Convergence rates of a family of barycentric osculatory rational interpolation |
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Authors: | Ke Jing Ning Kang Gongqin Zhu |
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Institution: | 1.School of Mathematics and Statistic,Fuyang Normal University,Fuyang,People’s Republic of China;2.School of Economics,Fuyang Normal University,Fuyang,People’s Republic of China;3.School of Mathematics,Hefei University of Technology,Hefei,People’s Republic of China |
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Abstract: | It is well-known that osculatory rational interpolation sometimes gives better approximation than Hermite interpolation, especially for large sequences of points. However, it is difficult to solve the problem of convergence and control the occurrence of poles. In this paper, we propose and study a family of barycentric osculatory rational interpolation function, the proposed function and its derivative function both have no real poles and arbitrarily high approximation orders on any real interval. |
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