|x|在调整的第三类Chebyshev结点的有理逼近问题研究  

RESEARCH ON RATIONAL APPROXIMATION TO |x| AT THE ADJUSTED CHEBYSHEV NODES OF THE THIRD KIND

作　　者：张慧明 李建俊[2] Zhang Huiming;Li Jianjun(School of Mathematics and Physics,Hebei GEO University,Shijiazhuang 050031;Minzu College Affaliated to Hebei Normal University,Shijiazhuang 050091)

机构地区：[1]河北地质大学数理学院,石家庄050031 [2]河北师范大学附属民族学院,石家庄050091

出　　处：《高等学校计算数学学报》2022年第2期107-115,共9页Numerical Mathematics A Journal of Chinese Universities

基　　金：河北省自然科学基金项目(A2015403050)。

摘　　要：1引言非光滑函数|x|在逼近论中起着非常重要的作用.Bernstein[1]在1913年,最先用n次代数多项式逼近|x|,得到确切的逼近阶为E(|x|)=O(1/n).Newman[2]在1964年发现R(|x|)远远优于其多项式的最佳逼近E(|x|).In this paper,we study the convergence rate of approximation to |x|by Newman type rational operators based on the adjusted Chebyshev nodes of the third kind,the upper bound estimation are used to get the exact order of approximation is O(1/n^(2)).Furthermore,by comparing with the rational approximation of other types of nodes,the result is better than the nodes take for the Chebyshev nodes,the Chebyshev nodes of the second kind,the tangent nodes and equidistant nodes.

关 键 词：有理逼近 最佳逼近 非光滑函数 代数多项式逼近 逼近论 逼近阶 Chebyshev结点 BERNSTEIN 

分 类 号：O174.41[理学—数学]