Past Event: Babuška Forum

Randomized Numerical Linear Algebra for Scientific Computing

Kate Pearce, Peter O'Donnell Postdoctoral Fellow

Abstract

In this talk, we survey a variety of techniques in randomized numerical linear algebra, focusing on their applications to frequently encountered problems in scientific computing and data science. We will highlight several important contributions to the field, including a detailed exploration of the randomized singular value decomposition (SVD), a cornerstone of efficient low-rank matrix approximation. Other key topics include randomized embeddings for dimensionality reduction, maximum eigenvalue and trace estimation, and the randomized rangefinder procedure. These methods have important applications in finding natural bases for the column or row space of a matrix (e.g. QR or interpolative decompositions) and in compressing rank-structured matrices, matrices which are not themselves low-rank but contain exploitable low-rank submatrices. Our goal is to showcase the accessibility and often straightforward implementations of these tools to solve large-scale problems in areas such as machine learning, model order reduction, and fast direct solvers for partial differential equations.

Biography

Dr. Pearce is an NSF MPS-ASCEND Postdoctoral Fellow, working with Professor Per-Gunnar Martinsson on randomized algorithms in numerical linear algebra as a member of the Center for Numerical Analysis at the Oden Institute. She earned her Ph.D. in Applied Mathematics from North Carolina State University for her work on parameter subset selection algorithms in data-driven mathematical modeling. Her research interests include problems that intersect with linear algebra, scientific computing, computational mathematics, and mathematical modeling. In particular, she develops and analyzes methods of low-rank approximation and algorithms for robust parameter identifiability analysis. She is also an advocate for prison education and has volunteered with the Texas Prison Education Initiative as an instructor of UT-Austin math courses at a local prison since her arrival at Oden as a Peter O’Donnell Jr. Postdoctoral Research Fellow in 2022.