Volume 3, Issue 2
A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators

Adv. Appl. Math. Mech., 3 (2011), pp. 204-218.

Published online: 2011-03

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• 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.

• Keywords

Frobenius-Perron operator, stationary density, maximum entropy, orthogonal polynomials, Chebyshev polynomials.

41A35, 65D07, 65J10

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• TXT
@Article{AAMM-3-204, author = {Jiu Ding , and Rhee , Noah H.}, title = {A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2011}, volume = {3}, number = {2}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1022}, url = {http://global-sci.org/intro/article_detail/aamm/165.html} }
TY - JOUR T1 - A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators AU - Jiu Ding , 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 -

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.

Jiu Ding & Noah H. Rhee. (1970). A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators. Advances in Applied Mathematics and Mechanics. 3 (2). 204-218. doi:10.4208/aamm.10-m1022
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