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Randomized algorithms for linear algebraic computations
ABSTRACT:
The talk will describe how randomized algorithms can effectively, accurately, and reliably solve linear algebraic problems that are omnipresent in scientific computing and in data analysis. We will focus on techniques for low rank approximation, since these methods are particularly simple and powerful, and are well understood mathematically. The talk will also briefly survey how randomized techniques can be applied to approximate global operators that arise in scientific computing such as solution operators to elliptic PDEs, boundary-to-boundary operators such as the Dirichlet-to-Neumann map, and time evolution operators of parabolic PDEs.
Per-Gunnar Martinsson - Bio
Gunnar Martinsson is a Professor of Mathematics at the University of Texas at Austin. He is also Deputy Director of the Oden Institute for Computational Engineering and Sciences, and he holds the W.A. "Tex" Moncrief, Jr. Chair in Simulation-Based Engineering and Sciences. Prior to joining UT Austin, Martinsson served as a Professor of Mathematics at the University of Oxford, and he has previously held faculty positions at the University of Colorado at Boulder and at Yale University. He earned his Ph.D. in computational and applied mathematics in 2002 from UT Austin. He received an M.Sc. degree in Engineering Physics in 1996 and a "Licentiate" degree in Mathematics in 1998, both from the Chalmers University of Technology in Sweden. Martinsson was the recipient of the SIAM 2017 Germund Dahlquist Prize, was named a Fellow of SIAM in 2021, and held a Simons Fellowship in 2025/26.
Martinsson's research concerns the development of faster algorithms for ubiquitous computational tasks in scientific computing and data sciences. Recent work has focused on randomized methods in linear algebra, fast solvers for elliptic PDEs, O(N) complexity direct solvers, structured matrix computations, and high order accurate methods for scattering and fluid problems.
