Title: Randomized Numerical Linear Algebra for Scientific Computing and Data Science

Abstract: Numerical linear algebra (NLA) is a cornerstone of applied mathematics, scientific computing, and data science, which considers classical linear algebraic techniques through the lens of floating point operations. Throughout its long history, NLA algorithmic development has been driven by two competing imperatives, accuracy and efficiency, with the extant challenge to strike the right balance between them. 

In this talk, we focus on recent advances in randomized algorithms in numerical linear algebra, emphasizing applications to scientific computing and data science. We first review foundational concepts, such as randomized dimension reduction and range-finding. We then discuss several important applications of randomized algorithms, e.g. finding natural bases for the column or row space of a matrix or compressing rank-structured matrices (which are not themselves low-rank but contain exploitable low-rank submatrices). The aim of this talk is to showcase the utility and simplicity of randomized algorithms in problems across a variety of areas in scientific computing and data science.