论文标题
欧几里得距离度和混合体积
Euclidean distance degree and mixed volume
论文作者
论文摘要
我们在稀疏多项式的背景下对欧几里得距离度进行了研究。具体而言，我们考虑由多项式f定义的高表情F = 0，它通常是鉴于其支持的一般，因此支持包含原点。我们表明，F = 0的欧几里得距离度等于相关Lagrange乘数方程的牛顿多型的混合体积。我们讨论了结果对计算复杂性的影响，并在牛顿多层室是矩形并行牵引时给出欧几里得距离度的公式。
We initiate a study of the Euclidean Distance Degree in the context of sparse polynomials. Specifically, we consider a hypersurface f=0 defined by a polynomial f that is general given its support, such that the support contains the origin. We show that the Euclidean Distance Degree of f=0 equals the mixed volume of the Newton polytopes of the associated Lagrange multiplier equations. We discuss the implication of our result for computational complexity and give a formula for the Euclidean distance degree when the Newton polytope is a rectangular parallelepiped.
