2025/01/30 by Chen, Tyler, Huber, Caroline, Lin, Ethan +1 · 2 citations
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2501.18717
We describe a randomized variant of the block conjugate gradient method for solving a single positive-definite linear system of equations. Our method provably outperforms preconditioned conjugate gradient with a broad-class of Nyström-based preconditioners, without ever explicitly constructing a preconditioner. In analyzing our algorithm, we derive theoretical guarantees for new variants of Nyström preconditioned conjugate gradient which may be of separate interest. We also describe how our approach yields state-of-the-art algorithms for key data-science tasks such as computing the entire ridge regression regularization path and generating multiple independent samples from a high-dimensional Gaussian distribution.