Section: New Results

A common symmetrization framework for iterative (linear) maps

Participants: Alain Sarlette

The results of this section were presented at [29] .

We review a “symmetrization” abstraction of iterative consensus algorithms, which allows to generalize them to general discrete group operations including those acting on quantum systems and on sequences of control actions. We highlight a few new applications of the framework including: consensus networks with antagonistic interactions; sub-stochastic matrix iterations; and coordinate descent on (locally) quadratic functions. The purpose is to show which types of iterative dynamics can be covered by this group-theoretic framework, and potentially operationally generalized to non-classical systems.