Xiaoyan Liu
University of La Verne, La Verne CA, USA

The $C-3$ parametric interpolation spline function is presented in this paper, which has the similar properties of the classical cubic Hermite interpolation spline with additional flexibility and higher approximation rates. To be specific, a group of eighth-degree base functions with three parameters is constructed. Furthermore, the interpolation spline function is defined based on the proposed base functions. The interpolation error and the technique for determining the optimal interpolation are also given.

The results show that when the interpolation conditions remain unchanged, the proposed interpolation spline functions possess $C-3$ continuity, and the shape of the curve can be controlled by the parameters. When the optimal values of parameters are chosen, the interpolation spline function can reach high approximation rates.