Padé-type rational and barycentric interpolation
For researchers in numerical analysis and approximation theory, this work provides a flexible interpolation framework, though it is an incremental extension of existing rational interpolation techniques.
This paper develops a rational interpolation method combining Padé-type approximation at the origin with barycentric interpolation at other points, enabling control over poles and zeros. Numerical examples demonstrate the method's effectiveness in removing spurious poles and achieving accurate approximation.
In this paper, we consider the particular case of the general rational Hermite interpolation problem where only the value of the function is interpolated at some points, and where the function and its first derivatives agree at the origin. Thus, the interpolants constructed in this way possess a Padé--type property at 0. Numerical examples show the interest of the procedure. The interpolation procedure can be easily modified to introduce a partial knowledge on the poles and the zeros of the function to approximated. A strategy for removing the spurious poles is explained. A formula for the error is proved in the real case. Applications are given.