计算不变密度的一种二次样条最大熵方法（英文）  

A quadratic spline maximum entropy method for the computation of invariant densities

作　　者：丁玖 Tulsi Upadhyay 

机构地区：[1]南密西西比大学数学系,哈蒂斯堡美国39406

出　　处：《上海师范大学学报（自然科学版）》2015年第3期291-303,224,共13页Journal of Shanghai Normal University(Natural Sciences)

摘　　要：用二次样条函数来数值逼近对应于非奇异变换的Frobenius-Perron算子的不变密度.所提出的方法消除了使用多项式函数的最大熵方法中出现的坏条件性.只要不变密度有足够的光滑度,由于算法的高阶收敛速率,随着矩量函数个数的增加,数值计算的精度会迅速增加.给出的数值例子验证了算法收敛速度的理论分析.The numerical recovery of an invariant density of the Frobenius-Perron operator corresponding to a nonsingular transformation is depicted by using quadratic spline functions. We implement a maximum entropy method to approximate the invariant density. The proposed method removes the ill-conditioning in the maximum entropy method, which arises by the use of polynomials. Due to the smoothness of the functions and a good convergence rate, the accuracy in the numerical calculation increases rapidly as the number of moment functions increases. The numerical results from the proposed method are supported by the theoretical analysis.

关 键 词：Frobenius—Perron算子 不变密度 最大熵 样条函数 

分 类 号：O241.5[理学—计算数学]