The talk will describe how methods based on randomised projections can be used to effectively, accurately, and reliably solve important problems that arise in data analytics and in large scale matrix computations. We will focus in particular on accelerated algorithms for computing full or partial matrix factorisations such as the eigenvalue decomposition, the QR factorisation, etc. Randomised projections are used in this context to reduce the effective dimensionality of intermediate steps in the computation. The resulting algorithms execute faster on modern hardware than traditional algorithms, and are particularly well suited for processing very large data sets.

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