Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/11499
Title: Finding the maximum eigenvalue of essentially nonnegative symmetric tensors via sum of squares programming
Authors: Hu, S
Li, G
Qi, L 
Song, Y
Keywords: Maximum eigenvalue
Semi-definite programming problem
Sum of squares of polynomials
Symmetric tensors
Issue Date: 2013
Publisher: Springer
Source: Journal of optimization theory and applications, 2013, v. 158, no. 3, p. 717-738 How to cite?
Journal: Journal of optimization theory and applications 
Abstract: Finding the maximum eigenvalue of a tensor is an important topic in tensor computation and multilinear algebra. Recently, for a tensor with nonnegative entries (which we refer it as a nonnegative tensor), efficient numerical schemes have been proposed to calculate its maximum eigenvalue based on a Perron-Frobenius-type theorem. In this paper, we consider a new class of tensors called essentially nonnegative tensors, which extends the concept of nonnegative tensors, and examine the maximum eigenvalue of an essentially nonnegative tensor using the polynomial optimization techniques. We first establish that finding the maximum eigenvalue of an essentially nonnegative symmetric tensor is equivalent to solving a sum of squares of polynomials (SOS) optimization problem, which, in its turn, can be equivalently rewritten as a semi-definite programming problem. Then, using this sum of squares programming problem, we also provide upper and lower estimates for the maximum eigenvalue of general symmetric tensors. These upper and lower estimates can be calculated in terms of the entries of the tensor. Numerical examples are also presented to illustrate the significance of the results.
URI: http://hdl.handle.net/10397/11499
ISSN: 0022-3239
EISSN: 1573-2878
DOI: 10.1007/s10957-013-0293-9
Appears in Collections:Journal/Magazine Article

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

SCOPUSTM   
Citations

14
Last Week
0
Last month
0
Citations as of Oct 8, 2017

WEB OF SCIENCETM
Citations

11
Last Week
0
Last month
1
Citations as of Oct 13, 2017

Page view(s)

41
Last Week
1
Last month
Checked on Oct 15, 2017

Google ScholarTM

Check

Altmetric



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