14:00
From Chebfun3 to RTSMS: A journey into deterministic and randomized Tucker decompositions
Abstract
In this talk we will first focus on the continuous framework and revisit how Tucker decomposition forms the foundation of Chebfun3 for numerical computing with 3D functions and the deterministic algorithm behind Chebfun3. The key insight is that separation of variables achieved via low-rank Tucker decomposition simplifies and speeds up lots of subsequent computations.
We will then switch to the discrete framework and discuss a new algorithm called RTSMS (randomized Tucker with single-mode sketching). The single-mode sketching aspect of RTSMS allows utilizing simple sketch matrices which are substantially smaller than alternative methods leading to considerable performance gains. Within its least-squares strategy, RTSMS incorporates leverage scores for efficiency with Tikhonov regularization and iterative refinement for stability. RTSMS is demonstrated to be competitive with existing methods, sometimes outperforming them by a large margin.