Random-sketching Techniques to Enhance the Numerical Stability of Block Orthogonalization Algorithms for s-step GMRES
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911184541712384 |
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| author | Yamazaki, Ichitaro Higgins, Andrew J. Boman, Erik G. Szyld, Daniel B. |
| author_facet | Yamazaki, Ichitaro Higgins, Andrew J. Boman, Erik G. Szyld, Daniel B. |
| contents | We integrate random sketching techniques into block orthogonalization schemes needed for s-step GMRES. The resulting block orthogonalization schemes generate the basis vectors whose overall orthogonality error is bounded by machine precision as long as each of the corresponding block vectors are numerically full rank. We implement these randomized block orthogonalization schemes using standard distributed-memory linear algebra kernels for s-step GMRES available in the Trilinos software packages. Our performance results on the Perlmutter supercomputer (with four NVIDIA A100 GPUs per node) demonstrate that these randomized techniques can enhance the numerical stability of the orthogonalization and overall solver, without a significant increase in the execution time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16717 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Random-sketching Techniques to Enhance the Numerical Stability of Block Orthogonalization Algorithms for s-step GMRES Yamazaki, Ichitaro Higgins, Andrew J. Boman, Erik G. Szyld, Daniel B. Numerical Analysis Distributed, Parallel, and Cluster Computing We integrate random sketching techniques into block orthogonalization schemes needed for s-step GMRES. The resulting block orthogonalization schemes generate the basis vectors whose overall orthogonality error is bounded by machine precision as long as each of the corresponding block vectors are numerically full rank. We implement these randomized block orthogonalization schemes using standard distributed-memory linear algebra kernels for s-step GMRES available in the Trilinos software packages. Our performance results on the Perlmutter supercomputer (with four NVIDIA A100 GPUs per node) demonstrate that these randomized techniques can enhance the numerical stability of the orthogonalization and overall solver, without a significant increase in the execution time. |
| title | Random-sketching Techniques to Enhance the Numerical Stability of Block Orthogonalization Algorithms for s-step GMRES |
| topic | Numerical Analysis Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2503.16717 |