  If A_1,...,A_N are real square matrices then the p-radius, generalised
Lyapunov exponent or matrix pressure is defined to be the asymptotic
exponential growth rate of the sum $\sum_{i_1,\ldots,i_n=1}^N \|A_{i_n}\cdots
A_{i_1}\|^p$, where p is a real parameter. Under its various names this
quantity has been investigated for its applications to topics including wavelet
regularity and refinement equations, fractal geometry and the large deviations
theory of random matrix products. In this article we present a new algorithm
for computing the p-radius under the hypothesis that the matrices are all
positive, or more generally under the hypothesis that they satisfy a weaker
condition called domination. This algorithm is based on interpreting the
p-radius as the leading eigenvalue of a trace-class operator on a Hilbert space
and estimating that eigenvalue via approximations to the Fredholm determinant
of the operator. In this respect our method is closely related to the work of
Z.-Q. Bai and M. Pollicott on computing the top Lyapunov exponent of a random
matrix product. For pairs of positive matrices of low dimension our method
yields substantial improvements over existing methods.
