Papers › On the numerical stability of sketched GMRES
On the numerical stability of sketched GMRES
Liam Burke, Erin Carson, Yuxin Ma
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
We perform a backward stability analysis of preconditioned sketched GMRES [Nakatsukasa and Tropp, SIAM J. Matrix Anal. Appl, 2024] for solving linear systems Ax=b, and show that the backward stability at iteration i depends on the conditioning of the Krylov basis B_(1:i) as long as the condition number of A B_(1:i) can be bounded by 1/O(u), where u is the unit roundoff. Under this condition, we show that sketched GMRES is backward stable as long as the condition number of B_(1:i) is not too large. Under additional assumptions, we then show that the stability of a restarted implementation of sketched GMRES can be independent of the condition number of B_(1:i), and restarted sketched GMRES is backward stable. We also derive sharper bounds that better capture the attainable backward error especially for cases when the basis B_(1:i) is very ill-conditioned, which has been observed in the literature but not yet explained theoretically. We present numerical experiments to demonstrate the conclusions of our analysis, and also show that adaptively restarting where appropriate allows us to recover backward stability in sketched GMRES.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections