实解的Khovanskii-Rolle延拓法
Khovanskii-Rolle continuation for real solutions
AI总结：
提出一种新的延拓算法，用于求解多项式方程组的所有非退化实解，通过追踪连接不同方程组解之间的实曲线，避免计算复解，并利用fewnomial界控制追踪曲线数量。
摘要：
我们提出了一种新的延拓算法，用于求解多项式方程组的所有非退化实解。与同伦方法不同，它不基于系统的形变；相反，它追踪连接一个方程组解到另一个方程组解的实曲线，最终导向所需的实解。它也与同伦方法不同，因为它只追踪实路径，不计算原始方程的复解。追踪的曲线数量受实解的fewnomial界限制，并且该方法利用了该界中的任何松弛。
英文摘要：
We present a new continuation algorithm to find all nondegenerate real solutions to a system of polynomial equations. Unlike homotopy methods, it is not based on a deformation of the system; instead, it traces real curves connecting the solutions of one system of equations to those of another, eventually leading to the desired real solutions. It also differs from homotopy methods in that it follows only real paths and computes no complex solutions of the original equations. The number of curves traced is bounded by the fewnomial bound for real solutions, and the method takes advantage of any slack in that bound.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
