On the convergence of some cubic spline interpolation schemes
On the convergence of some cubic spline interpolation schemes
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几种三次样条插值格式的收敛性研究
DOI：
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发表时间：
1986
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通讯作者：
R. Beatson
中科院分区：
文献类型：
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作者：
R. Beatson
三次样条插值方案在端点处不需要导数信息，具有重要的实际意义，并已包含在几个通用软件库中。本文针对这种“无导数”型的三种常用格式，给出了最优阶误差估计。$C^1 [a，b] *斜线C^2 [a，b]$函数的近似通过任何这样的“无导数”的方法来再现立方体，必然显示出对局部网格比的一些依赖。然而，对于这里研究的样条插值，这种依赖关系仅限于第一和最后一个子区间。
Cubic spline interpolation schemes which require no derivative information at the end points are of great practical importance and have been included in several general purpose software libraries. In this paper optimal order error estimates are developed for three popular schemes of this “derivative free” type. The approximation of $C^1 [a,b]ackslash C^2 [a,b]$ functions by any such “derivative free” method that reproduces cubics, necessarily displays some dependence on the local mesh ratio. However, for the spline interpolants studied here this dependence is restricted to the first and last subintervals.