For a subdivision △ of a region in d-dimensional Euclidean space. we consider computation of dimension and of basis function in spline space S(△)consisting of all C(?)piecewise Polynomial func- tions over△of degree...For a subdivision △ of a region in d-dimensional Euclidean space. we consider computation of dimension and of basis function in spline space S(△)consisting of all C(?)piecewise Polynomial func- tions over△of degree at most k. A computational scheme is presented for computing the dimension and bases of spline space S(?)(△).This scheme based On the Grobner basis algorithm and the smooth co-factor method for computing multivariate spline. For bivariate splines, explicit basis functions of S(△)age obtained for any integer k and r when△is a cross-cut partition.展开更多
Presents information on a study which outlined the blossom approach to the dimension count of bivariate spline space. Smoothness conditions in blossoming form; Application of the approach to the case of Morgan-Scott p...Presents information on a study which outlined the blossom approach to the dimension count of bivariate spline space. Smoothness conditions in blossoming form; Application of the approach to the case of Morgan-Scott partition.展开更多
In this paper, the dimension of the spaces of bivariate spline with degree less that 2r and smoothness order r on the Morgan-Scott triangulation is considered. The concept of the instability degree in the dimension of...In this paper, the dimension of the spaces of bivariate spline with degree less that 2r and smoothness order r on the Morgan-Scott triangulation is considered. The concept of the instability degree in the dimension of spaces of bivariate spline is presented. The results in the paper make us conjecture the instability degree in the dimension of spaces of bivariate spline is infinity.展开更多
基金The Project is partly supported by the Science Technology New Star Plan of Beijing Education Committee of Beijing
文摘For a subdivision △ of a region in d-dimensional Euclidean space. we consider computation of dimension and of basis function in spline space S(△)consisting of all C(?)piecewise Polynomial func- tions over△of degree at most k. A computational scheme is presented for computing the dimension and bases of spline space S(?)(△).This scheme based On the Grobner basis algorithm and the smooth co-factor method for computing multivariate spline. For bivariate splines, explicit basis functions of S(△)age obtained for any integer k and r when△is a cross-cut partition.
基金the 973 Project on Mathematical Mechanics!G1998030600NSF and SF of National Educational Committee of China
文摘Presents information on a study which outlined the blossom approach to the dimension count of bivariate spline space. Smoothness conditions in blossoming form; Application of the approach to the case of Morgan-Scott partition.
基金Project Supported by the national Natural Science Foundation of China(No.19871010,No.69973010).
文摘In this paper, the dimension of the spaces of bivariate spline with degree less that 2r and smoothness order r on the Morgan-Scott triangulation is considered. The concept of the instability degree in the dimension of spaces of bivariate spline is presented. The results in the paper make us conjecture the instability degree in the dimension of spaces of bivariate spline is infinity.
