A Maximum Entropy Method Based on Piecewise Linear Functions for the Recovery of a Stationary Density of Interval Mappings
文献类型：期刊论文
| 作者 | Ding, Jiu2; Jin, Congming3; Rhee, Noah H.1; Zhou, Aihui4
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| 刊名 | JOURNAL OF STATISTICAL PHYSICS
 |
| 出版日期 | 2011-12-01 |
| 卷号 | 145期号:6页码:1620-1639 |
| ISSN号 | 0022-4715 |
| 关键词 | Frobenius-Perron operator Stationary density Maximum entropy Piecewise linear approximations |
| DOI | 10.1007/s10955-011-0366-9 |
| 英文摘要 | Let S:[0,1]->[0,1] be a nonsingular transformation such that the corresponding Frobenius-Perron operator P (S) :L (1)(0,1)-> L (1)(0,1) has a stationary density f (au). We propose a maximum entropy method based on piecewise linear functions for the numerical recovery of f (au). An advantage of this new approximation approach over the maximum entropy method based on polynomial basis functions is that the system of nonlinear equations can be solved efficiently because when we apply Newton's method, the Jacobian matrices are positive-definite and tri-diagonal. The numerical experiments show that the new maximum entropy method is more accurate than the Markov finite approximation method, which also uses piecewise linear functions, provided that the involved moments are known. This is supported by the convergence rate analysis of the method. |
| 资助项目 | Chinese Academy of Sciences ; National Science Foundation of China[11001244] ; National Science Foundation of China[10871198] ; National Science Foundation of China[10971059] ; Funds for Creative Research Groups of China[11021101] ; National Basic Research Program of China[2011CB309703] |
| WOS研究方向 | Physics |
| 语种 | 英语 |
| 出版者 | SPRINGER |
| WOS记录号 | WOS:000297594700011 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/13015]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Rhee, Noah H. |
| 作者单位 | 1.Univ Missouri, Dept Math & Stat, Kansas City, MO 64110 USA 2.Univ So Mississippi, Dept Math, Hattiesburg, MS 39406 USA 3.Zhejiang Sci Tech Univ, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Ding, Jiu,Jin, Congming,Rhee, Noah H.,et al. A Maximum Entropy Method Based on Piecewise Linear Functions for the Recovery of a Stationary Density of Interval Mappings[J]. JOURNAL OF STATISTICAL PHYSICS,2011,145(6):1620-1639. |
| APA | Ding, Jiu,Jin, Congming,Rhee, Noah H.,&Zhou, Aihui.(2011).A Maximum Entropy Method Based on Piecewise Linear Functions for the Recovery of a Stationary Density of Interval Mappings.JOURNAL OF STATISTICAL PHYSICS,145(6),1620-1639. |
| MLA | Ding, Jiu,et al."A Maximum Entropy Method Based on Piecewise Linear Functions for the Recovery of a Stationary Density of Interval Mappings".JOURNAL OF STATISTICAL PHYSICS 145.6(2011):1620-1639. |
入库方式： OAI收割
来源：数学与系统科学研究院
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