Topic: matrix-vector products

Chris Musco studies how to approximate an unknown matrix by a structured one using a limited, adaptively chosen sequence of matrix-vector products. This models operator learning in scientific machine learning as well as computational algorithms. Randomized SVD provides strong guarantees for low-rank targets; analogous results for sparse and hierarchical structures are less developed. The talk presents progress on efficient algorithms for these classes and a broader complexity theory. Joint work with Noah Amsel, Pratyush Avi, Tyler Chen, Prathamesh Dharangutte, Chinmay Hegde, Feyza Duman Keles,

Per-Gunnar Martinsson presents randomized black-box algorithms that compress rank-structured matrices, including H-matrices and HSS matrices, into data-sparse representations. Access is through matrix-vector products, which suits Schur-complement construction and matrix multiplication. When both the operator and its transpose admit O(N) application, the overall compression can also have linear complexity. A featured method combines compression and factorization of an H-matrix under strong admissibility.