中文摘要：

渐进式构造公式具有渐进性,即假设得到n次逼近阶的n次多项式且需要计算具有n＋1次逼近阶的n＋1次多项式时,在n次多项式的基础上增加一项新的多项式及其对应的常系数即可,从而极大地简化了相应的计算量,且在多项式逼近等方面有着较重要的应用。该文给出了多点泰勒展开式的渐进式构造方法及其显式公式,并应用于曲线的逼近问题中。数值例子表明,与已有的方法相比,该文方法在次数变化时具有更小的计算量,或更好的逼近效果。

英文摘要：

A progressive formula of multi-point Taylor expansion can utilize the previous computation and obtain the resulting polynomial by adding one polynomial item with some constant parameter,which saves most of computation. This paper presents a method for progressively constructing multi-point Taylor expansion of an analytic function. Its application in curve approximation is discussed. Numerical examples show that the proposed method can achieve better approximation than some previous methods.