Differentiating Through Linear Solvers
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916237614776320 |
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| author | Hovland, Paul Hückelheim, Jan |
| author_facet | Hovland, Paul Hückelheim, Jan |
| contents | Computer programs containing calls to linear solvers are a known challenge for automatic differentiation. Previous publications advise against differentiating through the low-level solver implementation, and instead advocate for high-level approaches that express the derivative in terms of a modified linear system that can be solved with a separate solver call. Despite this ubiquitous advice, we are not aware of prior work comparing the accuracy of both approaches. With this article we thus empirically study a simple question: What happens if we ignore common wisdom, and differentiate through linear solvers? |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17039 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differentiating Through Linear Solvers Hovland, Paul Hückelheim, Jan Mathematical Software Numerical Analysis Computer programs containing calls to linear solvers are a known challenge for automatic differentiation. Previous publications advise against differentiating through the low-level solver implementation, and instead advocate for high-level approaches that express the derivative in terms of a modified linear system that can be solved with a separate solver call. Despite this ubiquitous advice, we are not aware of prior work comparing the accuracy of both approaches. With this article we thus empirically study a simple question: What happens if we ignore common wisdom, and differentiate through linear solvers? |
| title | Differentiating Through Linear Solvers |
| topic | Mathematical Software Numerical Analysis |
| url | https://arxiv.org/abs/2404.17039 |