Low-rank matrix approximations, such as partial spectral decompositions or principal component analysis (PCA), play a central role in data analysis and scientific computing. The talk will describe a set of randomized algorithms for efficiently computing such approximations. These techniques exploit modern computational architectures more fully than classical methods and enable many computations involving massive data sets.

The algorithms described are supported by a rigorous mathematical analysis that exploits recent work in random matrix theory. The talk will briefly review some of the key theoretical results.