Title: On the stability of normalized Powell-Sabin B-splines
Authors: Maes, Jan ×
Vanraes, Evelyne
Dierckx, Paul
Bultheel, Adhemar #
Issue Date: Sep-2004
Publisher: Elsevier
Series Title: Journal of computational and applied mathematics vol:170 issue:1 pages:181-196
Abstract: In this paper we show that the normalized Powell-Sabin B-splines form a stable basis for the max norm. The approximation constants depend only on the smallest angle in the underlying triangulation. Since the B-splines refer to the size of the Powell-Sabin triangles, we find that small Powell-Sabin triangles yield better approximation constants than big Powell-Sabin triangles. Next, in addition to the max norm, we treat the L-P norm. Here the approximation constants depend also on a fraction proper to the triangulation, thus the B-splines are not stable for the L-P norm. Finally, as a special case, we consider the B-spline bases obtained from Powell-Sabin triangles with minimal area and pay extra attention to the approximation constants for the max norm.
ISSN: 0377-0427
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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