Linear Systems: Recent Developments

This talk will cover recent research on faster algorithms for solving linear systems. I will discuss how randomization can be used to accelerate linear system solving, both via preconditioning and via stochastic iterative methods like the randomized Kaczmarz method. We will also discuss recent progress on randomized solvers for ultra-sparse linear systems. Finally, I will briefly touch on the active and broad area of research on solvers for structured linear systems arising in the computational sciences and data sciences. No prior knowledge will be assumed beyond topics covered in Mark Embree's prior introductory lecture.