Volume 10, Issue 2
A Maximum-Entropy Meshfree Method for Computation of Invariant Measures

East Asian J. Appl. Math., 10 (2020), pp. 338-353.

Published online: 2020-04

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• Abstract

Let $S$ : $X$ → $X$ be a nonsingular transformation such that the correspond-ing Frobenius-Perron operator $P$: $L$1 ($X$) → $L$1 ($X$) has a stationary density $f$. We propose a maximum-entropy method based on a meshfree approach to the numerical recovery of $f$. Numerical experiments show that this approach is more accurate than the maximum-entropy method based on piecewise linear functions, provided that the moments involved are known. Moreover, it has a smaller computational cost than the method mentioned.

• Keywords

Invariant measure, maximum-entropy, meshfree method, basis function, Frobenius- Perron operator.

37M25, 41A35

1375480828@qq. om (Tingting Fang)

861655259@qq.com ( Hongxia Jia)

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@Article{EAJAM-10-338, author = {Fang , Tingting and Jia , Hongxia and Jin , Congming and Ding , Jiu }, title = {A Maximum-Entropy Meshfree Method for Computation of Invariant Measures}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {2}, pages = {338--353}, abstract = {

Let $S$ : $X$ → $X$ be a nonsingular transformation such that the correspond-ing Frobenius-Perron operator $P$: $L$1 ($X$) → $L$1 ($X$) has a stationary density $f$. We propose a maximum-entropy method based on a meshfree approach to the numerical recovery of $f$. Numerical experiments show that this approach is more accurate than the maximum-entropy method based on piecewise linear functions, provided that the moments involved are known. Moreover, it has a smaller computational cost than the method mentioned.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.160419.030919 }, url = {http://global-sci.org/intro/article_detail/eajam/16130.html} }
TY - JOUR T1 - A Maximum-Entropy Meshfree Method for Computation of Invariant Measures AU - Fang , Tingting AU - Jia , Hongxia AU - Jin , Congming AU - Ding , Jiu JO - East Asian Journal on Applied Mathematics VL - 2 SP - 338 EP - 353 PY - 2020 DA - 2020/04 SN - 10 DO - http://dor.org/10.4208/eajam.160419.030919 UR - https://global-sci.org/intro/article_detail/eajam/16130.html KW - Invariant measure, maximum-entropy, meshfree method, basis function, Frobenius- Perron operator. AB -

Let $S$ : $X$ → $X$ be a nonsingular transformation such that the correspond-ing Frobenius-Perron operator $P$: $L$1 ($X$) → $L$1 ($X$) has a stationary density $f$. We propose a maximum-entropy method based on a meshfree approach to the numerical recovery of $f$. Numerical experiments show that this approach is more accurate than the maximum-entropy method based on piecewise linear functions, provided that the moments involved are known. Moreover, it has a smaller computational cost than the method mentioned.

Tingting Fang, Hongxia Jia, Congming Jin & Jiu Ding. (2020). A Maximum-Entropy Meshfree Method for Computation of Invariant Measures. East Asian Journal on Applied Mathematics. 10 (2). 338-353. doi:10.4208/eajam.160419.030919
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