切比雪夫多项式的极性在定积分计算中的应用  

Application of Chebyshev Polynomial’s Polarity in Definite Integral Calculation

作　　者：赵云云 王勇强 ZHAO Yunyun;WANG Yongqiang(Huzhou No.1 Middle School,Huzhou 313000,China;Huzhou Educational Scientific Research Center,Huzhou 313000,China)

机构地区：[1]湖州市第一中学,浙江湖州313000 [2]湖州市教育科学研究中心,浙江湖州313000

出　　处：《湖州师范学院学报》2021年第4期8-13,共6页Journal of Huzhou University

基　　金：湖州市教育科学规划课题(SZS349837)。

摘　　要：将切比雪夫多项式的极性应用于插值型求积公式的构建,得到以切比雪夫多项式的零点为插值节点的插值型求积公式,其截断误差可达到极小化.在此基础上得到相应的复化求积公式,并通过实例验证算法的有效性.In this paper,applying the polarity of Chebyshev polynomial to the construction of the interpolation quadrature formula,the interpolation quadrature formula with the zero points of Chebyshev polynomial as the interpolation node is obtained,and the truncation error can be minimized.Based on this result,the corresponding complex quadrature formula is achieved,and the validity of the algorithm is verified by numerical examples.

关 键 词：插值型求积公式 截断误差 复化求积公式 切比雪夫多项式 极性 

分 类 号：O241.7[理学—计算数学]