We examine several of the normal-form multivariate polynomial rootfinding methods of Telen, Mourrain, and Van Barel and some variants of those methods. We analyze the performance of these variants in terms of their asymptotic temporal complexity as well as speed and accuracy on a wide range of numerical experiments. All variants of the algorithm are problematic for systems in which many roots are very close together. We analyze performance on one such system in detail, namely the 'devastating example' that Noferini and Townsend used to demonstrate instability of resultant-based methods.

翻译：我们检查了Telen、Mourrain和Van Barel的几种正常形式的多变多式多元根底调查方法,以及这些方法的一些变体。 我们从这些变体的无症状时间复杂性以及大量数字实验的速度和准确性的角度分析了这些变体的性能。 算法的所有变体对于许多种都非常接近的系统都有问题。 我们详细分析了其中一种系统的性能, 即诺弗里尼和汤森德用来证明基于结果的方法不稳定的“ 脱轨示例 ” 。