保无穷极限的向量值连分式插值  

VECTOR-VALUED CONTINUED FRACTION INTERPOLATION OF PRESERVING INFINITE LIMITS

作　　者：吴开文 徐冲坤 赵前进 Wu Kaiwen;Xu Chongkun;Zhao Qianjin(College of Education,Nanchang Normal College of Applied Technology,Nanchang 330108;School of Mathematics and Big Data,Anhui University of Science&Technology,Huainan 232001)

机构地区：[1]南昌应用技术师范学院教育学院,南昌330108 [2]安徽理工大学数学与大数据学院,淮南232001

出　　处：《高等学校计算数学学报》2023年第4期313-324,共12页Numerical Mathematics A Journal of Chinese Universities

基　　金：江西省教育厅科学技术研究项目(GJJ219018).

摘　　要：1引言.给定一组n+1个不同的实点[x_(i)∈R,i=0,1,2..,n],设[V_(i)∈C^(d):i=0,1,2,.,n]是复值向量的集合,每个V;与ci,i=0,1,2,..n相关.所谓向量值有理插值就是寻求向量值有理函数。The classical Thiele-type vector-valued continued fraction interpola-tion is an important method of rational interpolation.However,the vector-valued rational interpolation based on the classical Thiele-type vector-valued continued fractions cannot maintain the infinite limits when the interpolated function is of infinite limits.By means of the relationship between the reciprocal differences and the leading coeficients of the numerator and the denominator of the vector-valued continued fraction interpolation,a novel algorithm for the vector-valued continued fraction interpolation is constructed in an effort to preserve the infinite limits while approximating the given function with infinite limits.The uniqueness of the interpolation problem is proved,numerical examples are given to verify the effectiveness of the presented algorithm.

关 键 词：向量值有理插值 有理函数 向量值连分式 复值 极限 

分 类 号：O241.5[理学—计算数学]