基于纵向尺度因子变化的分形插值函数误差分析

Error Analysis for Fractal Interpolation Functions Based on the Changes of Vertical Scaling Factors

分形函数插值是拟合实验数据的一种新的有效的插值方法.分形插值函数是由迭代函数系产生的,迭代函数系中的纵向尺度因子对分形插值函数有重要的影响.本文定量地分析了纵向尺度因子的变化所引起的分形插值函数的误差问题,给出具体的误差解析表达式及上界估计.此外,通过数值实验,显示了分形插值函数的图像与纵向尺度因子之间的变化关系.

Fractal function interpolation is a novel and effective interpolating method for fitting experimental data. Fractal interpolation functions （FIFs） are generated by iterated function systems （IFSs）,and the vertical scaling factors in IFSs have important influence on FIFs. The errors of the FIFs caused by the changes of vertical scaling factors are analyzed quantitatively in this work. The concrete error expression is presented, and the upper bound of errors is estimated. In addition, by means of the numerical experiments,the change relations between vertical scaling factors and FIFs are demonstrated clearly.