Near-optimal convergence of the full orthogonalization method
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929518965424128 |
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| author | Chen, Tyler Meurant, Gérard |
| author_facet | Chen, Tyler Meurant, Gérard |
| contents | 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} |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07259 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Near-optimal convergence of the full orthogonalization method Chen, Tyler Meurant, Gérard Numerical Analysis 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} |
| title | Near-optimal convergence of the full orthogonalization method |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2403.07259 |