Frontiers of Mathematics in China >
Rank-r decomposition of symmetric tensors
Received date: 28 Sep 2016
Accepted date: 19 Jan 2017
Published date: 27 Nov 2017
Copyright
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.
Jie WEN , Qin NI , Wenhuan ZHU . Rank-r decomposition of symmetric tensors[J]. Frontiers of Mathematics in China, 2017 , 12(6) : 1339 -1355 . DOI: 10.1007/s11464-017-0632-5
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