安徽理工大学学报（自然科学版）
安徽理工大學學報（自然科學版）
안휘리공대학학보（자연과학판）
JOURNAL OF ANHUI UNIVERSITY OF SCIENCE AND TECHNOLOGY(NATURAL SCIENCE)
2013年
3期
78-82
,共5页
迭代函数系%分形插值函数%吸引子%连续依赖性%扰动误差
迭代函數繫%分形插值函數%吸引子%連續依賴性%擾動誤差
질대함수계%분형삽치함수%흡인자%련속의뢰성%우동오차
iterated function system%fractal interpolation function%attractor%continuous dependence%perturbation error
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。
基于分形插值方法，構造瞭一類具有較大靈活性的分形插值迭代函數繫。證明瞭這類迭代函數繫的吸引子是經過給定插值點的分形插值麯線，併給齣兩箇具體的例子，展示瞭此類分形插值麯線的形狀。研究瞭這類分形插值函數關于自由參數的連續依賴性。最後，討論瞭此類迭代函數繫髮生擾動時相應的分形插值函數的變化規律。在一定條件下，給齣瞭由擾動迭代函數繫和原始迭代函數繫所產生分形插值函數之間的誤差估計式。
기우분형삽치방법，구조료일류구유교대령활성적분형삽치질대함수계。증명료저류질대함수계적흡인자시경과급정삽치점적분형삽치곡선，병급출량개구체적례자，전시료차류분형삽치곡선적형상。연구료저류분형삽치함수관우자유삼수적련속의뢰성。최후，토론료차류질대함수계발생우동시상응적분형삽치함수적변화규률。재일정조건하，급출료유우동질대함수계화원시질대함수계소산생분형삽치함수지간적오차고계식。
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 .
