A posteriori error bounds for the block-Lanczos method for matrix function approximation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916203726897152 |
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| author | Xu, Qichen Chen, Tyler |
| author_facet | Xu, Qichen Chen, Tyler |
| contents | We extend the error bounds from [SIMAX, Vol. 43, Iss. 2, pp. 787-811 (2022)] for the Lanczos method for matrix function approximation to the block algorithm. Numerical experiments suggest that our bounds are fairly robust to changing block size and have the potential for use as a practical stopping criteria. Further experiments work towards a better understanding of how certain hyperparameters should be chosen in order to maximize the quality of the error bounds, even in the previously studied block-size one case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_15643 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A posteriori error bounds for the block-Lanczos method for matrix function approximation Xu, Qichen Chen, Tyler Numerical Analysis 65G99 (Primary), 15A15 (Secondary) G.1.3 We extend the error bounds from [SIMAX, Vol. 43, Iss. 2, pp. 787-811 (2022)] for the Lanczos method for matrix function approximation to the block algorithm. Numerical experiments suggest that our bounds are fairly robust to changing block size and have the potential for use as a practical stopping criteria. Further experiments work towards a better understanding of how certain hyperparameters should be chosen in order to maximize the quality of the error bounds, even in the previously studied block-size one case. |
| title | A posteriori error bounds for the block-Lanczos method for matrix function approximation |
| topic | Numerical Analysis 65G99 (Primary), 15A15 (Secondary) G.1.3 |
| url | https://arxiv.org/abs/2211.15643 |