图引导分形插值函数
Graph-Directed Fractal Interpolation Functions
摘要：
已知存在一个插值函数，使得该函数的图形是一个迭代函数系统的吸引子，这种函数称为分形插值函数。将分形插值函数的概念推广到图定向的情形，证明了对于有限个数据集，存在插值函数，每个插值函数插值$\mathbb{R}^2$中相应的数据集，使得插值函数的图是图定向迭代函数系统的吸引子.
英文摘要：
It is known that there exists a function interpolating a given data set such that the graph of the function is the attractor of an iterated function system which is called fractal interpolation function. We generalize the notion of fractal interpolation function to the graph-directed case and prove that for a finite number of data sets there exist interpolation functions each of which interpolates corresponding data set in $\mathbb{R}^2$ such that the graphs of the interpolation functions are attractors of a graph-directed iterated function system.
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