Sinkhorn and power method for tensors with positive entries

For positive matrices, the power method and the Sinkhorn method have in common that their convergence can be analyzed with tools of the nonlinear Perron-Frobenius theory such as the Hilbert projective metric and the Birkhoff-Hopf theorem. We present a generalization of these tools for positive tensors of any order and discuss the convergence and implementation of the corresponding higher order power method and higher order Sinkhorn method. Joint work with Matthias Hein and Francesco Tudisco.