中文摘要：

主要考虑利用重节点差商法求解一阶不完全Hermite插值问题。建立相应的Hermite插值公式，推导出误差估计式，并与现有的Lagrange基函数法进行比较，以说明新提出算法的优越性。

英文摘要：

This paper mainly considers solving the first order incomplete Hermite interpolation problem by the method of difference quotient. The corresponding Hermite interpolating formulas are presented and error estimates are processed. The advantage of the method reported in this paper is indicated by comparison with existing Lagrange primary function method.