The necessary and sufficient conditions of copositive tensors
By Yisheng Song, Liqun Qi. 2013
74 citations recorded by the source corpus.
In this paper, it is proved that (strict) copositivity of a symmetric tensor $\mathcal{A}$ is equivalent to the fact that every principal sub-tensor of $\mathcal{A}$ has no a (non-positive) negative $H^{++}$-eigenvalue. The necessary and sufficient conditions are also given in terms of the $Z^{++}$-eigenvalue of the principal sub-tensor of the given tensor. This presents a method of testing (strict) copositivity of a symmetric tensor by means of the lower dimensional tensors. Also the equivalent definition of strictly copositive tensors is given on entire space $\mathbb{R}^n$.
View Paper: https://www.semanticscholar.org/paper/761cfff162f1dcae0554518f7cfd6100134288c8
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Citations in the corpus
- Properties of Tensor Complementarity Problem and Some Classes of Structured Tensors (2014, background): “(semi-)definition of B-(B0)tensors, Song and Qi [20] for infinite and finite dimensional Hilbert tensors, Song and Qi [22] for structure properties and an equivalent definition of (strictly) copositive tensors, Chen and Qi [23] for Cauchy tensor, Song and Qi [24] for E-eigenvalues of weakly symmetri”
- Nonsingular $H$-tensor and its criteria (2016, background): “Hence, tensor analysis and computing have received much attention of researchers in recent decade and the research branches include spectral hypergraph theory [13, 29], best low-rank approximation to tensors [15, 17, 37], positive definiteness identification of even order homogenous polynomials [12,”