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Title: Iterative algorithms for computing US- and U-eigenpairs of complex tensors
Authors: Che, M
Qi, LQ 
Wei, Y
Keywords: Complex symmetric matrices
Complex symmetric tensors
Complex tensors
Takagi factorization
Issue Date: 2017
Publisher: North-Holland
Source: Journal of computational and applied mathematics, 2017, v. 317, p. 547-564 How to cite?
Journal: Journal of computational and applied mathematics 
Abstract: This paper is devoted to the computation of US-eigenpairs of complex symmetric tensors and U-eigenpairs of complex tensors. Based on the Takagi factorization of complex symmetric matrices, we derive an iterative algorithm for computing US-eigenpairs of complex symmetric tensors, denoted as QRCST Algorithm. We also observe that multiple US-eigenpairs can be found from a local permutation heuristic, which is effectively a tensor similarity transformation, resulting in the permuted version of QRCST. We then generalize our techniques to general complex tensors. Finally, we derive a higher order power type method for computing a US- or a U-eigenpair, similar to the higher-order power method for computing Z-eigenpairs of real symmetric tensors or a best rank-one approximation of real tensors. We illustrate our algorithms via numerical examples.
ISSN: 0377-0427
EISSN: 1879-1778
DOI: 10.1016/
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