A low-rank approximation of parameter-dependent matrices via CUR decomposition

by Taejun Park (University of Oxford)

Thursday 13 Jun 2024, 11:00 → 12:00 Europe/Rome

Sala Riunioni (Dipartimento di Matematica)

Finding a low-rank approximation for parameter-dependent matrices $A(t)$ is an important task appearing in dynamical systems and image series compression. In this talk, we present an efficient randomized algorithm that computes a low-rank approximation of $A(t)$ at finite specified parameter values using the CUR decomposition. The key idea lies in reusing the same or a similar set of column and row indices for the CUR decomposition at nearby parameter values. The resulting algorithm is rank-adaptive, certifiable and has complexity that compares favorably to existing methods. This is joint work with Yuji Nakatsukasa.