Adaptive hierarchical approximation
Matrix-free algorithms for discovering and exploiting low-rank structure in large scientific operators.
Motivation
Large scientific operators are often too expensive to assemble or store explicitly even when their action on vectors can be computed efficiently. This project studies adaptive algorithms that learn hierarchical low-rank structure directly from matrix-vector products.
Approach
The work combines randomized sampling, adaptive rank selection, and hierarchical representations to build compact approximations that can support fast application, factorization, and solution while respecting a prescribed accuracy target.