A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators

A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators

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.

Author Details

Jiu Ding

Noah H. Rhee