ABSTRACT: We will discuss accelerating convergence to numerical solutions of eigenvalue problems using a simple post-processing step applied to standard eigensolver techniques. We will motivate extrapolation-based acceleration approaches which reuse previous steps of an iterative process to define the next term in an approximation sequence. We will introduce using a heavy-ball momentum type of extrapolation and review recent results using both static and dynamically assigned momentum parameters to accelerate the power and inverse iterations. The theory will be illustrated with numerical results.

BIO: Sara Pollock is an Associate Professor in the Department of Mathematics at the University of Florida. She obtained her Ph.D. in Mathematics with a specialization in Computational Science from UC San Diego in 2012, an MS in Applied Mathematics from the University of Washington in 2008 and a BS in Mathematics from the University of New Mexico in 2007. Her research is focused on the design and analysis of efficient and accurate numerical methods for nonlinear and multiscale partial differential equations and for eigenvalue problems. She has been funded by multiple grants from the NSF including a CAREER award in 2021. Her work on PDE includes well-posedness and efficient solvers for nonlinear discrete problems arising from physical and multi-physical systems. Recently her work has included advances in the understanding and implementation of Anderson acceleration for numerical PDE, and the development of novel extrapolation methods for matrix and tensor eigenvalue problems. Since joining UF in 2018, she founded and co-mentors the UF student chapter of the Association for Women in Mathematics (AWM), and she currently serves as the secretary of the SIAM activity group on computational science and engineering (CSE).

Professor Pollock will also give Mathematics Colloquium on October 7 at 4:00pm.