Real eigenvalues of nonsymmetric tensors

Jiawang Nie () and Xinzhen Zhang ()
Additional contact information
Jiawang Nie: University of California San Diego
Xinzhen Zhang: Tianjin University

Computational Optimization and Applications, 2018, vol. 70, issue 1, No 1, 32 pages

Abstract: Abstract This paper discusses the computation of real $$\mathtt {Z}$$ Z -eigenvalues and $$\mathtt {H}$$ H -eigenvalues of nonsymmetric tensors. A generic nonsymmetric tensor has finitely many Z-eigenvalues, while there may be infinitely many ones for special tensors. The number of $$\mathtt {H}$$ H -eigenvalues is finite for all tensors. We propose Lasserre type semidefinite relaxation methods for computing such eigenvalues. For every tensor that has finitely many real $$\mathtt {Z}$$ Z -eigenvalues, we can compute all of them; each of them can be computed by solving a finite sequence of semidefinite relaxations. For every tensor, we can compute all its real $$\mathtt {H}$$ H -eigenvalues; each of them can be computed by solving a finite sequence of semidefinite relaxations.

Keywords: Tensor; $$\mathtt {Z}$$ Z -eigenvalue; $$\mathtt {H}$$ H -eigenvalue; Lasserre’s hierarchy; Semidefinite relaxation; 15A18; 15A69; 90C22 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://link.springer.com/10.1007/s10589-017-9973-y 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:70:y:2018:i:1:d:10.1007_s10589-017-9973-y

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

DOI: 10.1007/s10589-017-9973-y

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 ().