Flexible GMRES exhibits two phases of convergence, with a sharp residual bound that is geometric for tight inner tolerances and more pronounced in two phases for looser tolerances, and the bound is shown to be unimprovable with an equality example.
Stabilizing randomized GMRES through flexible GMRES
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abstract
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.
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2026 1verdicts
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Flexible GMRES converges in two phases
Flexible GMRES exhibits two phases of convergence, with a sharp residual bound that is geometric for tight inner tolerances and more pronounced in two phases for looser tolerances, and the bound is shown to be unimprovable with an equality example.