一类具有3组参数的分形插值迭代函数系及其性质

Kind of fractal interpolation iterated function system with three systems of parameters and their properties

对于给定的插值点集,构造了一类具有3组参数的迭代函数系。与经典的迭代函数系的构造不同,文章采用一般形式的抽象函数来构造迭代函数系,无需考虑函数的具体结构,并将迭代函数系的插值条件归结为选取合适的参数。所构造的迭代函数系涵盖了一些已有的迭代函数系作为特殊情形,研究了迭代函数系中自由参数和数据集中纵坐标发生扰动时,相应的分形插值函数的变化情况,给出了扰动误差的估计式。

With a data set selected before, a class of iterated function system with three systems of parameters is constructed on. It is different from classic constructions of IFS that in this paper we construct IFS by generally abstract functions and neglect the specific structure of functions in IFS. Hence the interpolation conditions of FIF are attributed to the selections of parameters. IFS constructed in previous studies can be regarded as special situations of IFS constructed in this paper. The changes of the corresponding FIFs are studied when the free parameter in IFS and the ordinate of data set has a perturbation, and the formulas of error estimating are obtained.