Splines with Free Knots, the Heat Equation, and the Gauß Transform

Walz, Guido

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URL: http://ub-madoc.bib.uni-mannheim.de/1707
URN: urn:nbn:de:bsz:180-madoc-17072
Document Type: Working paper
Year of publication: 1996
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 41A30 65D07 35A22 35K05 ,
Subject headings (SWD): Knotentheorie , Gauß-Approximation , Approximation , Transformation
Keywords (English): Gauß Transform , Free Knot Splines , Heat Equation , Approximation
Abstract: The Gauß (or Weierstraß) transform has applications in many fields of applied mathematics. One of its most important properties within approximation theory is the fact that it maps weak Chebychev spaces onto Chebychev spaces. The aim of this paper is twofold. First, after proving some elementary invariance properties of the Gauß transform, necessary and sufficient conditions for best approximation by (Gauß transformed) free knot spline spaces are given. Then, in Section 3, we develop a method for the numerical solution of an initial value problem for the heat equation. The present paper can be viewed as a continuation of two recent publications by Meinardus [5,6].
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