Computing the generalized eigenvalues of weakly symmetric tensors

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• 作者：Na Zhao ; Qingzhi Yang ; Yajun Liu
• 关键词：Weakly symmetric ; Generalized tensor eigenpair ; Gradient projection method ; Armijo rule ; BB iteration
• 刊名：Computational Optimization and Applications
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：66
• 期：2
• 页码：285-307
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Optimization; Operations Research, Management Science; Operation Research/Decision Theory; Statistics, general; Convex and Discrete Geometry;
• 出版者：Springer US
• ISSN：1573-2894
• 卷排序：66

文摘

Tensor is a hot topic in the past decade and eigenvalue problems of higher order tensors become more and more important in the numerical multilinear algebra. Several methods for finding the Z-eigenvalues and generalized eigenvalues of symmetric tensors have been given. However, the convergence of these methods when the tensor is not symmetric but weakly symmetric is not assured. In this paper, we give two convergent gradient projection methods for computing some generalized eigenvalues of weakly symmetric tensors. The gradient projection method with Armijo step-size rule (AGP) can be viewed as a modification of the GEAP method. The spectral gradient projection method which is born from the combination of the BB method with the gradient projection method is superior to the GEAP, AG and AGP methods. We also make comparisons among the four methods. Some competitive numerical results are reported at the end of this paper.