The Maximum Entropy Method Based On Piecewise Functions

Let S:[0,1]?[0,1]be a nonsingular transormation such that the correspond-ing Frobenius-Perron operator Ps:L1(0,1)?L1(0,1)has a stationary density f*.In this paper,according to the property of continuity and summing is one,etc,by using different interval dividing to research the calculation precision of the maxi-mum entropy method based on piecewise linear function and piecewise quadratic function.At the same time,we construct a piecewise cubic function as the base function,and put forward a maximum entropy method based on piecewise cubic function.Numerical simulation research reveals the influence of different interval differentiate method of the maximum entropy method.Firstly,for piecewise linear basis functions.We compared the calculation accuracy of the maximum entropy method when h-1/n,h=1/2n,h=1/3n,h-1/4n,Pointed out that the convergence accuracy of the method is not only affected by h,and associated with the specific form of mapping,Matlab simulation verify the conclusion.Secondly,in view of the piecewise quadratic function,through numerical study we got the same conclusion with piecewise linear function maximum entropy method.Finally,we construct the piecewise cubic basis function,proved the convergence of the maximum en-tropy method based on piecewise cubic function,and points out that the method of convergence speed can reach o(n-4).