The metric projection for free knot splines

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URL:	http://ub-madoc.bib.uni-mannheim.de/1688
URN:	urn:nbn:de:bsz:180-madoc-16888
Document Type:	Working paper
Year of publication:	1990
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: 41A15 41A50 41A65 ,
Subject headings (SWD):	Knotentheorie , Spline , Gleichmäßige Approximation , Metrische Projektion
Keywords (English):	best uniform approximation , metric projection
Abstract:	Only few results are known on continuity properties of the set-valued metric projection in nonlinear uniform approximation. In this paper we investigate this mapping in the case of best uniform approximation by splines of degree m with k free knots. A characterization of those functions at which the metric projection is upper semicontinuous is given. It follows that the metric projection is upper semicontinuous if and only if k ≤ m, and that it is upper semicontinuous at all "normal" functions. On the other hand, it is shown that the metric projection is never lower semicontinuous.
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BASE: Nürnberger, Günther

Google Scholar: Nürnberger, Günther

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