Thomas Trogdon

Friday, January 19, 2018
Location: Goldsmith 317
Thomas Trogdon, University of California at Irvine
Numerical analysis and random matrix theory

Abstract:  Numerical analysis and random matrix theory have long been coupled, going (at least) back to the seminal work of Goldstine and von Neumann (1951) on the condition number of random matrices. The works of Trotter (1984) and Silverstein (1985) incorporate numerical techniques to assist in the analysis of random matrices. One can also consider the problem of computing distributions (i.e., Tracy-Widom) from random matrix theory. In addition to these considerations, I will discuss other numerical analysis problems: (1) using random matrices to analyze the halting time (or runtime) of numerical algorithms and (2) developing random matrix theory for randomized algorithms. For the former, I will focus primarily on recent proofs of universality for the (inverse) power method, the QR algorithm and the Toda algorithm.