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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

Blossoming begets $ B$-spline bases built better by $ B$-patches

Authors: Wolfgang Dahmen, Charles A. Micchelli and Hans-Peter Seidel
Journal: Math. Comp. 59 (1992), 97-115
MSC: Primary 41A15; Secondary 41A63, 65D07
MathSciNet review: 1134724
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Abstract: The concept of symmetric recursive algorithm leads to new, s-dimensional spline spaces. We present a general scheme for constructing a collection of multivariate B-splines with $ k - 1$ continuous derivatives whose linear span contains all polynomials of degree at most k. This scheme is different from the one developed earlier by Dahmen and Micchelli and, independently, by Höllig, which was based on combinatorial principles and the geometric interpretation of the B-spline. The new spline space introduced here seems to offer possibilities for economizing the computation for evaluating linear combinations of B-splines.

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PII: S 0025-5718(1992)1134724-1
Keywords: Symmetric recursive algorithms, polar forms, multivariate B-splines, approximation, stability
Article copyright: © Copyright 1992 American Mathematical Society