On the Chebyshev Norm of Polynomial B-Splines

Meinardus, Günter ; Walz, Guido

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URL: https://ub-madoc.bib.uni-mannheim.de/1684
URN: urn:nbn:de:bsz:180-madoc-16849
Document Type: Working paper
Year of publication: 1992
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Mathematik und Informatik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
Subject headings (SWD): B-Spline , Hermite-Polynome , Cebysev-Spline
Abstract: Polynomial B-splines of given order m and with knots of arbitrary multiplicity are investigated with respect to their Chebyshev norm. We present a complete characterization of those B-splines with maximal and with minimal norm, compute these norms explicitly and study their behavior as m tends to infinity. Furthermore, the norm of the B-spline corresponding to the equidistant distribution of knots is studied. Finally, we analyse those types of knot distributions, for which the norms of the corresponding B-splines converge to zero as m ∞.
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