基于Hermite插值的高精度数值积分公式

A High Accurate Numerical Integration Formula Base on Hermite Interpolation Formula

构造Hermite插值多项式,得到插值型求积公式.分析积分中值定理中间点的渐近性,得到具有更高精度的数值求积公式.对数值积分公式中的导数进行处理,最终得到不用计算导数值,只需计算节点处函数值的高精度数值求积公式.

A numerical integration formula is given after the construction of the Herrnite interpolation formula. By analyzing the asymptotic property for the location of medium point to the mean value theorem for integral, the second numerical integration formula is present. It＇s algebra accuracy is higher. Finally the third numerical integration formula is constructed, which only need to calculate the function value. It has higher accuracy and without derivative calculation.