A convergent family of linear Hermite barycentric rational interpolants
Received:December 17, 2019  Revised:April 06, 2020
Key Word: linear Hermite rational interpolation   convergence rate   Hermite interpolation  barycentric form   higher order derivative.  
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ke jing Nanjing University of Finance and Economics 9120171058@nufe.edu.cn 
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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 dicult 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.
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