The <i>C</i><sup>3</sup> parametric eighth-degree interpolation spline function

Jin Xie; Xiaoyan Liu; Lei Zhu; Yuqing Ma; Ke Zhang; Jin Xie; Xiaoyan Liu; Lei Zhu; Yuqing Ma; Ke Zhang

doi:10.3934/math.2023748

AIMS Mathematics

2023, Volume 8, Issue 6: 14623-14632. doi: 10.3934/math.2023748

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Research article

The C³ parametric eighth-degree interpolation spline function

1.
School of Artificial Intelligence and Big Data, Hefei University, Hefei, 230601, China
2.
School of Urban Construction and Transportation, Hefei University, Hefei, 230601, China
3.
Department of Mathematics, University of La Verne, CA, 91750, USA

Received: 26 December 2022 Revised: 17 February 2023 Accepted: 16 March 2023 Published: 20 April 2023
MSC : 65D07

The C³ parametric interpolation spline function is presented this paper, which has the similar properties of the classical cubic Hermite interpolation spline with additional flexibility and high approximation rates. Moreover, a group of eighth-degree bases with three parameters is constructed. Then, the interpolation spline function is defined based on the proposed basis functions. And 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 retain C³ 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 achieve higher approximation rates.
- cubic Hermite spline,
- interpolated function,
- approximation,
- C³ continuity
Citation: Jin Xie, Xiaoyan Liu, Lei Zhu, Yuqing Ma, Ke Zhang. The C3 parametric eighth-degree interpolation spline function[J]. AIMS Mathematics, 2023, 8(6): 14623-14632. doi: 10.3934/math.2023748

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Abstract

The C³ parametric interpolation spline function is presented this paper, which has the similar properties of the classical cubic Hermite interpolation spline with additional flexibility and high approximation rates. Moreover, a group of eighth-degree bases with three parameters is constructed. Then, the interpolation spline function is defined based on the proposed basis functions. And 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 retain C³ 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 achieve higher approximation rates.

References

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