  This paper studies algorithms for efficiently computing Brascamp-Lieb
constants, a task that has recently received much interest. In particular, we
reduce the computation to a nonlinear matrix-valued iteration, whose
convergence we analyze through the lens of fixed-point methods under the
well-known Thompson metric. This approach permits us to obtain (weakly)
polynomial time guarantees, and it offers an efficient and transparent
alternative to previous state-of-the-art approaches based on Riemannian
optimization and geodesic convexity.
