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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A matrix solution to the inverse Perron-Frobenius problem


Authors: P. Góra and A. Boyarsky
Journal: Proc. Amer. Math. Soc. 118 (1993), 409-414
MSC: Primary 58F11; Secondary 28D05
MathSciNet review: 1129877
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Abstract: Let $ f$ be a probability density function on the unit interval $ I$. The inverse Perron-Frobenius problem involves determining a transformation $ \tau :I \to I$ such that the one-dimensional dynamical system $ {x_{i + 1}} = \tau ({x_i})$ has $ f$ as its unique invariant density function. A matrix method is developed that provides a simple relationship between $ \tau $ and $ f$, where $ f$ is any piecewise constant density function. The result is useful for modelling and predicting chaotic data.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1129877-8
PII: S 0002-9939(1993)1129877-8
Article copyright: © Copyright 1993 American Mathematical Society