منابع مشابه
What is a multivariate spline?
The various concepts and ideas that have contributed to univariate spline theory are considered with a view to finding a suitable definition of a multivariate spline. In this way, an overview of the existing more or less complete univariate spline theory is given along with a survey of some of the high points of the current research in multivariate splines. My very first paper dealt with multiv...
متن کاملOn Smooth Multivariate Spline Functions
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 applie...
متن کاملSpaces of Bivariate Spline
We consider the spaces of bivariate C-splines of degree k deened over arbitrary triangulations of a polygonal domain. We get an explicit formula for the dimension of such spaces when k 3 + 2 and construct a local supported basis for them. The dimension formula is valid for any polygonal domain even it is complex connected , and the formula is sharp since it arrives at the lower-bound which is g...
متن کاملExact Iterative Reconstruction Algorithm for Multivariate Irregularly Sampled Functions in Spline-like Spaces: the L-theory
We prove that the exact reconstruction of a function s from its samples s(xi) on any “sufficiently dense” sampling set {xi}i∈Λ can be obtained, as long as s is known to belong to a large class of spline-like spaces in Lp(Rn). Moreover, the reconstruction can be implemented using fast algorithms. Since a limiting case is the space of bandlimited functions, our result generalizes the classical Sh...
متن کاملOn the dimension of multivariate spline spaces, especially on Alfeld splits
A computational method to obtain explicit formulas for the dimension of spline spaces over simplicial partitions is described. The method is applied to conjecture the dimension formula for the Alfeld split of an n-simplex and for several other tetrahedral partitions. AMS classification: Primary 41A15, Secondary 14Q99
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1983
ISSN: 0022-247X
DOI: 10.1016/0022-247x(83)90014-8