CCM Colloquium: John Urschel (MIT)

Wednesday Sep 18, 2024, 10:00 AM → 11:00 AM America/New_York

3rd floor classroom (162)

Presenter: John Urschel (MIT)

Title: The Growth Factor in Gaussian Elimination

Abstract: The solution of a linear system, i.e., given a matrix A and vector b, finding a vector x satisfying Ax = b, is one of the oldest problems in mathematics. Gaussian elimination is one of the most fundamental and well-known techniques for solving linear systems, by factoring a matrix into the product of a lower and upper triangular matrix. Surprisingly, a number of questions regarding the worst-case stability of this algorithm remains. In this talk, we will study the history of this subject, a story that spans over seventy-five years, and discuss some recent progress.

Bio: John Urschel is an Assistant Professor of Mathematics at MIT, and a Junior Fellow at the Harvard Society of Fellows. Previously, he was a member of the Institute for Advanced Study. He received his B.S. and M.A. in Mathematics from Penn State, and his Ph.D. in Mathematics from MIT, under the supervision of Michel Goemans. His main research interests include matrix analysis, numerical linear algebra, and spectral graph theory. He recently received the SIAM DiPrima Prize and the SIAM Early Career Prize in Linear Algebra.