|x|在对数结点的有理插值  

On rational interpolation to|x|at the logarithmic nodes

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

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：《华中师范大学学报（自然科学版）》2024年第4期419-423,共5页Journal of Central China Normal University：Natural Sciences

基　　金：河北省自然科学基金项目(A2019403169).

摘　　要：|x|的有理逼近是逼近论中非常重要的课题.该文首先研究了|x|在一类新的结点组(对数结点)的有理插值,对于|x|的逼近误差采用适当的放缩法得到逼近阶为O(1/nlog n).然后,在零点附近增加一些结构相同的结点,逼近阶可以提高到O(1/n^(2)logn).最后,分析逼近阶相同的五类结点组的结构,并揭示其逼近本质:因为四类结点组都和对数结点组等价,所以|x|在五类结点组的误差是同阶的.这个结论说明结点组的结构特点对|x|的有理插值问题起到关键性作用.The rational approximation of|x|is a very important topic in approximation theory.Firstly,the rational interpolation of|x|at a new class of node groups(logarithmic nodes)is studied in this paper,and it is obtained that the exact order of approximation is O(1/nlogn) by using appropriate scaling methods for approximation errors of|x|.Then,by adding some nodes with the same structure near the zero point,the approximation order can be increased to O(1/n^(2)log n).Finally,the structure of five node groups with the same approximation order is analyzed to reveal their essence:because four types of node groups are equivalent to the logarithmic node groups,the error of|x|in five types of node groups is the same order.This conclusion indicates that the structural characteristics of node groups play a crucial role in the rational interpolation problem of|x|.

关 键 词：对数结点 有理插值 Newman型有理算子 逼近阶 

分 类 号：O174.41[理学—数学]