Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/6103
PIRA download icon_1.1View/Download Full Text
Title: The best rank-one approximation ratio of a tensor space
Authors: Qi, L 
Issue Date: 2011
Source: SIAM journal on matrix analysis and applications, 2011, v. 32, no. 2, p. 430–442
Abstract: In this paper we define the best rank-one approximation ratio of a tensor space. It turns out that in the finite dimensional case this provides an upper bound for the quotient of the residual of the best rank-one approximation of any tensor in that tensor space and the norm of that tensor. This upper bound is strictly less than one, and it gives a convergence rate for the greedy rank-one update algorithm. For finite dimensional general tensor spaces, third order finite dimensional symmetric tensor spaces, and finite biquadratic tensor spaces, we give positive lower bounds for the best rank-one approximation ratio. For finite symmetric tensor spaces and finite dimensional biquadratic tensor spaces, we give upper bounds for this ratio.
Keywords: Tensors
Best rank-one approximation ratio
Bounds
Publisher: Society for Industrial and Applied Mathematics
Journal: SIAM journal on matrix analysis and applications 
ISSN: 0895-4798
EISSN: 1095-7162
DOI: 10.1137/100795802
Rights: © 2011 Society for Industrial and Applied Mathematics
Appears in Collections:Journal/Magazine Article

Files in This Item:
File Description SizeFormat 
Qi_Best_Rank-One_Approximation.pdf595.04 kBAdobe PDFView/Open
Open Access Information
Status open access
File Version Version of Record
Access
View full-text via PolyU eLinks SFX Query
Show full item record

Page views

83
Last Week
0
Last month
Citations as of May 15, 2022

Downloads

203
Citations as of May 15, 2022

SCOPUSTM   
Citations

53
Last Week
0
Last month
0
Citations as of May 20, 2022

WEB OF SCIENCETM
Citations

52
Last Week
0
Last month
0
Citations as of May 19, 2022

Google ScholarTM

Check

Altmetric


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