论文标题
刚性延续路径ii。结构化多项式系统
Rigid continuation paths II. Structured polynomial systems
论文作者
论文摘要
这项工作研究了以低评估成本为特征的结构化多项式系统的平均复杂性，而不是先前使用的密集随机模型。首先，我们设计了一种延续算法，该算法以高概率计算，仅作为黑盒评估程序给出的多项式系统的大约为零。其次，我们引入了具有规定的评估复杂性的随机多项式系统的通用模型L。结合两者，我们表明我们可以在N变量中，在N变量中，在N temδ的n方程中，只有poly（n，δ）l操作的随机结构性多项式系统的近似为零。这超出了Smale的第17个问题中隐含的期望。
This work studies the average complexity of solving structured polynomial systems that are characterized by a low evaluation cost, as opposed to the dense random model previously used. Firstly, we design a continuation algorithm that computes, with high probability, an approximate zero of a polynomial system given only as black-box evaluation program. Secondly, we introduce a universal model of random polynomial systems with prescribed evaluation complexity L. Combining both, we show that we can compute an approximate zero of a random structured polynomial system with n equations of degree at most δ in n variables with only poly(n, δ) L operations with high probability. This exceeds the expectations implicit in Smale's 17th problem.
