Stabilizing randomized GMRES through flexible GMRES

2025/06/23 by Güttel, Stefan, Pearson, John W.
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2506.18408

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.

Citations

• Randomized sketched TT-GMRES for linear systems with tensor structure
• Inner Product Free Krylov Methods for Large-Scale Inverse Problems
• GMRES with randomized sketching and deflated restarting
• A sketch-and-select Arnoldi process
• Randomized Numerical Linear Algebra : A Perspective on the Field With an Eye to Software
• Randomized Gram-Schmidt process with application to GMRES
• Randomized Numerical Linear Algebra: Foundations & Algorithms
• The university of Florida sparse matrix collection
• A Flexible Inner-Outer Preconditioned GMRES Algorithm
• A fast randomized algorithm for the approximation of matrices

Related

• A Flexible Inner-Outer Preconditioned GMRES Algorithm
• Kaczmarz-type inner-iteration preconditioned flexible GMRES methods for consistent linear systems
• Improving the Performance of the GMRES Method using Mixed-Precision Techniques
• Techniques for Accelerating the Convergence of Restarted GMRES Based on the Projection
• GMRES with randomized sketching and deflated restarting