Strong unicity in nonlinear approximation and free knot splines

Nürnberger, Günther

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URN: urn:nbn:de:bsz:180-madoc-16890
Document Type: Working paper
Year of publication: 1991
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: 41A50 41A52 41A15 ,
Subject headings (SWD): Eindeutigkeit , Beste Approximation , Spline
Keywords (English): Best uniform approximation , Splines with free knots , Uniqueness of best approximations , Strong uniqueness of best approximations , Suns
Abstract: We give a necessary alternation condition for unique local best approximation from Sm,k, the set of splines of degree m with k free knots. This result is related to a conjecture of L.L. Schumaker. Moreover, we give a characterization of functions from the interior of the strong unicity set for S1m,k, the set of splines of degree m with k free simple knots, and show that this set is dense in the unicity set. Then we give a general characterization of suns for strong unicity and show that S1m,k is a set of this type, although it is not a sun.
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