In this talk, I will discuss a framework for iteratively embedding aggregate pieces of information from a matrix, A, to generate sketches (approximations) of a matrix. In each iteration, the aggregate pieces of information from the matrix is small, size (s1 x s2), and is obtained by computing the product, Uk^T * A * Vk, where Uk and Vk are sampled from a specified distribution. We will show that the sequence of matrix sketches, Bk, converge to A. We will also touch on current efforts to efficiently generate sequences of low-rank approximations to A, as well as a sequence of sketches, Hk, that converge to A^-1. This is joint work with Dr. Joy Azzam (MTU) and Prof Allan Struthers (MTU)

Ben is an assistant professor in the department of mathematical at Michigan Tech. He has numerous research interests, including parallel time integrators, non-linear dimension reduction, boundary integral methods, and more recently, randomized numerical linear algebra, which he will tell us about today.