Applied Math Seminar — Jamie Haddock (HMC)

Title: Connections between Iterative Methods for Linear Systems and Consensus Dynamics on Networks

Abstract:
There is a well-established linear algebraic lens for studying consensus dynamics on networks, which has yielded significant theoretical results in areas like distributed computing, modeling of opinion dynamics, and ranking methods. Recently, strong connections have been made between problems of consensus dynamics on networks and classical iterative methods in numerical linear algebra. This talk will discuss an instance of these connections, in particular between the gossip methods in distributed computing and the Kaczmarz methods in numerical linear algebra. We will present theoretical convergence results, empirical and numerical simulation results, and discuss future work in applying these numerical linear algebraic techniques to broader and more complex consensus dynamics models, especially those coming from opinion dynamics and ranking.