Near-optimal convergence of the full orthogonalization method
<|reference_start|>Near-optimal convergence of the full orthogonalization method: We establish a near-optimality guarantee for the full orthogonalization method (FOM), showing that the overall convergence of FOM is nearly as good as GMRES. In particular, we prove that at every iteration $k$, there exists an iteration $j\leq k$ for which the FOM residual norm at iteration $j$ is no more than $\sqrt{k+1}$ times larger than the GMRES residual norm at iteration $k$. This bound is sharp, and it has implications for algorithms for approximating the action of a matrix function on a vector.\end{abstract}<|reference_end|>
@article{chen2024near-optimal,
    title={Near-optimal convergence of the full orthogonalization method},
    author={Tyler Chen and G'erard Meurant},
    journal={Electronic Transactions on Numerical Analysis, Volume 60, pp.
  421-427, 2024},
    year={2024},
    doi={10.1553/etna_vol60s421},
    archivePrefix={arXiv},
    eprint={2403.07259},
    primaryClass={math.NA cs.NA}
}