标题： 数值计算最小问题的伽罗瓦群 显示英文标题

标题： Numerically Computing Galois Groups of Minimal Problems

摘要： 我讨论代数、数值计算和计算机视觉之间看似不太可能的交汇点。 其驱动问题是求解参数族代数（多项式或有理函数）方程组的多个实例。 毫无疑问，这个问题已经引起了ISSAC与会者的兴趣，它出现在计算机视觉社区当前使用的鲁棒模型拟合范式中（即“随机采样与共识”，简称“RanSaC”。） 本次演讲将概述过去5年多以来的相关工作，这些工作旨在衡量求解此类参数系统的内在难度，并朝着实际解决方案取得进展。 显示英文摘要

摘要： I discuss a seemingly unlikely confluence of topics in algebra, numerical computation, and computer vision. The motivating problem is that of solving multiples instances of a parametric family of systems of algebraic (polynomial or rational function) equations. No doubt already of interest to ISSAC attendees, this problem arises in the context of robust model-fitting paradigms currently utilized by the computer vision community (namely "Random Sampling and Consensus", aka "RanSaC".) This talk will give an overview of work in the last 5+ years that aspires to measure the intrinsic difficulty of solving such parametric systems, and makes strides towards practical solutions.