Symmetric Hermitian decomposability criterion, decomposition, and its applications

In this paper, we establish an equivalence relation between partially symmetric tensors and homogeneous polynomials, prove that every partially symmetric tensor has a partially symmetric canonical polyadic (CP)-decomposition, and present three semidefinite relaxation algorithms. The first algorithm is used to check whether there exists a positive partially symmetric real CP-decomposition for a partially symmetric real tensor and give a decomposition if it has. The second algorithm is used to compute general partial symmetric real CP-decompositions. The third algorithm is used to compute positive partially symmetric complex CP-decomposition of partially symmetric complex tensors. Because for different parameters [Formula: see text], partially symmetric tensors [Formula: see text] represent different kinds of tensors. Hence, the proposed algorithms can be used to compute different types of tensor real/complex CP-decomposition, including general nonsymmetric CP-decomposition, positive symmetric CP-decomposition, positive partially symmetric CP-decomposition, general partially symmetric CP-decomposition, etc. Numerical examples show that the algorithms are effective.

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Symmetric Hermitian decomposability criterion, decomposition, and its applications

Cited by 2 publications

References 33 publications

Separability discrimination and decomposition of quantum mixed states based on the Broyden-Fletcher-Goldfarb-Shanno algorithm

Separability discrimination and decomposition of quantum mixed states based on the Broyden-Fletcher-Goldfarb-Shanno algorithm

A Semidefinite Relaxation Method for Partially Symmetric Tensor Decomposition

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