Computing the generalized eigenvalues of weakly symmetric tensors

Na Zhao (), Qingzhi Yang () and Yajun Liu ()
Additional contact information
Na Zhao: Nankai University
Qingzhi Yang: Nankai University
Yajun Liu: Nankai University

Computational Optimization and Applications, 2017, vol. 66, issue 2, No 4, 285-307

Abstract: Abstract 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.

Keywords: Weakly symmetric; Generalized tensor eigenpair; Gradient projection method; Armijo rule; BB iteration (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-016-9865-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:66:y:2017:i:2:d:10.1007_s10589-016-9865-6

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-016-9865-6

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().