Properties Of Rational Fractal Spline Function

The classical calculus theory is a good tool for studying smooth regular functions,but those functions with non smooth and irregular can not be solved well.This function is not worth studying before.But over time,it is found that it is necessary to describe and explore the properties of the functions with non smooth and irregular features in detail In recent years,many good results have been obtained in the research of function construction,dimension calculation and property analysis,But because of its own limitations,fractal interpolation functions can not be solved well for most irregular and complex problems,especially for highly irregular data or derivative irregularities.Traditional interpolation methods such as polynomial interpolation have its limitations in dealing with irregular data.Rational fractal interpolation is also used to solve this kind of problem The problem provides an effective geometric modeling method.This paper introduces the basic theory of spline function,and constructs a classic rational cubic spline function based on the definition of rational spline function,and then deals with it,and obtains its bounded condition,positive condition and policy adjustment condition.Secondly,based on the classical rational cubic spline function constructed,combined with the theory of fractal interpolation function,we first give the definition of fractal interpolation function,give the general form of FIF,and then,on the basis of the rational cubic spline function constructed in the previous paper,we can get the disturbance basis function similar to the rational cubic spline function.According to the definition of fractal function,the rational cubic spline function is constructed The paper discusses that when the scale factor is 0,the rational fractal function is degenerated to the classical rational cubic spline function,so it is more general than the classical rational cubic spline function,which can be used to solve more problems.Finally,we guarantee its normality,policy adjustment is studied and based on the previous rational cubic spline function boundedness,combining the inequality theory and trigonometric inequality theory in previous literature,a new conclusion about the constructed rational fractal function is obtained.