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

Published online by Cambridge University Press:  03 June 2015

Jiu Ding  and
Noah H. Rhee
Jiu Ding*
Affiliation:
Department of Mathematics, The University of Southern Mississippi, Hattiesburg, MS 39406-5045, USA
Noah H. Rhee*
Affiliation:
Department of Mathematics and Statistics, University of Missouri-Kansas City, Kansas City, MO 64110-2499, USA
*
Corresponding author. URL: http://r.web.umkc.edu/rheen/ Email: Jiu.Ding@usm.edu
Email: rheen@umkc.edu
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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.

Keywords

41A3565D0765J10Frobenius-Perron operatorstationary densitymaximum entropyorthogonal polynomialsChebyshev polynomials
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 2 , April 2011 , pp. 204 - 218
Copyright
Copyright © Global-Science Press 2011

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