Weighted and preconditioned GMRES can realize any prescribed pair of convergence curves, with an exact singular-value condition on a triangular linking matrix governing the cases where the weight or preconditioner is fixed.
A comparative study of sparse approximate inverse preconditioners.Appl
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Any nonincreasing convergence curves are simultaneously possible for GMRES and weighted GMRES, as well as for left and right preconditioned GMRES
Weighted and preconditioned GMRES can realize any prescribed pair of convergence curves, with an exact singular-value condition on a triangular linking matrix governing the cases where the weight or preconditioner is fixed.