On smooth multivariate spline functions

Authors:
Charles K. Chui and Ren Hong Wang

Journal:
Math. Comp. **41** (1983), 131-142

MSC:
Primary 41A15; Secondary 41A63

DOI:
https://doi.org/10.1090/S0025-5718-1983-0701629-1

MathSciNet review:
701629

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper the dimensions of bivariate spline spaces with simple cross-cut grid partitions are determined and expressions of their basis functions are given. Consequently, the closures of these spaces over all partitions of the same type can be determined. A somewhat more detailed study on bivariate splines with rectangular grid partitions is included. The results in this paper can be applied to problems on interpolation and approximation by bivariate spline functions.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1983-0701629-1

Keywords:
Multivariate spline functions,
total degree,
*B*-splines,
conformality condition,
basis,
cross-cuts

Article copyright:
© Copyright 1983
American Mathematical Society