A MATRIX SOLUTION TO THE INVERSE PERRON-FROBENIUS PROBLEM

Let f be a probability density function on the unit interval I. The inverse Perron-Frobenius problem involves determining a transformation tau: I --> 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.