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<p>We used the C-product to study the properties and calculations of the eigentubes and eigenslices of third-order tensors. The definition of the tensor eigenpair under the C-product is provided. Tensor eigentubes and eigenslices calculation methods are considered and analyzed, including the tensor QR algorithm, tensor power algorithm, and tensor inverse power method. Presented examples demonstrate the performance of the proposed methods.</p>

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Computing eigenvalues of third-order tensors using the C-product

  • 期刊论文

  • 发表日期：

    2025年9月24日

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  • Hongwei Jin,
  • Siran Chen,
  • Jie Liu,
  • Predrag S. Stanimirović

摘要

We used the C-product to study the properties and calculations of the eigentubes and eigenslices of third-order tensors. The definition of the tensor eigenpair under the C-product is provided. Tensor eigentubes and eigenslices calculation methods are considered and analyzed, including the tensor QR algorithm, tensor power algorithm, and tensor inverse power method. Presented examples demonstrate the performance of the proposed methods.