报告主题：Generating Polynomials and Symmetric Tensor Decompositions
报告人：Jiawang Nie 教授 （加州大学圣地亚哥分校）
报告时间：2017年 12月18日（周一）9:00
报告地点：校本部G507
邀请人：白延琴 教授
报告摘要：This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial. The homogenization of a generating polynomial belongs to the apolar ideal of the tensor. A symmetric tensor decomposition can be determined by a set of generating polynomials, which can be represented by a matrix. We call it a generating matrix. Generally, a symmetric tensor decomposition can be determined by a generating matrix satisfying certain conditions. We characterize the sets of such generating matrices and investigate their properties (e.g., the existence, dimensions, nondefectiveness). Using these properties, we propose methods for computing symmetric tensor ecompositions. Extensive examples are shown to demonstrate the efficiency of proposed methods.
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