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Recurrence relations for multivariate $B$-splines


Authors: Carl de Boor and Klaus Höllig
Journal: Proc. Amer. Math. Soc. 85 (1982), 397-400
MSC: Primary 41A15
DOI: https://doi.org/10.1090/S0002-9939-1982-0656111-8
MathSciNet review: 656111
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Abstract: We prove recurrence relations for a general class of multivariate ${\text {B}}$-splines, obtained as ’projections’ of convex polyhedra. Our results are simple consequences of Stokes’ theorem and include, as special cases, the recurrence relations for the standard multivariate simplicial ${\text {B}}$-spline.


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