| 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. |
| 关键词: Frobenius-Perron算子 不变密度 最大熵 样条函数 |
| DOI： |
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| A quadratic spline maximum entropy method for the computation of invariant densities |
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DING Jiu, UPADHYAY Tulsi
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Department of Mathematics, The University of Southern Mississippi
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| Abstract: |
| 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. |
| Key words: Frobenius-Perron operator invariant density maximum entropy spline function |
