二维分形插值函数及其小波类型级数表示  

TWO DIMENSIONAL FRACTAL INTERPOLATION FUNCTION AND ITS EXPRESSION WITH WAVELET SERIES

作　　者：李红达[1] 

机构地区：[1]信息安全国家重点实验室(中国科学院研究生院),北京100039

出　　处：《应用数学学报》2003年第4期675-681,共7页Acta Mathematicae Applicatae Sinica

基　　金：中国科学院王宽诚博士后工作奖励基金

摘　　要：本文对一类很广泛的二维分形插值函数进行了研究,给出了分形插值函数连续的充分必要条件和一种构造迭代函数系统使其吸引子是连续函数的方法,并将分形插值函数表示为一个二维小波类型级数,其“母函数”是由迭代函数系统中的位移函数所决定。这种表示方式不仅提供了一种生成分形插值函数有效方法,而且对研究分形插值函数的性质及所描述的物理对象的特性也是十分有意义。In this paper, two dimensional fractal interpolation function is discussed. The theorem of the sufficient and necessary condition for its continuity is proved. Meanwhile the method to construct a iterated function system that generate a fractal interpolated continuous function is derived from these conditions. In addition, fractal interpolation function is expressed as a wavelet series, and its mother function is defined by the translations of iterated function system. This expression of fractal interpolation surface is a very useful tool for generating a fractal interpolation surface and studying its properties.

关 键 词：二维分形插值函数 级数 吸引子 迭代函数系统 位移函数 函数逼近论 

分 类 号：O174.4[理学—数学] O415.5[理学—基础数学]