基于函数尺度因子的有理分形插值及其应用

吉林大学学报(理学版) ›› 2021, Vol. 59 ›› Issue (6): 1469-1480.

基于函数尺度因子的有理分形插值及其应用

宋刚¹, 杨晓梅¹, 姜群², 包芳勋¹, 张云峰²

1. 山东大学数学学院, 济南 250100; 2. 山东财经大学计算机科学与技术学院, 济南 250014

收稿日期:2020-09-10 出版日期:2021-11-26 发布日期:2021-11-26
通讯作者: 包芳勋 E-mail:fxbao@sdu.edu.cn

Rational Fractal Interpolation Based on Function Scaling Factors and Its Application

SONG Gang¹, YANG Xiaomei¹, JIANG Qun², BAO Fangxun¹, ZHANG Yunfeng²

1. School of Mathematics, Shandong University, Jinan 250100, China;
2. School of Computer Science and Technology, Shandong University of Finance and Economics, Jinan 250014, China

Received:2020-09-10 Online:2021-11-26 Published:2021-11-26

摘要/Abstract

摘要： 首先, 提出一种用于曲线建模的具有函数尺度因子的有理分形插值函数, 该函数能精确地刻画自相似较弱的不规则数据；其次, 讨论分形曲线的稳定性、收敛性及计盒维数. 实验结果表明, 该方法相比于三次样条插值、函数尺度因子多项式分形插值、常数尺度因子有理分形插值, 更适用于重建真实数据与不规则数据.

关键词: 有理样条, 分形插值, 函数尺度因子, 曲线建模

Abstract: Firstly, we proposed a rational fractal interpolation functions with function scaling factors for curve modeling, which could accurately characterize irregular data with weak self-similarity. Secondly, we discussed the stability, the convergence and box-dimension of fractal curves. The experimental results show that the proposed method performs better than cubic spline interpolation, polynomial fractal interpolation with function scaling factors and rational fractal interpolation with constant vertical scaling factors, which is more suitable for reconstructing real data and irregular data.

Key words: rational spline, fractal interpolation, function scaling factor, curve modeling

中图分类号:

O174.1

宋刚, 杨晓梅, 姜群, 包芳勋, 张云峰. 基于函数尺度因子的有理分形插值及其应用[J]. 吉林大学学报(理学版), 2021, 59(6): 1469-1480.

SONG Gang, YANG Xiaomei, JIANG Qun, BAO Fangxun, ZHANG Yunfeng. Rational Fractal Interpolation Based on Function Scaling Factors and Its Application[J]. Journal of Jilin University Science Edition, 2021, 59(6): 1469-1480.