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

Jiu Ding & Noah H. Rhee

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 PS: L1→L1 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. AMS subject classif

  • Keywords

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

  • AMS Subject Headings

41A35 65D07 65J10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-3-204, author = {Jiu Ding and Noah H. Rhee}, 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 PS: L1→L1 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. AMS subject classif

}, 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 & Noah H. Rhee JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 204 EP - 218 PY - 2011 DA - 2011/03 SN - 3 DO - http://dor.org/10.4208/aamm.10-m1022 UR - https://global-sci.org/intro/aamm/165.html KW - Frobenius-Perron operator KW - stationary density KW - maximum entropy KW - orthogonal polynomials KW - 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 PS: L1→L1 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. AMS subject classif

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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