基于函数尺度因子的有理分形插值及其应用  

Rational Fractal Interpolation Based on Function Scaling Factors and Its Application

作　　者：宋刚 杨晓梅 姜群 包芳勋[1] 张云峰[2] SONG Gang;YANG Xiaomei;JIANG Qun;BAO Fangxun;ZHANG Yunfeng(School of Mathematics,Shandong University,Jinan 250100,China;School of Computer Science and Technology,Shandong University of Finance and Economics,Jinan 250014,China)

机构地区：[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

出　　处：《吉林大学学报（理学版）》2021年第6期1469-1480,共12页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:61672018,61972227,61873117,U1609218);山东省自然科学基金(批准号:ZR201808160102,ZR2019MF051);山东省重点研发计划项目(批准号:GG201710090122,2017GGX10109,2018GGX101013);山东省高等学校优势科研人才团队培育计划基金.

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.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.

关 键 词：有理样条 分形插值 函数尺度因子 曲线建模 

分 类 号：O174.1[理学—数学]