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arXiv · 2311.07895

A Feasible Conjugate Gradient Method for Calculating $\mathcal B$-Eigenpairs of Symmetric Tensors

Jiefeng Xu·Can Li·Dong-Hui Li
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Abstract

In this paper, we propose a feasible conjugate gradient (FCG) method for calculating ${\mathcal B}$-eigenpairs of a symmetric tensor ${\mathcal A}$. The method is an extension of the well-known conjugate gradient method for unconstrained optimization problems to some curve constrained optimization problems. The proposed FCG method can find a ${\mathcal B}$-eigenpair of a symmetric tensor ${\mathcal A}$ without the requirement that the orders of ${\mathcal A}$ and $\mathcal B$ are equal. We pay particular attention to the Polak-Rib\'ire-Polyak (PRP) type conjugate gradient method. We show that the FCG method with some Armijo-type line search is globally convergent. Our numerical experiments indicate the promising performance of the proposed method.

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Jiefeng Xu, Can Li, Dong-Hui Li. 2023-11-14. A Feasible Conjugate Gradient Method for Calculating $\mathcal B$-Eigenpairs of Symmetric Tensors. https://arxiv.org/abs/2311.07895

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