Speaker
Description
In this talk we investigate zeros of nonlinear operators on the cone of positive definite operators over a Hilbert space. The unique zero of such nonlinear operators define means of positive definite operators. Moreover these nonlinear operators generate strictly exponentially contracting semigroups in some metric defined on positive operators. We survey recent results that establish the operator norm convergence of deterministic and stochastic resolvent and proximal type algorithms, in particular versions coming from a Trotter-Kato type splitting formula. Applications include generalizations of results proved under strong moment conditions for generalized Karcher means. The talk is based on recent joint work with Zoltán Léka and is a continuation of our earlier project.