In latest years, several advancements have been made in symbolic-numerical eigenvalue techniques for solving polynomial systems. In this article, we add to this list. We design an algorithm which solves systems with isolated solutions reliably and efficiently. In overdetermined cases, it reduces the task to an eigenvalue problem in a simpler and considerably faster way than in previous methods, and it can outperform the homotopy continuation approach. We provide many examples and an implementation in the proof-of-concept Julia package EigenvalueSolver.jl.
翻译:近些年来,在解决多元体系的象征性数字电子价值技术方面,取得了一些进步。在本篇文章中,我们添加到此列表中。我们设计了一种算法,以可靠和高效的方式用孤立的解决方案解决系统问题。在超常情况下,它以比以往方法更简单和更快的速度将任务降低为电子价值问题,并且它能够比同质延续方法更完善。我们在Julia 套件EigenvalueSolver.jl的验证中提供了许多实例和实施。