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.

翻译：我们重新审视了通过数值同伦延拓法计算出的近似解路径正确性认证问题。提出了一种基于区间算术中Krawczyk方法参数化变体的概念简化方案。与大多数现有认证路径追踪方法不同，本方法适用于求解多项式方程组时常用的参数同伦通设场景。我们还描述了一种新颖的预处理策略，并给出了理论上的正确性与终止性结论。初步实现的方法实验表明，尽管适用范围更为广泛，本方法与文献中此前出现的专用方法相比仍具有竞争力。