منابع مشابه
On 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 کاملWhat 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 کاملGeD spline estimation of multivariate Archimedean copulas
A new multivariate Archimedean copula estimation method is proposed in a non-parametric setting. The method uses the so called Geometrically Designed splines (GeD splines), recently introduced by Kaishev et al. (2006 a,b) [10] and [11], to represent the cdf of a random variable Wθ, obtained through the probability integral transform of an Archimedean copula with parameter θ. Sufficient conditio...
متن کاملThree topics in multivariate spline theory
We examine three topics at the interface between spline theory and algebraic geometry. In the first part, we show how the concept of domain points can be used to give an original explanation of Dehn–Sommerville equations relating the numbers of i-faces of a simplicial polytope in R, i = 0. . . . , n − 1. In the second part, we echo some joint works with T. Sorokina and with P. Clarke on computa...
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 Approximation Theory
سال: 1974
ISSN: 0021-9045
DOI: 10.1016/0021-9045(74)90001-x