Among the most exciting recent developments in numerical linear algebra is the advent of randomized algorithms that are fast, scalable, robust, and reliable.
Low-rank approximation is among the most significant problems for which randomization has had a significant impact.
In this talk I will first review some of the most successful randomized algorithms for low-rank approximation of matrices. I will then turn to tensors, and describe an algorithm RTSMS (Randomized Tucker with single-mode sketching) for an approximate Tucker decomposition. RTSMS only sketches one mode at a time, so the sketch matrices are significantly smaller than alternative approaches, and RTSMS can outperform existing methods by a large margin. RTSMS is a joint work with Behnam Hashemi (Leicester).