| 一类二维样条插值函数的最佳误差估计 |
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| 引用本文： | 许有信.一类二维样条插值函数的最佳误差估计[J].南京航空航天大学学报,1986(4). |
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| 作者姓名： | 许有信 |
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| 摘 要： | 本文主要结果为下述定理。 定理:设x(uw)是矩形域上关于该矩形上均匀分割的二维双三次样条插值函数,且x(uw)满足条件(5),则x(uw)在矩形域R边界上的节点处的四阶混合偏导数有估计式: |S_(i,0)|≦|Ai,n—1]||ε_(n,0)| |Bi,n—2]||ε_(0,0)|=0,-4,(-1)~2 4,…(-1)~i 4]/0,-4,(-1)~2…(-1)~n 4]|ε_(n,0)| sum from h=i to n-2 (-1)~(k(k-2)-(i 1)(i-2))0,-4,(-j)~2 4…(-1)~i 4]/0,-4,(-1)~2 4,…(-1)~(k 1) 4]0,-4,(-1)~2 4,…,(-1)~(k 2)4] (-1)~(i(i 1)/2)/0,-4,(-1)~2 4,…(-1)~n 4]|ε_(0,0)|其中等号成立的条件分别为: Ai,n—1] Bi,n—2] ε_(n0),ε_(00)>0 Ai,n—1] Bi,n—2] ε_(nm),ε_(0m)>0 其中 i=1,2,…,n—1. j=1,2 …,m—1.
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| 关 键 词： | 应用数学 样条函数 插值方法 误差估计 |
A Class of Optimal Estimation of Error of the Two-Dimensional Spline Interpolating Function |
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| Xu Youxin.A Class of Optimal Estimation of Error of the Two-Dimensional Spline Interpolating Function[J].Journal of Nanjing University of Aeronautics & Astronautics,1986(4). |
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| Authors: | Xu Youxin |
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| Abstract: | The main result of the present paper is the following theorem.Let x(u,w)be the two-dimensional Bi-cubic spline interpolating function which is a uniform division in a rectangle,and satisfies (5) of the Reference 7],then we have the following estimation equation for the fourth order mixed partial derivatives at the nodes on boundaries of the rectangle.The above inequalities will become equalitres whenare true repectively and. |
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| Keywords: | applied mathematics spline functioin interpolation methods error estimate |
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