Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/65469
Title: SOS tensor decomposition : theory and applications
Authors: Chen, H 
Li, G
Qi, LQ 
Keywords: H-eigenvalue
Positive semi-definite tensor
SOS rank
SOS tensor decomposition
Structured tensor
Issue Date: 2016
Publisher: International Press
Source: Communications in mathematical sciences, 2016, v. 14, no. 8, p. 2073-2100 How to cite?
Journal: Communications in mathematical sciences 
Abstract: In this paper, we examine structured tensors which have sum-of-squares (SOS) tensor decomposition, and study the SOS-rank of SOS tensor decomposition. We first show that several classes of even order symmetric structured tensors available in the literature have SOS tensor decomposition. These include positive Cauchy tensors, weakly diagonally dominated tensors, B0-tensors, double Btensors, quasi-double B0-tensors, MB0-tensors, H-tensors, absolute tensors of positive semi-definite Z-tensors, and extended Z-tensors. We also examine the SOS-rank of SOS tensor decompositions and the SOS-width for SOS tensor cones. The SOS-rank provides the minimal number of squares in the SOS tensor decomposition, and, for a given SOS tensor cone, its SOS-width is the maximum possible SOS-rank for all the tensors in this cone. We first deduce an upper bound for general tensors that have SOS decomposition and the SOS-width for general SOS tensor cone using the known results in the literature of polynomial theory. Then, we provide an explicit sharper estimate for the SOS-rank of SOS tensor decomposition with bounded exponent and identify the SOS-width for the tensor cone consisting of all tensors with bounded exponent that have SOS decompositions. Finally, as applications, we show how the SOS tensor decomposition can be used to compute the minimum H-eigenvalue of an even order symmetric extended Z-tensor and test the positive definiteness of an associated multivariate form. Numerical examples ranging from small size to large size are provided to show the efficiency of the proposed numerical methods.
URI: http://hdl.handle.net/10397/65469
ISSN: 1539-6746
EISSN: 1945-0796
DOI: 10.4310/CMS.2016.v14.n8.a1
Appears in Collections:Journal/Magazine Article

Access
View full-text via PolyU eLinks SFX Query
Show full item record

SCOPUSTM   
Citations

11
Last Week
0
Last month
Citations as of Dec 8, 2018

WEB OF SCIENCETM
Citations

9
Last Week
0
Last month
Citations as of Dec 10, 2018

Page view(s)

84
Last Week
0
Last month
Citations as of Dec 10, 2018

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.