A degree by degree recursive construction of Hermite spline interpolants
A degree by degree recursive construction of Hermite spline interpolants
复制标题
DOI：
10.1016/j.cam.2008.07.005
复制
发表时间：
2009-03
影响因子：
2.4
通讯作者：
Xuli Han
中科院分区：
文献类型：
--
作者：
Xuli Han
基于经典的Hermite样条插值H2n−1，即Cn−1类、2n−1次的分段插值多项式，给出了2n次的分段插值多项式H2n。显示了通过 H2n−1 计算 H2n 和通过 H2n 计算 H2n+1 的公式。因此，提出了一种构造分段插值多项式集{Hj}的简单递归方法。分段插值多项式H2ns满足与插值H2n-1相同的插值条件，并且是插值H2n+1的最佳近似。还证明了一些有趣的性质。
Based on the classical Hermite spline interpolant H2n−1, which is the piecewise interpolation polynomial of class Cn−1and degree 2n−1, a piecewise interpolation polynomial H2nof degree 2n is given. The formulas for computing H2nby H2n−1and computing H2n+1by H2nare shown. Thus a simple recursive method for the construction of the piecewise interpolation polynomial set {Hj} is presented. The piecewise interpolation polynomial H2nsatisfies the same interpolation conditions as the interpolant H2n−1, and is an optimal approximation of the interpolant H2n+1. Some interesting properties are also proved.