A Convergent Family of Linear Hermite Barycentric Rational Interpolants  

作　　者：Ke JING Yezheng LIU Ning KANG Gongqin ZHU 

机构地区：[1]School of Applied Mathematics,Nanjing University of Finance and Economics,Jiangsu 210023,P.R.China [2]School of Management,Hefei University of Technology,Anhui 230009,P.R.China [3]School of Economics,Nanjing Lhiiversity of Finance and Economics,Jiangsu 21QQ23,P.R.China [4]School of Mathematics,Hefei University of Technology,Anhui 230009,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2020年第6期628-646,共19页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11601224);the Science Foundation of Ministry of Education of China(Grant No.18YJC790069);the Natural Science Foundation of Jiangsu Higher Education Institutions of China(Grant No.18KJD110007);the National Statistical Science Research Project of China(Grant No.2018LY28)。

摘　　要：It is well-known that Hermite rational interpolation gives a better approximation than Hermite polynomial interpolation,especially for large sequences of interpolation points,but it is difficult to solve the problem of convergence and control the occurrence of real poles.In this paper,we establish a family of linear Hermite barycentric rational interpolants r that has no real poles on any interval and in the case k=0,1,2,the function r^(k)(x)converges to f^(k)(x)at the rate of O(h^3d+3-k)as h→0 on any real interpolation interval,regardless of the distribution of the interpolation points.Also,the function r(x)is linear in data.

关 键 词：linear Hermite rational interpolation convergence rate Hermite interpolation barycentric form higher order derivative 

分 类 号：O241.3[理学—计算数学]