On smooth multivariate spline functions

Chui, Charles K.; Wang, Ren Hong

doi:10.1090/S0025-5718-1983-0701629-1

On smooth multivariate spline functions
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by Charles K. Chui and Ren Hong Wang PDF

Math. Comp. 41 (1983), 131-142 Request permission

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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Approximation of Functions of Several Variables