u-generation: solving systems of polynomials equation-by-equation
u-generation: solving systems of polynomials equation-by-equation
复制标题
u 代：逐个方程求解多项式方程组
DOI：
10.1007/s11075-023-01590-1
复制
发表时间：
2023
影响因子：
2.1
通讯作者：
Rodriguez, Jose Israel
中科院分区：
文献类型：
--
作者：
Duff, Timothy;Leykin, Anton;Rodriguez, Jose Israel
我们开发了一种新的方法，提高了效率的方程方程同伦连续方法求解多项式系统。我们的方法是基于一种新的几何结构，并减少了同伦路径的总数，必须继续数值。这些改进可以应用于数值代数几何的基本算法中的设置投影和多投影品种。我们的计算实验表明，在几个基准系统上获得了显着的节省。我们还提出了一个扩展的情况下研究的最大似然估计秩约束矩阵，其中多投影生成允许我们完成列表的ML度为
We develop a new method that improves the efficiency of equation-by-equation homotopy continuation methods 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 symmetricmatrices, in which multiprojectiveu-generation allows us to complete the list of ML degrees for