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PreprintCC BY 4.0arXiv

M-Eigenpairs of Partially Symmetric Tensors: Exact Reformulation and Perturbation Bounds

  • Zhuolin Du
  • Hanxin Liu
  • Yisheng Song
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Abstract

In this paper, we consider the computation of M-eigenpairs of fourth order partially symmetric tensors arising from elasticity theory. First, a lifted fourth order tensor is constructed, and the original M-eigenvalue problem is reformulated as a parameterized generalized tensor eigenvalue problem under the Bα,β-normalization. Then, an exact correspondence between the two eigenvalue problems is established, which provides a procedure for computing all real M-eigenpairs through the proposed reformulation. Furthermore, perturbation bounds for the largest M-eigenvalue are derived, and the lifted reformulation is shown to preserve these bounds without introducing any additional relaxation. Finally, numerical experiments are reported to show the effectiveness of the proposed method.

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Cite

BibTeXRIS
BibTeX
@misc{du2026meigenpairs,
  title = {{$\mathrm M$-Eigenpairs of Partially Symmetric Tensors: Exact Reformulation and Perturbation Bounds}},
  author = {Zhuolin Du and Hanxin Liu and Yisheng Song},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07202},
  eprint = {2609.07202},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07202},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - M-Eigenpairs of Partially Symmetric Tensors: Exact Reformulation and Perturbation Bounds
AU  - Zhuolin Du
AU  - Hanxin Liu
AU  - Yisheng Song
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07202
UR  - https://arxiv.org/abs/2609.07202
AB  - In this paper, we consider the computation of M-eigenpairs of fourth order partially symmetric tensors arising from elasticity theory. First, a lifted fourth order tensor is constructed, and the original M-eigenvalue problem is reformulated as a parameterized generalized tensor eigenvalue problem under the B_α,β-normalization. Then, an exact correspondence between the two eigenvalue problems is established, which provides a procedure for computing all real M-eigenpairs through the proposed reformulation. Furthermore, perturbation bounds for the largest M-eigenvalue are derived, and the lifted reformulation is shown to preserve these bounds without introducing any additional relaxation. Finally, numerical experiments are reported to show the effectiveness of the proposed method.
ER  -