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US- and U-Eigenpairs of Complex Tensors

In: Theory and Computation of Complex Tensors and its Applications

Author

Listed:
  • Maolin Che

    (Southwestern University of Finance and Economics, School of Economics Mathematics)

  • Yimin Wei

    (Fudan University, School of Mathematical Sciences)

Abstract

In this chapter we discuss the computation of US-eigenpairs of complex symmetric tensors and U-eigenpairs of complex tensors. We derive an iterative algorithm for computing US-eigenpairs of complex symmetric tensors which is based on the Takagi factorization of complex symmetric matrices that are denoted as the QRCST Algorithm. We 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 also present a generalization of their techniques to general complex tensors and 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 the algorithms via numerical examples.

Suggested Citation

  • Maolin Che & Yimin Wei, 2020. "US- and U-Eigenpairs of Complex Tensors," Springer Books, in: Theory and Computation of Complex Tensors and its Applications, chapter 0, pages 187-214, Springer.
    • Handle: RePEc:spr:sprchp:978-981-15-2059-4_7
    DOI: 10.1007/978-981-15-2059-4_7
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