Consensus and contraction of the Hilbert metric
Rodolphe Sepulchre, Université de Liège
Abstract:
The Hilbert metric is a projective metric originally defined on a convex subset of the euclidean space. In 1957, Birkhoff proved that any positive linear map is a contraction mapping for the Hilbert metric. Perron-Frobenius result is a direct corollary. The talk will review those basic results and the fact that they exend to any symmetric cone. We will then show the close connection to the convergence analysis of consensus algorithms and report on current work to properly define a consensus algorithm on the cone of positive definite matrices. This generalization finds several applications, most notably in quantum estimation.