Speaker:

Per-Gunnar Martinsson, University of Colorado

Title:

Matrix factorizations and randomized sampling

Abstract:

A standard technique in science and engineering is to approximate
a large matrix, or even a linear operator on an infinite-dimensional
space, by an operator of low rank. The purpose is sometimes to
accelerate scientific computations, and sometimes to elucidate
properties of the operator - for instance by computing approximate
spectral decompositions.

In this talk, I will discuss why approximate low-rank matrix
factorizations are of interest, and describe classical methods for
computing them such as the Gram-Schmidt process. I will also
describe some newly developed algorithms based on randomized
sampling that outperform the existing methods in essentially all
environments. Since these new algorithms are randomized, there is a
non-zero probability that they may fail; however, this probability
can be rendered entirely negligible (failure probabilities of
10^(-15) or less being typical).

To be preceded by a 15h30 tea in the Mathematics Lounge
which students are encouraged to attend.