A Maximum Entropy Method Based on Piecewise Linear Functions for the Recovery of a Stationary Density of Interval Mappings

doi:10.1007/s10955-011-0366-9

	A Maximum Entropy Method Based on Piecewise Linear Functions for the Recovery of a Stationary Density of Interval Mappings
	Ding, Jiu 2; Jin, Congming 3; Rhee, Noah H.1; Zhou, Aihui4
	2011-12-01
发表期刊	JOURNAL OF STATISTICAL PHYSICS
ISSN	0022-4715
卷号	145 期号:6 页码:1620-1639
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.
关键词	Frobenius-Perron operator Stationary density Maximum entropy Piecewise linear approximations
DOI	10.1007/s10955-011-0366-9
语种	英语
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
WOS类目	Physics, Mathematical
WOS记录号	WOS:000297594700011
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/13016
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.