Year: 2011
Author: Jiu Ding, Noah H. Rhee
Advances in Applied Mathematics and Mechanics, Vol. 3 (2011), Iss. 2 : pp. 204–218
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.10-m1022
Advances in Applied Mathematics and Mechanics, Vol. 3 (2011), Iss. 2 : pp. 204–218
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Frobenius-Perron operator stationary density maximum entropy orthogonal polynomials Chebyshev polynomials.