CAJ | 학술논문

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。
점진식구조공식구유점진성，즉가설득도n차핍근계적n차다항식차수요계산구유n＋1차핍근계적n＋1차다항식시，재n차다항식적기출상증가일항신적다항식급기대응적상계수즉가，종이겁대지간화료상응적계산량，차재다항식핍근등방면유착교중요적응용。해문급출료다점태륵전개식적점진식구조방법급기현식공식，병응용우곡선적핍근문제중。수치례자표명，여이유적방법상비，해문방법재차수변화시구유경소적계산량，혹경호적핍근효과。
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 .