The Maximum Problem Of A Kind Of Fractal Interpolation Function

" How to find the peak of the fractal interpolation curve " is a basic problem which is frequently encountered in the practical application.Based on iterated function system,the author researches the maximum of a class of fractal interpolation functions from the iterative process.Firstly,an iterated function system is constructed.Then the representations of horizontal and vertical coordinates of the discrete points which are obtained in the iterative process are discussed.Finally,according to the changes of vertical scaling factors,the maximum of the fractal interpolation function in three cases and the distribution of maximum points are given.This thesis provides a new idea for finding the highest point of the fractal interpolation functions in practical application.This thesis consists of four chapters.The first chapter is a brief introduction of the research background,the current research progress at home and abroad as well as the main contents,and innovation points of this paper are presented.In Chapter 2,the basic knowledge of fractal science is reviewed.The definition of fractal set,Cantor three diversity,the Iterated Function System(IFS),the Fractal Interpolation Function(FIF),and the fractal dimension of the fractal interpolation function are introduced one by one.In Chapter 3,firstly,the interpolation nodes obtained in the iterative process are discussed.Then,the methods of the representation of the horizontal and vertical coordinates are given.On this basis,the fractal interpolation representations of a class of quadratic functions are obtained,and the proof is given.In Chapter 4,based on the effect of vertical scale factor on the fractal interpolation function,the fractal interpolation function is divided into three different situations.The iterative rules of the maximal interpolation nodes in the process are discussed from the iterative process.Then,the maximum of the fractal interpolation function is obtained,finally distribution of the maximum comes into being.In Chapter 5,the summary of the research contents is presented,and some suggestions about further study of this thesis are put forward.