GMRES
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Related Articles from SNS
Any nonincreasing convergence curves are simultaneously possible for GMRES and weighted GMRES, as well as for left and right preconditioned GMRES
arXiv:2506.17193v2 Announce Type: replace Abstract: The convergence of the GMRES linear solver is notoriously hard to predict. A particularly enlightening result by [Greenbaum, Pt\'ak, Strako\v{s}, 1996] is that, given any convergence curve, one can build a linear system for which GMRES realizes that convergence curve. What is even more extraordinary is that the eigenvalues of the problem matrix can be chosen arbitrarily.
Accelerating GMRES with Matrix-Free Multiscale Robin Preconditioners
arXiv:2606.08883v1 Announce Type: new Abstract: We propose a matrix-free right-preconditioning strategy for the Generalized Minimal Residual (GMRES) method based on the Multiscale Robin Coupled Method with oversampling (MRCM-OS) for the numerical solution of elliptic problems arising in subsurface flow. The resulting preconditioner is constructed through local subdomain solves with oversampling and smoothing, and can be applied without explicit assembly of the global operator. After a...
Robust spectral preconditioning for high-P\'{e}clet number convection-diffusion
arXiv:2509.17531v2 Announce Type: replace Abstract: We introduce a two-level hybrid restricted additive Schwarz (RAS) preconditioner for heterogeneous steady-state convection-diffusion equations at high P\'{e}clet numbers. Our construction builds on the multiscale spectral generalized finite element method (MS-GFEM), wherein the coarse space is spanned by locally optimal basis functions obtained from local generalized eigenproblems on operator-harmonic spaces. Extending the theory of Ma...
Spectral coarse spaces based on indefinite operators: the $H_k$-GenEO method
arXiv:2605.31552v1 Announce Type: new Abstract: GenEO (`Generalised Eigenvalue problems on the Overlap') is a method for constructing coarse spaces used in the preconditioning of iterative solvers for discrete PDEs. This method combines a (small) number of modes of local PDE eigenproblems to obtain a global coarse space. A coarse solve is then combined with local solves of the global PDE to obtain the preconditioner.