Abstract
� 2016 Elsevier B.V. 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.
Original language | English |
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Pages (from-to) | 547-564 |
Number of pages | 18 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 317 |
DOIs | |
Publication status | Published - 1 Jun 2017 |
Keywords
- Complex symmetric matrices
- Complex symmetric tensors
- Complex tensors
- Takagi factorization
- U-eigenpairs
- US-eigenpairs
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics