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URN: urn:nbn:de:bsz:180-madoc-19291
Document Type: Working paper
Year of publication: 1983
The title of a journal, publication series: None
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
Classification: MSC: 65D99 65D15 41A15 41A52 ,
Subject headings (SWD): Spline-Approximation , Approximationsalgorithmus
Keywords (English): Stability , unique best uniform approximations , characterization , extremal subsets , weak Chebyshev spaces
Abstract: The set of functions in C(T) which have a strongly unique best approximation from a given finite-dimensional subspace is denoted by SU(G). Since strong unicity plays an important role in numerical computations and since there the functions are only known up to some error, it is natural to ask what are the functions from the interior of SU(G). A complete characterization of those functions is given and the result is applied to weak Chebyshev and spline subspaces.
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