An Efficient Memory Gradient Method for Extreme M-Eigenvalues of Elastic type Tensors

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Autori principali:	Du, Zhuolin, Song, Yisheng
Natura:	Preprint
Pubblicazione:	2026
Soggetti:	Optimization and Control
Accesso online:	Acceder al recurso
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_version_	1866915767277060096
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

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