摘要
基于分形插值方法,构造了一类具有较大灵活性的分形插值迭代函数系。证明了这类迭代函数系的吸引子是经过给定插值点的分形插值曲线,并给出两个具体的例子,展示了此类分形插值曲线的形状。研究了这类分形插值函数关于自由参数的连续依赖性。最后,讨论了此类迭代函数系发生扰动时相应的分形插值函数的变化规律。在一定条件下,给出了由扰动迭代函数系和原始迭代函数系所产生分形插值函数之间的误差估计式。
Based on the method of construction of fractal interpolation ,a class of fractal interpolation iterated func-tion systems with more flexibility is constructed .It’ s proved that the attractor of this iterated function system is the fractal interpolation curve which passing through the given interpolation points ,and two specific examples are given ,which shows the shapes of such fractal interpolation curves .It is studied that the continuous dependence of this fractal interpolation function with respect to free parameters .Finally ,the character of changes for the corre-sponding FIF is investigated when this kind of iterated function systems has a small perturbation .Under certain conditions,the error estimation between the FIF generated by the perturbed IFS and the FIF generated by the o-riginal IFS is established .
出处
《安徽理工大学学报（自然科学版）》
CAS
2013年第3期78-82,共5页
Journal of Anhui University of Science and Technology:Natural Science
基金
南京财经大学预研究资助项目(A2011019)
研究生教育课题资助项目(M12059)
关键词
迭代函数系
分形插值函数
吸引子
连续依赖性
扰动误差
iterated function system
fractal interpolation function
attractor
continuous dependence
perturbation error
