Upcoming Event: Babuška Forum

Fast algorithms for global operators

Professor Per-Gunnar Martinsson,

Abstract

That the linear systems arising upon the discretization of elliptic PDEs can be solved efficiently is well-known, and iterative solvers that often attain linear complexity (multigrid, Krylov methods, etc) have proven very successful. Interestingly, it has recently been demonstrated that it is often possible to directly compute an approximate inverse to the coefficient matrix in linear (or close to linear) time. The talk will describe some recent work in the field and will argue that direct solvers have several advantages, including improved stability and robustness, the ability to solve certain problems that have remained intractable to iterative methods, and dramatic improvements in speed in certain environments. 

An important component of the work concerns randomized techniques for recovering matrices from their action on test vectors. The talk will introduce the basic ideas underlying such techniques, and demonstrate how they can solve both basic problems such as low rank approximation, and more complex question such as recovering solution operators to elliptic PDEs.

Biography

Gunnar Martinsson has been a member of the Oden Institute and a professor of mathematics at UT-Austin since 2018. Prior to joining UT, he served as a professor of mathematics at the University of Oxford. He was on the faculty at the University of Colorado, Boulder between 2005 and 2017, and prior to that he was a Gibbs assistant professor at Yale University. He completed his Ph.D. at UT-Austin in Computational and Applied Mathematics (CAM) in 2002. CAM was the Ph.D. program that preceded the current Ph.D. program administered by the Oden Institute, the Computational Sciences, Engineering, and Mathematics (CSEM) program.

He was awarded the Germund Dahlquist Prize by SIAM in 2017. He is an affiliated professor of mathematics at the Royal Institute of Technology (KTH) in Stockholm, where he also chairs the scientific advisory board of the MathDataLab.