| A Convergent Family of Linear Hermite Barycentric Rational Interpolants |
| Received:December 17, 2019 Revised:April 23, 2020 |
| Key Words:
linear Hermite rational interpolation convergence rate Hermite interpolation barycentric form higher order derivative
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| Fund Project: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) and the National Statistical Science Research Project of China (Grant No.2018LY28). |
| Author Name | Affiliation | | Ke JING | School of Applied Mathematics, Nanjing University of Finance and Economics, Jiangsu 210023, P. R. China | | Yezheng LIU | School of Management, Hefei University of Technology, Anhui 230009, P. R. China | | Ning KANG | School of Economics, Nanjing University of Finance and Economics, Jiangsu 210023, P. R. China | | Gongqin ZHU | School of Mathematics, Hefei University of Technology, Anhui 230009, P. R. China |
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| Abstract: |
| 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 $h\rightarrow{0}$ on any real interpolation interval, regardless of the distribution of the interpolation points. Also, the function $r(x)$ is linear in data. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2020.06.007 |
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