  Classical mathematical models of information sharing and updating in
multi-agent networks use linear operators. In the paradigmatic DeGroot model,
agents update their states with linear combinations of their neighbors' current
states. In prior work, an accelerated averaging model employing the use of
memory has been suggested to accelerate convergence to a consensus state for
undirected networks. There, the DeGroot update on the current states is
followed by a linear combination with the previous states. We propose a
modification where the DeGroot update is applied to the current and previous
states and is then followed by a linear combination step. We show that this
simple modification applied to undirected networks permits convergence even for
periodic networks. Further, it allows for faster convergence than the DeGroot
and accelerated averaging models for suitable networks and model parameters.
