Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/6103
Title: The best rank-one approximation ratio of a tensor space
Authors: Qi, L 
Keywords: Tensors
Best rank-one approximation ratio
Bounds
Issue Date: 2011
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on matrix analysis and applications, 2011, v. 32, no. 2, p. 430–442 How to cite?
Journal: SIAM journal on matrix analysis and applications 
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.
URI: http://hdl.handle.net/10397/6103
ISSN: 0895-4798
EISSN: 1095-7162
DOI: 10.1137/100795802
Rights: © 2011 Society for Industrial and Applied Mathematics
Appears in Collections:Journal/Magazine Article

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