Stabilizing randomized GMRES through flexible GMRES
arXiv:2506.1840820.4h-index: 18
Predicted impact top 31% in NA · last 90 daysOriginality Synthesis-oriented
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For practitioners using randomized iterative methods for linear systems, this work provides a more stable and practical solver without extensive parameter tuning.
The paper proposes using flexible GMRES as an outer wrapper for sketched GMRES to create a randomized solver that is efficient, robust, and requires minimal parameter tuning, with non-increasing residual norms.
We explore the use of flexible GMRES as an outer wrapper for sketched GMRES. Building on a new bound for the residual of FGMRES in terms of the residual of the preconditioner, we derive a practical randomized solver that requires very little parameter tuning, while still being efficient and robust in the sense of generating non-increasing residual norms.