论文标题
$ u $ - 代：求解多项式方程的系统
$u$-generation: solving systems of polynomials equation-by-equation
论文作者
论文摘要
我们开发了一种新方法，以提高方程式划分算法的效率，以求解多项式系统。我们的方法基于一种新颖的几何结构，并减少了必须在数值上继续进行的同质路径的总数。这些改进可以应用于投影和多注射剂品种的设置中数值几何形状的基本算法。我们的计算实验表明，在多个基准系统上获得了明显的节省。我们还提供了一项扩展的案例研究，内容涉及对对称对称的对称$ n \ times n $矩阵的最大似然估计，其中多主体$ u $ u $ generation允许我们完成$ N \ le 6的ML学位列表。
We develop a new method that improves the efficiency of equation-by-equation algorithms for solving polynomial systems. Our method is based on a novel geometric construction, and reduces the total number of homotopy paths that must be numerically continued. These improvements may be applied to the basic algorithms of numerical algebraic geometry in the settings of both projective and multiprojective varieties. Our computational experiments demonstrate significant savings obtained on several benchmark systems. We also present an extended case study on maximum likelihood estimation for rank-constrained symmetric $n\times n$ matrices, in which multiprojective $u$-generation allows us to complete the list of ML degrees for $n\le 6.$
