用重节点差商法求解埃尔米特插值函数

Solving Herm ite Interpolation Functionswith theM ethod ofDivided Difference at the Same Node

摘要: 为了求三次埃尔米特插值函数,采用重节点差商的方法,得到了类似于牛顿插值的结果.与Lagrange插值基函数法相比,本方法十分简便.就一般情况给出了三次埃尔米特插值函数的误差公式,并介绍了误差公式的证明方法.
- 埃尔米特插值 /
- 牛顿插值 /
- 分段插值 /
- 误差估计 /
- 重节点差商法
Abstract: To solve cubic-Hermite interpolation functions, the method of divided difference at same nodewas used, and the result similar toNewton s interpolation function was obtained. The proposed method ismuch simpler comparedwith Lagrange interpolationwith base function. An error formula for cubic-Hermite s interpolation functionwas derived and proven for general cases.
- Hermite interpolation /
- Newton interpolation /
- subsection interpolation /
- error estimation /
- divided difference at same node

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