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arXiv · 2602.01152

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

Zhuolin Du·Yisheng Song
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Abstract

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.

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Zhuolin Du, Yisheng Song. 2026-02-01. An Efficient Memory Gradient Method for Extreme M-Eigenvalues of Elastic type Tensors. https://arxiv.org/abs/2602.01152

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