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://doi.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 - <p style="text-align: justify;">Let $S$ : $X$ → $X$ be a nonsingular transformation such that the corresponding Frobenius-Perron operator $P$<sub>S&nbsp;</sub>: $L$<sup>1</sup> ($X$) → $L$<sup>1</sup> ($X$) has a stationary density $f$<sup>∗</sup>. We propose a maximum-entropy method based on a meshfree approach to the numerical recovery of $f$<sup>∗</sup>. 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.</p>