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Seminar No.1554 Generating Polynomials and Symmetric Tensor Decompositions

Created Date 12/8/2017 福平   View Numbers  715 Return    
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Title: Generating Polynomials and Symmetric Tensor Decompositions
Reporter: Prof. Jiawang Nie (University of California San Diego)
Time: 2017-12-18(Monday) 9:00
Place: G507

Abstract: 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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