利用插值基函数很容易得到拉格朗日插值多项式，公式结构紧凑，在理论分析中甚为方便，但当插值节点增减时全部插值基函数lk(x)(k=0,1,…,n)均要随之变化，整个公式也将发生变化， 这在实际计算中是很不方便的，为了克服这一缺点，提出了牛顿插值。

-The use of interpolation basis function can easily obtain the Lagrange interpolation polynomial, the formula is compact and in the theoretical analysis is easy, but when the interpolation nodes change all the interpolation basis function lk (x) (k = 0,1, ..., n) changes have to be followed, the whole formula will also change, which in the actual calculation is very convenient, in order to overcome this shortcoming, the Newton interpolation.