Exact Solutions in Structured Low-Rank Approximation
Exact Solutions in Structured Low-Rank Approximation
复制标题
结构化低阶近似中的精确解
DOI：
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发表时间：
2013
影响因子：
1.5
通讯作者：
B. Sturmfels
中科院分区：
文献类型：
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作者：
G. Ottaviani;P. Spaenlehauer;B. Sturmfels
结构化的低级别近似值是将加权的Frobenius距离最小化至矩阵线性级别固定等级的所有矩阵中给定矩阵的问题。我们通过计算代数几何形状来研究此问题的确切解决方案。特别的重点在于汉克矩阵，sylvester矩阵和通用线性空间。
Structured low-rank approximation is the problem of minimizing a weighted Frobenius distance to a given matrix among all matrices of fixed rank in a linear space of matrices. We study exact solutions to this problem by way of computational algebraic geometry. A particular focus lies on Hankel matrices, Sylvester matrices and generic linear spaces.