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Constructing the Explicit Expression of Bivariate Simplex Splines and Applications

Author: ZuoXinChun
Tutor: ZhaoGuoHui
School: Dalian University of Technology
Course: Computational Mathematics
Keywords: Simplex splines Cone Spline Explicit expression Homogeneous
CLC: O174.41
Type: Master's thesis
Year: 2006
Downloads: 61
Quote: 1
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Abstract


Spline function is called with a certain smoothness segment or slice defined polynomial function . Multivariate splines in function approximation , scientific and engineering computing , computer-aided geometric design , finite element wavelets and other fields have a wide range of applications . On the other hand , based on multivariate splines with some areas of mathematics , such as abstract algebra , algebraic geometry , differential equations , and combinatorial mathematics , are also closely related . Since multivariate spline function is heavily dependent on the geometric properties of the domain split , thus showing a very complicated situation. As for the general location of the plane in the m points, each connecting two points , i.e. to get a complete view , constitute S m-3 m-4 two dimensional simplex splines support set of split . In this paper, on one yuan B- spline function Homogeneitisation expressions and symmetry derived multivariate B- spline function, the two-dimensional simplex spline function, on the one hand can be given for each complete graph traversal cell- explicit expression on the other hand, for the plane which m points , there has m cone spline by spline function of these cones are given a combination of simplex splines explicit expressions. Then the two-dimensional simplex splines Homogeneitisation expressions to polished multi-faceted corners , and finally the use of combinations of cone spline function given simplex spline expression demonstrated with minimum support set of S 4 < / sub> 2 spline function can be composed of two S 1 0 simplex spline convolution form .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions > Constructive theory of functions > Approximation Theory
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