A hybrid algorithm for multi-homogeneous Bézout number
A hybrid algorithm for multi-homogeneous Bézout number
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DOI：
10.1016/j.amc.2006.12.053
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发表时间：
2007-06
期刊：
影响因子：
--
通讯作者：
Yuhui Tao;Heng Liang;F. Bai
中科院分区：
文献类型：
--
作者：
Yuhui Tao;Heng Liang;F. Bai
多齐次同伦延拓方法可以求解多项式方程组的所有孤立解。不同的变量划分产生不同的多重齐次Bézout数，从而给出孤立解个数的上界.然而，多齐次Bézout数的计算是困难的。本文研究了多重齐次Bézout数的永久形式。本文对带记忆行展开法、精确永久法和近似永久法进行了深入系统的计算。这些方法都有自己的优势。因此，一个混合算法自然。该方法适用于n约为30的情况，而以前是15，其中n是多项式系统的变量数。
The multi-homogenous homotopy continuation method can solve all isolated solutions of polynomial systems. Different variable partition yields different multi-homogenous Bézout number, which gives the upper bound of the number of isolated solutions. However, the computation of the multi-homogenous Bézout number is hard. In this paper, the permanent formulation of the multi-homogenous Bézout number is considered. The intensive and systemic computations are made for the method of row expansion with memory, the precise and the approximate permanent methods. Each of these methods has its own advantage. Hence a hybrid algorithm is naturally presented. This method works for n about 30 contrasting with 15 before, where n is the number of the variables of the polynomial system.