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方法计算的近似解路径的正确性认证问题。我们提出了一种概念简单的方法，该方法基于区间算术中Krawczyk方法的参数化变体。与大多数先前的认证路径追踪方法不同，我们的方法适用于常用于求解多项式方程组的参数同伦的一般设置。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和终止性结果。使用该方法的初步实现进行的实验表明，尽管我们的设置更为通用，但我们的方法与文献中先前出现的专门方法相比具有竞争力。