Stability of tensor product B-splines on domains

Authors:
Bernhard Mößner;Ulrich Reif
Affiliations:
Department of Applied Mathematics, University of Freiburg, Hermann-Herder-Str. 10, 79104 Freiburg i.Br., Germany;Fachbereich Mathematik, AG 3, University of Technology Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany
Venue:
Journal of Approximation Theory
Year:
2008

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Abstract

We construct a uniformly stable family of bases for tensor product spline approximation on domains in R^d. These bases are derived from the standard B-spline basis by normalization with respect to the L^p-norm and a selection process relying on refined estimates for the de Boor-Fix functionals.