Construction And Perturbation Error Analysis Of Iterated Function Systems With Some Parameters Of Fractal Interpolation

Based on the theory of iterated function systems(IFSs),Barnsley came up with the fractal interpolation functions(FIFs)and the method of construction of FIFs in 1986.It's unsuitable for traditional interpolation methods to fit non-smooth or irregular patterns and data because the interpolation functions generated by traditional interpolation methods are usually smooth or piecewise smooth.Fractal interpolation has showed special superiority in this respect,so fractal interpolation method has been a powerful tool to model objects with a certain self-similar which are widespread in nature.Fractal interpolation theory and method have been used in many fields such as Economy,Finance and computer sciences.In this thesis,a series of IFSs are constructed by abstract functions with some parameters based on the existing research results of fractal interpolation theory.The existence of attractor of the IFSs constructed in this dissertation is discussed and some examples and images of FIFs are provided.Then we consider the changes of FIFs derived from the perturbances of IFSs and data sets and obtain the estimation formulas of perturbances.Contrasted with the existing IFSs,the IFSs constructed are more general and more flexible.The estimation formulas of perturbances obtained cover many estimation formulas of perturbances of other IFSs.This dissertation is organized as follows:In chapter ?,a brief introduction of background about fractal interpolation theory and existing research results are given.Then we introduce the content and significance of this work.In chapter ?,basic conceptions and related theorems about fractal interpolation theory and methods are given,which are theoretical basis of our study.In chapter ?,a kind of univariate IFS is constructed by abstract functions with three parameters.Two examples are given and the corresponding graphs are plotted.Then the changes of FIFs caused by the perturbances of both the free-parameter of IFSs and data sets are studied,the estimation formulas of perturbances is given.In chapter ?,we extend the method used in chapter III to the case of two variables IFS,abstract functions with five parameters are used to construct IFSs.We demonstrate this kind of IFS possessing unique attractor and the attractor is just as the graph of a function passing the given data set.An example is given and the corresponding graph is plotted.In addition,we consider the changes of FIFs when the free-parameter of IFS and the given data set are perturbed,and the estimation formula of perturbances is given.In chapter ?,we make a conclusion and give a prospect for future research.