Abstract
Quasi-hierarchical Powell-Sabin (QHPS) splines are quadratic splines with a global C 1-continuity. They are defined on a locally refined hierarchical triangulation, and they admit a compact representation in a normalized B-spline basis. We show that sufficiently smooth functions and their derivatives can be approximated up to optimal order by a Hermite interpolating QHPS spline.
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Speleers, H., Dierckx, P., Vandewalle, S. (2010). On the Local Approximation Power of Quasi-Hierarchical Powell-Sabin Splines. In: Dæhlen, M., Floater, M., Lyche, T., Merrien, JL., Mørken, K., Schumaker, L.L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2008. Lecture Notes in Computer Science, vol 5862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11620-9_27
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DOI: https://doi.org/10.1007/978-3-642-11620-9_27
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