计算理想的有限实簇的一个投影算法
A prolongation-projection algorithm for computing the finite real variety of an ideal
摘要：
我们提供了一个计算理想$I$的实簇$V_R(I)$的实代数符号-数值算法，假设它是有限的，而$V_C(I)$可能不是。我们的方法使用了一套线性泛函$R[X]$，消失在一组给定的多项式生成$I$和他们的expanations到一个给定的程度，以及多项式的真正的根理想的$I$，从一个适当定义的矩矩阵的内核假设是半正定和最大秩。我们制定了一个条件，这些集的线性泛函，这作为我们的算法停止标准的投影的尺寸。该算法的基础上，标准的数值线性代数例程和半定优化，结合技术，从以前的工作，作者与现有的算法复杂的品种。这就为实际和复杂的案件提供了统一的方法。
英文摘要：
We provide a real algebraic symbolic-numeric algorithm for computing the real variety $V_R(I)$ of an ideal $I$, assuming it is finite while $V_C(I)$ may not be. Our approach uses sets of linear functionals on $R[X]$, vanishing on a given set of polynomials generating $I$ and their prolongations up to a given degree, as well as on polynomials of the real radical ideal of $I$, obtained from the kernel of a suitably defined moment matrix assumed to be positive semidefinite and of maximum rank. We formulate a condition on the dimensions of projections of these sets of linear functionals, which serves as stopping criterion for our algorithm. This algorithm, based on standard numerical linear algebra routines and semidefinite optimization, combines techniques from previous work of the authors together with an existing algorithm for the complex variety. This results in a unified methodology for the real and complex cases.
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。
