相交代数簇的内蕴同伦
An intrinsic homotopy for intersecting algebraic varieties
AI总结：
本文提出将计算两个不可约代数集交集的同伦方法改写为内蕴坐标，使变量数减半，数值实验显示约两倍加速。
摘要：
最近我们开发了一种对角同伦方法，用于计算两个不可约代数集交集中所有正维数分量的数值表示。在本文中，我们将这种对角同伦改写为内蕴坐标形式，从而减少了变量数量，通常减少一半。这有可能节省大量计算，特别是在同伦路径跟踪器的迭代求解部分。我们的数值实验均显示出约两倍的加速。
英文摘要：
Recently we developed a diagonal homotopy method to compute a numerical representation of all positive dimensional components in the intersection of two irreducible algebraic sets. In this paper, we rewrite this diagonal homotopy in intrinsic coordinates, which reduces the number of variables, typically in half. This has the potential to save a significant amount of computation, especially in the iterative solving portion of the homotopy path tracker. There numerical experiments all show a speedup of about a factor two.
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。
