Differentiating Through Linear Solvers
<|reference_start|>Differentiating Through Linear Solvers: 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?<|reference_end|>
@article{hovland2024differentiating,
    title={Differentiating Through Linear Solvers},
    author={Paul Hovland, Jan H"uckelheim},
    journal={arXiv preprint arXiv:2404.17039},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.17039},
    primaryClass={cs.MS cs.NA math.NA}
}