TY - JOUR
T1 - A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators
AU - Ding , Jiu
AU - Rhee , Noah H.
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 204
EP - 218
PY - 2011
DA - 2011/03
SN - 3
DO - http://doi.org/10.4208/aamm.10-m1022
UR - https://global-sci.org/intro/article_detail/aamm/165.html
KW - Frobenius-Perron operator, stationary density, maximum entropy, orthogonal
polynomials, Chebyshev polynomials.
AB - <p style="text-align: justify;">Let $S$: [0, 1]→[0, 1] be a chaotic map and let $f^∗$ be a stationary density of
the Frobenius-Perron operator $P_S$: $L^1$→$L^1$ associated with $S$. We develop a numerical
algorithm for approximating $f^∗$, using the maximum entropy approach to an
under-determined moment problem and the Chebyshev polynomials for the stability
consideration. Numerical experiments show considerable improvements to
both the original maximum entropy method and the discrete maximum entropy
method.&nbsp;</p>