| 样条空间S~μ_k（△）的维数 |
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| 引用本文： | 施锡泉.样条空间S~μ_k（△）的维数[J].数学学报,1995,38(1). |
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| 作者姓名： | 施锡泉 |
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| 作者单位： | 大连理工大学数学科学研究所 |
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| 摘 要： | 本文考虑了欧式空间Ｒ￣ｎ中任意单纯形剖分上的样条函数空间．证明了当ｋ≥（３μ＋１）２￣（ｎ－２）＋１时，计算任意单纯形剖分Δ上的ｋ次μ阶光滑样条空间的维数，可归结为计算每个σ－关联域（ｉ－单纯形σ∈Δ）Ｒ（σ）上的２￣（ｎ－ｉ－１）μ次μ阶光滑（ｉ≤ｎ－１）样条空间的维数。这里σ－关联域Ｒ（σ）是指Δ中所有包含σ的单纯形所成的单纯形剖分．
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| 关 键 词： | 样条，维数，单纯形剖分 |
| 收稿时间： | 1992-1-14 |
| 修稿时间： | 1992-12-28 |
The Dimension of Spline Spaces |
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| Shi Xiquan.The Dimension of Spline Spaces[J].Acta Mathematica Sinica,1995,38(1). |
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| Authors: | Shi Xiquan |
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| Institution: | Shi Xiquan(Department of Mathematics,Dalian University of Technology, Dalian 116024,China) |
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| Abstract: | In this paper the dimension of spline spaces on an arbitrary simplicial complex in R￣nis discussed.It is proved that when k≥(3μ+1)2￣(n-2)+1,to derive the dimension of spline spacesof degree k and smooth order μ on an arbitrary simplicial complex Δ,one need only to obtainthe dimensions of spline spaces of degree 2￣(n-i-1)μ and smooth order μ on each i-incident regionR(σ)respectively,where i-simplex σ∈Δ and R(σ)means the simplicial complex of conforming by all the simplices in Δ which contain σ. |
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| Keywords: | pline dimension simplicial complex |
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