The C3 parametric eighth-degree interpolation spline function-Reference-Cited by-同舟云学术

The C3 parametric eighth-degree interpolation spline function

Published:2023 Issue:6 Volume:8 Page:14623-14632
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Xie Jin¹,Liu Xiaoyan²,Zhu Lei³,Ma Yuqing¹,Zhang Ke¹

Affiliation:

1. School of Artificial Intelligence and Big Data, Hefei University, Hefei, 230601, China

2. Department of Mathematics, University of La Verne, CA, 91750, USA

3. School of Urban Construction and Transportation, Hefei University, Hefei, 230601, China

Abstract

<abstract>The <italic>C</italic>3 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 <italic>C</italic>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 achieve higher approximation rates.</abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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