Rank-r decomposition of symmetric tensors
Jie WEN(
College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Abstract ：An algorithm is presented for decomposing a symmetric tensor into a sum of rank-1 symmetric tensors. For a given tensor, by using apolarity, catalecticant matrices and the condition that the mapping matrices are commutative, the rank of the tensor can be obtained by iteration. Then we can find the generating polynomials under a selected basis set. The decomposition can be constructed by the solutions of generating polynomials under the condition that the solutions are all distinct which can be guaranteed by the commutative property of the matrices. Numerical examples demonstrate the efficiency and accuracy of the proposed method.
Key words ：
Symmetric tensor
symmetric rank
decomposition
generating polynomial
catalectieant matrix
收稿日期: 2016-09-28
出版日期: 2017-11-27
Corresponding Author(s):
Jie WEN
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