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Generalized Divided Differences, with Applications to Generalized B-Splines
Walz, Guido
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URL:
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https://ub-madoc.bib.uni-mannheim.de/1678
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URN:
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urn:nbn:de:bsz:180-madoc-16782
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Dokumenttyp:
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Arbeitspapier
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Erscheinungsjahr:
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1992
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Titel einer Zeitschrift oder einer Reihe:
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None
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Sprache der Veröffentlichung:
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Englisch
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Einrichtung:
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Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
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MADOC-Schriftenreihe:
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Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
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Fachgebiet:
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510 Mathematik
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Fachklassifikation:
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MSC:
65D07 41A15 ,
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Normierte Schlagwörter (SWD):
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B-Spline , Differenzenquotient , Rekursion
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Freie Schlagwörter (Englisch):
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Generalized B-Splines , Divided Differences , Recursion Schemes
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Abstract:
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Within the theory of spline functions, there was always great interest in the study of B-splines, i.e. splines with a finite support. In addition to the classical polynomial case, there exist also various approaches to the definition of B-splines from other function classes, such as trigonometrie or hyperbolic ones (cf. section 0). In the present paper we define B-splines from a rat her general function space, which covers almost all existing approaches as special cases. The only condition that the spaces under consideration must satisfy is that of being translation invariant, a fundamental property which we are going to define in section 2. Our definition of generalized B-splines is based on generalized divided differences, which go back to Popoviciu [14] and were further investigated by Mühlbach [10, 11]. In the first section of this paper we therefore study these operators and prove new results, such as a contour integral representation and a multistep-formula; the latter one expresses - in closed form - a generalized divided difference of order m+j by those of order m, for arbitratry j ∈ IN. This makes it possible to compute generalized divided differences recursively, even if the underlying function space is spanned by a non-complete Chebyshev system.
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Zusätzliche Informationen:
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 | Das Dokument wird vom Publikationsserver der Universitätsbibliothek Mannheim bereitgestellt. |
 Suche Autoren in
BASE:
Walz, Guido
Google Scholar:
Walz, Guido
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