Certified homotopy tracking using the Krawczyk method
<|reference_start|>Certified homotopy tracking using the Krawczyk method: We revisit the problem of certifying the correctness of approximate solution paths computed by numerical homotopy continuation methods. We propose a conceptually simple approach based on a parametric variant of the Krawczyk method from interval arithmetic. Unlike most previous methods for certified path-tracking, our approach is applicable in the general setting of parameter homotopies commonly used to solve polynomial systems of equations. We also describe a novel preconditioning strategy and give theoretical correctness and termination results. Experiments using a preliminary implementation of the method indicate that our approach is competitive with specialized methods appearing previously in the literature, in spite of our more general setting.<|reference_end|>
@article{duff2024certified,
    title={Certified homotopy tracking using the Krawczyk method},
    author={Timothy Duff and Kisun Lee},
    journal={arXiv preprint arXiv:2402.07053},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.07053},
    primaryClass={math.NA cs.NA cs.SC math.AG}
}