Codes and Expansions (CodEx) Seminar

Jamie Haddock (Harvey Mudd College):
Randomized Kaczmarz Methods: Corruption, Consensus, and Concentration

The Kaczmarz methods are a family of simple, deterministic or randomized, iterative methods which can be employed for solving consistent systems of linear equations of the form \(Ax = b\), or related problems.  These methods have gained popularity in recent times due to their amenability to large-scale data and distributed computing environments.  This talk will focus on results in three areas, all related in some way to the Kaczmarz methods: iterative methods for adversarially corrupted systems of linear equations; analyzing the dynamics of simple models of consensus amongst interacting agents; and proving bounds on the concentration and variance of randomized iterative methods.