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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.01152 |
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| _version_ | 1866915767277060096 |
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| author | Du, Zhuolin Song, Yisheng |
| author_facet | Du, Zhuolin Song, Yisheng |
| contents | M-eigenvalues of fourth order hierarchically symmetric tensors play a significant role in nonlinear elastic material analysis and quantum entanglement problems. This paper focuses on computing extreme M-eigenvalues for such tensors. To achieve this, we first reformulate the M-eigenvalue problem as a sequence of unconstrained optimization problems by introducing a shift parameter. Subsequently, we develop a memory gradient method specifically designed to approximate these extreme M-eigenvalues. Under this framework, we establish the global convergence of the proposed method. Finally, comprehensive numerical experiments demonstrate the efficacy and stability of our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01152 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Efficient Memory Gradient Method for Extreme M-Eigenvalues of Elastic type Tensors Du, Zhuolin Song, Yisheng Optimization and Control M-eigenvalues of fourth order hierarchically symmetric tensors play a significant role in nonlinear elastic material analysis and quantum entanglement problems. This paper focuses on computing extreme M-eigenvalues for such tensors. To achieve this, we first reformulate the M-eigenvalue problem as a sequence of unconstrained optimization problems by introducing a shift parameter. Subsequently, we develop a memory gradient method specifically designed to approximate these extreme M-eigenvalues. Under this framework, we establish the global convergence of the proposed method. Finally, comprehensive numerical experiments demonstrate the efficacy and stability of our approach. |
| title | An Efficient Memory Gradient Method for Extreme M-Eigenvalues of Elastic type Tensors |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2602.01152 |