Title: Fast Randomized Solvers for Complex Physical Systems
Speaker: Anna Yesypenko
Abstract: Many problems in science and engineering—such as inverse problems, PDE-constrained optimization, and uncertainty quantification—lead to large linear systems that are difficult to solve efficiently. These systems often inherit smoothness and low-rank structure from their continuum formulations, reflecting the physics of the underlying partial differential equations (PDEs).
This talk presents a framework for identifying and exploiting this structure using only black-box access to matrix–vector products. By combining ideas from hierarchical matrix representations, fast multipole methods, and randomized numerical linear algebra, we develop scalable solvers with linear complexity in both computation and storage that remain robust to indefiniteness and ill-conditioning.
Connections to classical PDE solvers and modern randomized techniques will be discussed, along with future directions in scalable algorithms for large-scale scientific computing.