A Low-Rank BUG Method for Sylvester-Type Equations
Numerical Analysis
2025-11-04 v1 Numerical Analysis
Abstract
We introduce a low-rank algorithm inspired by the Basis-Update and Galerkin (BUG) integrator to efficiently approximate solutions to Sylvester-type equations. The algorithm can exploit both the low-rank structure of the solution as well as any sparsity present to reduce computational complexity. Even when a standard dense solver, such as the Bartels-Stewart algorithm, is used for the reduced Sylvester equations generated by our approach, the overall computational complexity for constructing and solving the associated linear systems reduces to O(kr(n^2+m^2 +mn + r^2)), for X in R^{m \times n}, where k is the number of iterations and r the rank of the approximation.
Cite
@article{arxiv.2511.01735,
title = {A Low-Rank BUG Method for Sylvester-Type Equations},
author = {Georgios Vretinaris},
journal= {arXiv preprint arXiv:2511.01735},
year = {2025}
}
Comments
14 pages, 5 figures