A sketch-and-select Arnoldi process
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916240854876160 |
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| author | Güttel, Stefan Simunec, Igor |
| author_facet | Güttel, Stefan Simunec, Igor |
| contents | A sketch-and-select Arnoldi process to generate a well-conditioned basis of a Krylov space at low cost is proposed. At each iteration the procedure utilizes randomized sketching to select a limited number of previously computed basis vectors to project out of the current basis vector. The computational cost grows linearly with the dimension of the Krylov space. The subset selection problem for the projection step is approximately solved with a number of heuristic algorithms and greedy methods used in statistical learning and compressive sensing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_03592 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A sketch-and-select Arnoldi process Güttel, Stefan Simunec, Igor Numerical Analysis 65F10, 65F50 A sketch-and-select Arnoldi process to generate a well-conditioned basis of a Krylov space at low cost is proposed. At each iteration the procedure utilizes randomized sketching to select a limited number of previously computed basis vectors to project out of the current basis vector. The computational cost grows linearly with the dimension of the Krylov space. The subset selection problem for the projection step is approximately solved with a number of heuristic algorithms and greedy methods used in statistical learning and compressive sensing. |
| title | A sketch-and-select Arnoldi process |
| topic | Numerical Analysis 65F10, 65F50 |
| url | https://arxiv.org/abs/2306.03592 |