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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Blossoming begets $B$-spline bases built better by $B$-patches
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by Wolfgang Dahmen, Charles A. Micchelli and Hans-Peter Seidel PDF
Math. Comp. 59 (1992), 97-115 Request permission

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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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 59 (1992), 97-115
  • MSC: Primary 41A15; Secondary 41A63, 65D07
  • DOI: https://doi.org/10.1090/S0025-5718-1992-1134724-1
  • MathSciNet review: 1134724