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arXiv · 2511.01735

A Low-Rank BUG Method for Sylvester-Type Equations

Georgios Vretinaris
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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.

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Georgios Vretinaris. 2025-11-03. A Low-Rank BUG Method for Sylvester-Type Equations. https://arxiv.org/abs/2511.01735

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