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 -

Let $S$ : $X$ → $X$ be a nonsingular transformation such that the corresponding 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.